Autonomous Droplet Microfluidic Design Framework with Large Language Models

Autonomous Droplet Microfluidic Design Framework with Large Language Models | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Autonomous Droplet Microfluidic Design Framework with Large Language Models NGOC-DUY DINH, Nguyen Nguyen, Raymond Tong This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6282521/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Droplet-based microfluidic devices have substantial promise as cost-effective alternatives to current assessment tools in biological research. Moreover, machine learning models that leverage tabular data, including input design parameters and their corresponding efficiency outputs, are increasingly utilised to automate the design process of these devices and to predict their performance. However, these models fail to fully leverage the data presented in the tables, neglecting crucial contextual information, including column headings and their associated descriptions. This study presents µ-Fluidic-LLMs, a framework designed for processing and feature extraction, which effectively captures contextual information from tabular data formats. µ-Fluidic-LLMs overcomes processing challenges by transforming the content into a linguistic format and leveraging pre-trained large language models (LLMs) for analysis. We evaluate our µ-Fluidic-LLMs framework on 11 prediction tasks, covering aspects such as geometry, flow conditions, regimes, and performance, utilising a publicly available dataset on flow-focusing droplet microfluidics. We demonstrate that our µ-Fluidic-LLMs framework can empower deep neural network models to be highly effective and straightforward while minimising the need for extensive data preprocessing. Moreover, the exceptional performance of deep neural network models, particularly when combined with advanced natural language processing models such as DistilBERT and GPT-2, reduces the mean absolute error in the droplet diameter and generation rate by nearly 5- and 7-fold , respectively, and enhances the regime classification accuracy by over 4% , compared with the performance reported in a previous study. This study lays the foundation for the huge potential applications of LLMs and machine learning in a wider spectrum of microfluidic applications. Physical sciences/Engineering/Biomedical engineering Biological sciences/Biological techniques/Lab-on-a-chip Droplet Microfluidics Large Language models Machine Learning Autonomous Design Artificial Intelligence Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 1. Introduction Droplet-based microfluidics has been recognised as a groundbreaking technology for miniaturising biological and chemical experiments. It has significantly advanced biotechnology 1 – 5 by enabling techniques such as next-generation sequencing, 6 – 8 single-cell RNA sequencing, 8 – 10 droplet digital PCR, 11 – 14 and liquid biopsies diagnostics. 15 However, the impact of microfluidics remains largely confined to single-use cartridges, integrated bench-top devices, and specialised lab setups. 16 , 17 In addition, the complex design and fabrication of custom microfluidic devices have limited their widespread adoption and general use. 18 , 19 Moreover, microfluidic design and operation can take months or years of iterative testing to optimise, even if fabrication is outsourced at a high cost. 20 To overcome these limitations, machine learning, which predicts patterns and behaviour, has been employed. Machine learning models are becoming more popular for predicting performance and automating design in microfluidic droplet generation. For instance, Mahdi et al . 21 used machine learning to predict the size of water droplets in glycerine oil from a T-junction setup. The model, trained with 742 data points, accurately predicted droplet size using Reynolds and capillary numbers across different flow rates and fluid properties within one geometry. Furthermore, in Lashkaripour et al ., 22 neural networks were used to predict droplet size, generation rate, and flow regime based on design geometry and flow conditions. The neural networks, which were trained on 888 data points with varying capillary numbers, flow rate ratio, and six geometric parameters, accurately predicted the droplet generation regime (95.1% accuracy), size (error < 10 µm), and generation rate (error < 20 Hz) for droplets ranging from 25 to 250 µm in size and 5 to 500 Hz in rate. Elsewhere, in Damiati et al ., 23 a machine learning model predicted the size of poly(lactic-co-glycolic acid) (PLGA) microparticles produced by flow-focusing droplet generators and dichloromethane solvent evaporation. The model was trained on data from 223 combinations of flow rates, PLGA concentrations, device types, and sizes to predict PLGA particle size (R² > 0.94) accurately. Furthermore, Hong et al . 24 applied machine learning models to automate the design of concentration gradient generators. A neural network trained on 9 million data points from a verified physics model was able to map desired concentration profiles to inlet settings, achieving an 8.5% error rate. Meanwhile, Ji et al . 25 applied machine learning to automate the iterative design of grid micromixers. Neural networks were trained on 4,320 simulated chips to map channel lengths to output concentrations. The designs met outlet concentration targets within 0.01 mol/m³, compared with simulations, for 91.5% of benchmarks. Moreover, Dressler et al . 26 compared two reinforcement learning algorithms, Deep-Q Networks (DQNs) and model-free episodic controllers (MFECs), in controlling laminar flow between fluids and droplet generation in water-in-oil emulsions. Both models achieved or exceeded superhuman performance and can be adapted to optimize complex systems, such as double emulsions or liposome formation . However, these machine learning models are limited to processing the explicit content within tables, without considering the surrounding contextual information, such as column headers and accompanying descriptions. Furthermore, the data processing becomes more complex when inconsistencies in units of measurement or data types are present across varying tabular data systems. These challenges could be mitigated by harnessing the power of language-based approaches, because language is a highly versatile data modality capable of representing information across diverse data points without the need for structural consistency. Additionally, recent advancements in large language models (LLMs) utilising Transformer architecture 27 have enabled state-of-the-art performance across a diverse array of language tasks, including translation, sentence completion, and question answering. These pre-trained models are frequently built using vast and diverse datasets, which allows them to leverage prior knowledge and make accurate predictions even with minimal training data. Some LLMs are specifically trained to address domain-specific knowledge and technical complexities, enhancing their utility in relevant applications. For instance, LLMs including ClinicalBERT, 28 BioBERT, 29 and BioGPT 30 have been used to fine-tune medical records and biomedical datasets, providing substantial benefits for healthcare-related tasks. In this study, we establish µ-Fluidic-LLMs , a systematic framework that utilises linguistic techniques to derive contextual information related to droplet microfluidic design parameters within tabular structures. This approach produces more comprehensive data representations. We handle tabular data by converting each data sample into a corresponding textual representation. This representation is integrated into the column attributes with their respective values while incorporating any relevant contextual information that may be present. Subsequently, the complete text is fed into a pre-trained LLM, which generates fixed-dimensional embeddings from its final layer . These embeddings are then utilised as input for standard machine learning models to perform downstream tasks. Then, we evaluate the effect on final task performance by comparing the performance when inputting the embeddings into standard machine learning models against the performance when inputting the original tabular features into the same models. Finally, we demonstrate that integrating deep neural networks (DNNs) with LLMs substantially enhances performance on downstream tasks. We also demonstrate the adaptability of this framework, enabling it to incorporate new LLMs as they become available. An overview of this study is illustrated in Fig. 1 . 2. Experimental 2.1 Data and Tasks We utilised a dataset on flow-focusing droplet microfluidics, 22 structured in tabular form and comprising 998 data points. This dataset includes 11 features: orifice width, normalised orifice length, normalised water inlet width, normalised oil inlet width, expansion ratio, aspect ratio, flow rate ratio, capillary number, droplet diameter, generation rate, and regime. Using this dataset, we conducted two regression tasks and one classification task focused on performance prediction, as well as eight regression tasks related to design automation. For the design automation aspect, we present the results of one regression task, with the remaining results in the supplementary file. 2.2 Text Serialisation for Performance Prediction and Design Automation Text serialisation is the process of converting structured data into a linear, text-based format that can be easily stored, transmitted, and reconstructed. In LLMs, text serialisation plays a vital role in processing and managing vast amounts of data 31 . These models rely on serialised text data to train on diverse datasets, often including a mix of natural language, structured information, and metadata. By converting complex input data into a serialised text format, LLMs can uniformly process this information, enabling them to generate meaningful predictions, responses, or completions based on the input. Furthermore, the serialised text is essential for fine-tuning models with specific data, allowing the LLMs to adapt to new tasks or domains by processing serialised input and output pairs. 32 , 33 Our framework implements manual text serialisation for individual data samples, as shown in Fig. 2 . By leveraging the column headers of tabular data, the framework systematically transforms each table row into a sequence of key–value pairs, with the keys originating from the column headers and the values corresponding to the respective data entries. For performance prediction, as shown in Fig. 2 A, the eight column headers and their corresponding values are transformed into a paragraph. This text is then input into pre-trained LLMs to generate embeddings from the final layer . These embeddings are subsequently used as input for baseline machine learning models, which predict output values such as droplet diameter, generation rate, and regime. For design automation, as illustrated in Fig. 2 B, the three column headers droplet diameter, generation rate, and regime, along with their respective values, are transformed into a paragraph. This paragraph is processed by pre-trained LLMs to produce embeddings from the final layer , which are then utilised as inputs for the baseline machine learning models to predict the remaining eight design parameters. This strategy is designed to maintain both the integrity and the contextual meaning of the original tabular data during serialisation. 2.3 Text Embeddings Text embedding is a technique used to convert textual data into a dense, fixed-size vector representation. These vectors capture the semantic meaning of the text by mapping words, phrases, or entire documents into a continuous vector space, where similar pieces of text are represented by vectors that are close to each other. The primary advantage of text embedding lies in its ability to represent complex linguistic relationships and contextual meanings in a numerical format that can be efficiently processed by machine learning algorithms. This makes text embedding an essential component in various natural language processing (NLP) tasks, such as sentiment analysis, text classification, and machine translation. 34 2.4 Large Language Model Selection LLMs play a pivotal role in generating high-quality text embeddings by leveraging their understanding of linguistic patterns and contextual relationships. Pre-trained language models, such as BERT, 35 GPT-2, 36 and their variants, are particularly effective in producing embeddings because they are trained on vast text corpora and can capture nuanced semantic information. These models transform input text into embeddings by processing it through multiple layers of neural networks, where each layer refines the representation by focusing on different aspects of the language, such as syntax, semantics, and context. The resulting embeddings are highly informative and can be used as input for downstream NLP tasks, enhancing the performance of models in applications like question-answering document retrieval and text summarisation. In our study, it was essential to carefully select the language model backbones that would be employed. While there are many potential options, we focused on DistilBERT, 37 SentenceTransformer, and GPT-2 for generating text embeddings in downstream tasks. DistilBERT, a more compact version of BERT, is particularly suitable for scenarios where computational efficiency is paramount, as it effectively balances speed and accuracy. SentenceTransformer 38 is specifically designed for creating sentence-level embeddings, making it ideal for tasks such as semantic similarity, clustering, and information retrieval. This model builds upon the BERT architecture, which has been fine-tuned for these particular applications. Finally, GPT-2, although more computationally demanding, produces contextually rich embeddings by considering a broader contextual scope. This makes it a robust choice for tasks that require deep comprehension and generative capabilities, such as text generation and complex language understanding. The choice of these three language models highlights the versatility of our framework, as it can be adapted to integrate any available language model. 2.5 Baseline Machine Learning Models To assess the effectiveness of text embeddings compared with non-text embeddings in downstream tasks, we employed a range of standard machine learning models, including XGBoost, 39 LightGBM, 40 and support vector machine (SVM). 41 Additionally, DNNs, an advanced form of traditional neural networks characterised by the addition of multiple hidden layers, 42 were designed and applied in this study. Subsequently, we optimised the hyperparameters for all baseline models, as well as for their respective combinations with pre-trained language models. 2.6 Evaluation Metrics After finalising the models, we performed 10-fold cross-validation 15 times to obtain more robust and reliable mean performance estimates, thereby reducing the variability introduced by random data partitioning. 43 For regression tasks, the evaluation utilised four metrics: mean absolute error (MAE), mean squared error (MSE), root mean squared error (RMSE), and the coefficient of determination (R²), along with their associated standard errors. For the classification task, five metrics were employed: accuracy, F1 score, precision, recall, and area under the receiver operating characteristic curve (ROC AUC), each accompanied by standard errors. Here, we present line graphs comparing MAE across models for regression and accuracy across models for classification. Line graphs for the remaining metrics are included in the supplementary file. In addition, we provide tables in the ‘Results & discussion’ section demonstrating the minimisation of standard error and the stabilisation of mean estimated performance for metrics across different models. Specifically, the values presented in the table are those obtained from repetitions in which the discrepancy between the mean and median of the corresponding metric is minimised, indicating that the data likely follows a normal distribution. 43 , 44 3. Results & discussion To verify the effectiveness of our µ-Fluidic-LLMs framework, we highlight selected results in this section, with the remaining findings provided in the supplementary file. 3.1 Enhanced Efficiency for Performance Prediction 3.1.1 Performance in Prediction of Droplet Diameter To assess the trends in accuracy in droplet diameter prediction across different models, a detailed comparison of 16 models over 15 repetitions was conducted, using MAE as the performance metric, as illustrated in Fig. 3 . DNNs integrated with DistilBERT and GPT-2 exhibited the most substantial improvement, with MAE decreasing from approximately 7.5 to around 2.5, demonstrating their adaptability and accuracy. In contrast, XGBoost and LightGBM, when paired with DistilBERT, consistently displayed high MAE values, approaching 20, indicating persistent inefficiencies and minimal improvement in performance. However, XGBoost and LightGBM achieved moderate performance, with MAE stabilising between 10 and 12.5 after initial reductions. This variability in model performance highlights the critical need for iterative testing and careful model selection to optimise predictive accuracy and reliability. Across the remaining metrics, the combination of DNNs with DistilBERT and GPT-2 consistently showed the best performance (see Supplementary Figs. 1, 2, and 3). Table 1 Metrics of evaluation for droplet diameter prediction, compared across models Droplet Diameter (µm) Model Metrics MAE MSE RMSE R² DNN 6.9375 ± 0.1782 98.6397 ± 6.5203 10.4152 ± 0.3664 0.9675 ± 0.0025 DNN–DistilBERT 2.9814 ± 0.1623 22.6262 ± 3.5155 3.9286 ± 0.219 0.9619 ± 0.0063 DNN–GPT-2 2.3941 ± 0.1159 12.8634 ± 1.3313 3.512 ± 0.1573 0.9966 ± 0.0004 DNN–SentenceTransformer 12.1736 ± 1.147 98.5915 ± 6.2758 15.112 ± 1.384 0.978 ± 0.0023 LightGBM 11.344 ± 0.217 399.2599 ± 13.8805 19.489 ± 0.5123 0.9019 ± 0.0031 LightGBM–DistilBERT 18.6042 ± 0.3312 835.1644 ± 52.8888 28.1189 ± 0.3305 0.8028 ± 0.0032 LightGBM–GPT-2 15.8265 ± 0.2479 642.6034 ± 17.0149 25.0282 ± 0.3484 0.8436 ± 0.0034 LightGBM–SentenceTransformer 17.2428 ± 0.3663 752.7167 ± 20.0303 27.1305 ± 0.3931 0.8161 ± 0.0033 SVM 20.4542 ± 0.3696 1136.2003 ± 35.1405 33.309 ± 0.4373 0.7203 ± 0.0058 SVM–DistilBERT 16.8047 ± 0.9945 851.9856 ± 34.0729 28.7854 ± 0.578 0.7916 ± 0.0059 SVM–GPT-2 14.7982 ± 0.3302 649.6983 ± 18.0926 25.1214 ± 0.368 0.8405 ± 0.0058 SVM–SentenceTransformer 17.3951 ± 0.2184 908.6298 ± 23.5036 29.7663 ± 0.3882 0.7779 ± 0.0069 XGBoost 10.6225 ± 0.1797 307.5357 ± 13.8743 17.3687 ± 0.3621 0.9233 ± 0.0019 XGBoost–DistilBERT 19.0411 ± 0.2699 742.1614 ± 17.4954 27.1867 ± 0.4374 0.8138 ± 0.0047 XGBoost–GPT-2 15.6338 ± 0.1782 545.6909 ± 12.6868 23.1538 ± 0.2716 0.862 ± 0.0046 XGBoost–SentenceTransformer 17.5008 ± 0.1626 679.0781 ± 13.921 25.8538 ± 0.2868 0.8298 ± 0.0044 To demonstrate the minimal standard error and the stabilisation of mean estimated performance across metrics of droplet diameter prediction for different models, a comprehensive evaluation of various machine learning models combined with language models is provided. This evaluation focuses on MAE, MSE, RMSE, and R², along with their corresponding standard errors, as shown in Table 1 . The table presents values derived from the repetitions in which the discrepancy between the mean and median of the respective metric was minimised. The models assessed include DNNs, LightGBM, SVM, and XGBoost, each tested with DistilBERT, GPT-2, and SentenceTransformer. DNN paired with GPT-2 emerged as the most effective model across all metrics. It achieved the lowest MAE of 2.3941 – approximately a factor of five smaller than the MAE of 10 reported in a previous study 22 – an MSE of 12.8634, and RMSE of 3.512, indicating minimal prediction error. Moreover, it recorded the highest R² value of 0.9966, demonstrating an exceptionally strong correlation between predicted and actual values, with a very low standard error of 0.0004, underscoring its reliability and stability. This combination significantly outperformed other models, highlighting the potential of GPT-2 in enhancing predictive accuracy when integrated with DNNs. In contrast, SVM models, particularly when combined with SentenceTransformer and DistilBERT, displayed the weakest performance. The SVM model without any language model integration showed a notably high MAE of 20.4542 and MSE of 1136.2003, alongside a low R² of 0.7203. Even with DistilBERT, the SVM model’s performance remained suboptimal, exhibiting considerable prediction errors. This suggests that SVM might not be as well-suited for the types of tasks or data considered in this evaluation, especially compared with other model and language model combinations. Another critical observation is the performance variability of LightGBM and XGBoost models when integrated with different language models. LightGBM showed poor performance with DistilBERT (MAE of 18.6042 and MSE of 835.1644) but significantly better results with GPT-2 (MAE of 15.8265 and MSE of 642.6034), although still not reaching the efficacy of DNN–GPT-2. XGBoost, while generally outperforming LightGBM and SVM, still lagged behind DNN in accuracy, particularly in its combination with SentenceTransformer, where it registered an RMSE of 25.8538 and an R² of 0.8298. 3.1.2 Performance in Prediction of Droplet Generation Rate To evaluate the trends in accuracy in droplet generation rate prediction across various models, a thorough comparison of the 16 models over 15 repetitions was carried out, utilising MAE as the performance metric, as depicted in Fig. 4 . DNNs combined with DistilBERT and GPT-2 demonstrated outstanding performance, with MAE values of around 3, indicating high accuracy and effective learning. This reflects robust model architecture and well-optimised hyperparameters, which contribute to their stability and precision. In contrast, XGBoost, LightGBM, and SVM, when paired with GPT-2, consistently exhibited MAE values above 35, indicating significant limitations in predictive capability. DNN paired with SentenceTransformer, XGBoost paired with SentenceTransformer, and standalone DNN models showed moderate performance, with MAE values between 12 and 25. Across the remaining metrics, DNN integrated with DistilBERT and GPT-2 consistently outperformed other models, showing significant improvements (see Supplementary Figs. 4, 5, and 6). Table 2 Metrics of evaluation for droplet generation rate, compared across models Droplet Generation Rate (Hz) Model Metrics MAE MSE RMSE R² DNN 25.3095 ± 0.4555 1624.4079 ± 139.5017 44.6364 ± 1.1816 0.8718 ± 0.0041 DNN–DistilBERT 3.478 ± 0.2272 49.2167 ± 11.2906 20.5089 ± 2.09 0.9969 ± 0.0008 DNN–GPT-2 3.1921 ± 0.178 39.8099 ± 7.8973 6.2534 ± 0.4721 0.9975 ± 0.0005 DNN–SentenceTransformer 12.4193 ± 0.3476 509.0871 ± 40.3895 21.3771 ± 0.8071 0.968 ± 0.0015 LightGBM 20.1445 ± 0.5134 1559.2185 ± 96.3836 38.9632 ± 0.6701 0.9089 ± 0.0089 LightGBM–DistilBERT 34.531 ± 1.023 4156.6292 ± 337.1268 63.9626 ± 1.2642 0.747 ± 0.016 LightGBM–GPT-2 33.3094 ± 0.72 3954.8462 ± 142.4064 61.8214 ± 1.1531 0.7634 ± 0.0055 LightGBM–SentenceTransformer 36.9546 ± 0.7657 5373.4073 ± 253.7448 71.6789 ± 2.0648 0.6851 ± 0.0066 SVM 39.6055 ± 0.9626 4613.4453 ± 131.3044 67.0637 ± 1.2258 0.7132 ± 0.035 SVM–DistilBERT 42.7807 ± 1.2286 7303.8329 ± 477.9589 84.2248 ± 1.8198 0.5687 ± 0.0102 SVM–GPT-2 41.7472 ± 0.5623 6699.5807 ± 226.8325 80.7062 ± 1.8152 0.6032 ± 0.0061 SVM–SentenceTransformer 38.0529 ± 0.4146 4218.9963 ± 337.7307 63.8702 ± 2.6419 0.7398 ± 0.0299 XGBoost 17.9172 ± 0.3871 1105.9582 ± 56.9718 32.3535 ± 0.5636 0.9325 ± 0.002 XGBoost–DistilBERT 35.2952 ± 0.4083 3444.8867 ± 100.9941 57.8354 ± 0.845 0.7891 ± 0.006 XGBoost–GPT-2 34.3704 ± 0.9647 3319.7046 ± 113.926 57.1386 ± 0.7216 0.792 ± 0.0052 XGBoost–SentenceTransformer 37.622 ± 0.6225 4099.8887 ± 359.9063 63.5527 ± 1.0436 0.7529 ± 0.0169 To illustrate the minimal standard error and the stabilisation of mean estimated performance across metrics of droplet generation rate prediction for different models, we present a comprehensive evaluation of the various machine learning models integrated with LLMs. This assessment again uses MAE, MSE, RMSE, and R², along with their associated standard errors, as presented in Table 2 . The table displays values obtained from the repetitions in which the difference between the mean and median of the corresponding metric was minimised. The DNN models integrated with NLP models—particularly DistilBERT and GPT-2—consistently outperformed other models, achieving significantly lower error metrics and higher R² values. For example, the DNN–GPT-2 model exhibited an MAE of 3.1921, roughly a factor of seven smaller than the MAE of 20 reported in a previous study, 22 and an R² of 0.9975, indicating an exceptional fit to the data with minimal prediction error. This strong performance underscores the effectiveness of combining deep learning with advanced NLP models in enhancing predictive accuracy. In contrast, traditional machine learning models such as SVM and LightGBM showed substantially higher error rates and lower R² values, particularly when combined with NLP models. For instance, the SVM–DistilBERT model, with an MAE of 42.7807 and an R² of 0.5687, demonstrated inadequate predictive power, suggesting that the integration of DistilBERT with SVM does not yield substantial improvements. Similarly, the LightGBM–SentenceTransformer combination resulted in a high MAE of 36.9546 and a relatively low R² of 0.6851, reflecting its limited efficacy. The analysis also reveals notable inconsistencies in the performance of models when combined with NLP techniques. While DNN-based models saw significant improvements when integrated with NLP models, traditional models like XGBoost and SVM did not consistently benefit from such integration. For instance, the XGBoost–GPT-2 combination, despite achieving a respectable R² of 0.792, showed only marginal improvement over XGBoost alone, indicating that the choice of model architecture plays a crucial role in determining the success of NLP integration. 3.1.3 Performance in Prediction of Droplet Regime To evaluate the trends in accuracy in droplet regime predictions across various models, a detailed comparison of 16 models across 15 repetitions was performed, with accuracy serving as the primary performance metric, as shown in Fig. 5 . DNNs paired with DistilBERT, GPT-2, and SentenceTransformer consistently demonstrated exceptional accuracy, with values approaching 1.00. This indicates that these models are highly effective, likely due to advanced algorithms or well-optimised training processes. Their consistent performance across repetitions suggests robustness and reliability, making them well-suited for tasks requiring high precision. In contrast, XGBoost paired with DistilBERT consistently showed lower accuracy, around 0.93. Meanwhile, DNN and LightGBM paired with SentenceTransformer, SVM paired with DistilBERT, and XGBoost exhibited moderate accuracy, generally ranging from 0.95 to 0.98, with slight improvements observed over repetitions. Across the remaining metrics, the combination of DNN and DistilBERT consistently outperformed other models, exhibiting superior predictive performance (see Supplementary Figs. 7, 8, 9, and 10). Table 3 Metrics of evaluation for droplet regime, compared across models Droplet Regime Model Metrics Accuracy F1 Score Precision Recall ROC AUC DNN 0.9801 ± 0.0014 0.9778 ± 0.0016 0.9778 ± 0.0024 0.9756 ± 0.0022 0.9682 ± 0.0034 DNN–DistilBERT 0.9999 ± 0.0001 0.9998 ± 0.0002 1.0 ± 0.0 0.9997 ± 0.0002 0.9998 ± 0.0002 DNN–GPT-2 0.99 ± 0.0022 0.9886 ± 0.0025 0.9969 ± 0.0007 0.9964 ± 0.0009 0.9908 ± 0.0019 DNN–SentenceTransformer 0.9905 ± 0.0024 0.9892 ± 0.0027 0.9975 ± 0.0007 0.997 ± 0.0007 0.9904 ± 0.0024 LightGBM 0.9653 ± 0.0027 0.9594 ± 0.0033 0.9767 ± 0.0026 0.9441 ± 0.0055 0.9628 ± 0.003 LightGBM–DistilBERT 0.9444 ± 0.0051 0.9337 ± 0.0021 0.9419 ± 0.004 0.9303 ± 0.0055 0.9422 ± 0.0029 LightGBM–GPT-2 0.9449 ± 0.007 0.9368 ± 0.0079 0.95 ± 0.0028 0.9317 ± 0.0115 0.9459 ± 0.0027 LightGBM–SentenceTransformer 0.9509 ± 0.0046 0.9438 ± 0.0026 0.9572 ± 0.0065 0.9318 ± 0.0042 0.9504 ± 0.0031 SVM 0.965 ± 0.0017 0.9599 ± 0.0026 0.9761 ± 0.0034 0.947 ± 0.0029 0.9635 ± 0.0023 SVM–DistilBERT 0.9549 ± 0.0061 0.9545 ± 0.0049 0.9546 ± 0.005 0.9566 ± 0.0056 0.9596 ± 0.0042 SVM–GPT-2 0.9647 ± 0.0023 0.9597 ± 0.0026 0.9567 ± 0.0075 0.9554 ± 0.0059 0.9642 ± 0.0024 SVM–SentenceTransformer 0.95 ± 0.0016 0.9432 ± 0.0019 0.9377 ± 0.0032 0.9453 ± 0.0117 0.948 ± 0.0026 XGBoost 0.9685 ± 0.0017 0.9633 ± 0.002 0.977 ± 0.003 0.9521 ± 0.0094 0.9657 ± 0.0023 XGBoost–DistilBERT 0.9351 ± 0.0034 0.9247 ± 0.0041 0.9384 ± 0.0043 0.9072 ± 0.0111 0.9327 ± 0.0036 XGBoost–GPT-2 0.9449 ± 0.0072 0.937 ± 0.0028 0.9434 ± 0.0042 0.9317 ± 0.0143 0.944 ± 0.0029 XGBoost–SentenceTransformer 0.9429 ± 0.0057 0.9339 ± 0.0066 0.9536 ± 0.003 0.9224 ± 0.0036 0.9407 ± 0.006 To demonstrate the minimal standard error and the stabilisation of mean estimated performance across metrics of droplet regime prediction for various models, we present an extensive comparative analysis of DNNs, LightGBM, SVM, and XGBoost. The performance of each model was evaluated when integrated with advanced NLP models, as outlined in Table 3 . Key metrics of accuracy, F1 score, precision, recall, and ROC AUC are employed to examine the efficacy of these models. The table reports values obtained from the repetitions in which the difference between the mean and median of the corresponding metric was minimised. DNN models, particularly when combined with DistilBERT, GPT-2, and SentenceTransformer, demonstrated superior performance across all metrics. Notably, the DNN–DistilBERT model achieved an exceptional accuracy of 0.9999 – representing an improvement of more than 4% over the accuracy of 0.951 reported in a previous study 22 – and an F1 score of 0.9998 and precision of 1.0, underscoring its exceptional ability to correctly classify instances with minimal error. This model also achieved a recall of 0.9997, reflecting its high sensitivity in detecting true positives. In contrast, other model combinations, such as LightGBM with DistilBERT and GPT-2, underperformed relative to DNN-based models. For instance, LightGBM–DistilBERT achieved a lower accuracy of 0.9444 and F1 score of 0.9337, indicating weaker overall performance and a greater likelihood of misclassifications. Similarly, SVM models paired with various NLP techniques exhibited varying degrees of performance, with the SVM–DistilBERT combination showing an accuracy of 0.9549 and an F1 score of 0.9545, but with increased variability in precision and recall, suggesting instability in classification consistency. XGBoost, although traditionally strong in structured data scenarios, did not perform as well when integrated with these NLP models, particularly in comparison with DNN-based approaches. For example, XGBoost–DistilBERT yielded an accuracy of 0.9351 and an F1 score of 0.9247, lower than the best-performing DNN combinations. Additionally, the larger standard errors observed in models like LightGBM–GPT-2 (e.g., recall standard error of 0.0115) indicate higher uncertainty. 3.2 Enhanced Efficiency for Design Automation To analyse the trends in accuracy in droplet capillary number predictions across various models, a detailed comparison of 16 models was conducted over 15 repetitions, employing MAE as the performance metric, as shown in Fig. 6 . The DNN paired with DistilBERT exhibited exceptional accuracy, with MAE decreasing significantly from approximately 0.04 to below 0.02, indicating robust learning and adaptability. Similarly, the DNN paired with GPT-2 and the DNN paired with SentenceTransformer showed improvements, although their MAE levels stabilised at higher values, around 0.03 to 0.05, suggesting moderate effectiveness. In contrast, SVM paired with DistilBERT, XGBoost paired with DistilBERT, LightGBM paired with DistilBERT, and SVM paired with SentenceTransformer consistently displayed high MAE values near 0.12. DNN and LightGBM maintained stable MAE values around 0.08, indicating average performance. DNN integrated with DistilBERT demonstrated exceptional performance across all metrics (Supplementary Figs. 11, 12, and 13). Table 4 Metrics of evaluation for droplet capillary number, compared across models Droplet Capillary Number Model Metrics MAE MSE RMSE R² DNN 0.0828 ± 0.0012 0.0185 ± 0.0004 0.1327 ± 0.0014 0.8301 ± 0.0042 DNN–DistilBERT 0.0115 ± 0.0009 0.0005 ± 0.0002 0.0163 ± 0.0016 0.9947 ± 0.0023 DNN–GPT-2 0.0663 ± 0.0057 0.0017 ± 0.0003 0.0354 ± 0.0017 0.9842 ± 0.0025 DNN–SentenceTransformer 0.092 ± 0.0086 0.0041 ± 0.0003 0.0603 ± 0.0018 0.9611 ± 0.0034 LightGBM 0.0819 ± 0.0010 0.0249 ± 0.0005 0.1565 ± 0.0016 0.7714 ± 0.0042 LightGBM–DistilBERT 0.1161 ± 0.0014 0.0341 ± 0.0006 0.1839 ± 0.0016 0.686 ± 0.0049 LightGBM–GPT-2 0.0945 ± 0.0016 0.0265 ± 0.0005 0.162 ± 0.0016 0.7546 ± 0.0107 LightGBM–SentenceTransformer 0.1061 ± 0.0021 0.0307 ± 0.0006 0.1741 ± 0.0016 0.7182 ± 0.0043 SVM 0.0918 ± 0.0020 0.0223 ± 0.0009 0.1487 ± 0.0030 0.7919 ± 0.0042 SVM–DistilBERT 0.1218 ± 0.0012 0.0316 ± 0.0006 0.1771 ± 0.0020 0.7061 ± 0.0055 SVM–GPT-2 0.1137 ± 0.0015 0.0296 ± 0.0007 0.1717 ± 0.0018 0.7289 ± 0.0073 SVM–SentenceTransformer 0.1267 ± 0.0022 0.0325 ± 0.0009 0.1795 ± 0.0026 0.6995 ± 0.0094 XGBoost 0.0936 ± 0.0009 0.0234 ± 0.0004 0.1522 ± 0.0013 0.7929 ± 0.0122 XGBoost–DistilBERT 0.1194 ± 0.0025 0.0341 ± 0.0007 0.1832 ± 0.0022 0.6893 ± 0.0083 XGBoost–GPT-2 0.0995 ± 0.0011 0.0269 ± 0.0015 0.1642 ± 0.0031 0.7479 ± 0.012 XGBoost–SentenceTransformer 0.1108 ± 0.0011 0.0308 ± 0.0011 0.1748 ± 0.0033 0.7151 ± 0.0051 To highlight the low standard error and the stabilisation of mean estimation performance across metrics of prediction for droplet capillary number for different models, we present an extensive comparative analysis of DNN, LightGBM, SVM, and XGBoost paired with the various NLP models, i.e., DistilBERT, GPT-2, and SentenceTransformer, as detailed in Table 4 . The performances of the models are rigorously evaluated using MAE, MSE, RMSE, and R². The table presents values derived from the repetitions in which the difference between the mean and median of the respective metric was minimised. This analysis provides key insights into the efficacy of these models in handling complex predictive tasks. The DNN model combined with DistilBERT emerged as the most effective, achieving an MAE of 0.0115, MSE of 0.0005, RMSE of 0.0163, and an R² value of 0.9947. These results indicate that DNN–DistilBERT has a remarkable ability to minimise error and maximise predictive accuracy, suggesting a strong synergy between deep learning architectures and transformer-based embeddings. The high R² value of almost 1 implies that the model can explain nearly all the variability in the data, making it highly reliable for predictive tasks. In contrast, other model–embedding combinations showed significant weaknesses in performance. For instance, LightGBM, while known for its efficiency in handling structured data, showed limitations when paired with NLP embeddings. The combination of LightGBM and SentenceTransformer resulted in a relatively high MAE of 0.1061 and a low R² of 0.7182, reflecting a less accurate prediction capability. Similarly, SVM, a model traditionally strong in classification tasks, demonstrated suboptimal performance with DistilBERT (MAE: 0.1218, R²: 0.7061), indicating that SVM may not fully capitalise on the rich semantic features offered by transformers. A critical observation is the consistent underperformance of SentenceTransformer across all models. Despite its theoretical promise, SentenceTransformer consistently yielded higher error rates and lower R² values than DistilBERT and GPT-2. This suggests that SentenceTransformer may not capture the linguistic nuances required for high-accuracy predictions in these scenarios. The underperformance of the models with this embedding highlights the importance of choosing the right embedding based on the specific task and dataset characteristics. Moreover, the data reveals that advanced transformers like DistilBERT and GPT-2 significantly enhance model performance, especially in deep learning contexts. For instance, the DNN model with GPT-2 achieved a competitive MAE of 0.0663 and an R² of 0.9842, although slightly inferior to DNN–DistilBERT. This reinforces the idea that the architecture of the embedding model plays a crucial role in determining the overall performance, with simpler embeddings potentially lacking the depth needed for nuanced predictions. XGBoost, often favoured for its robustness and speed in structured data tasks, also showed variability depending on the embedding used. While XGBoost–DistilBERT achieved a reasonable performance (MAE: 0.1194, R²: 0.6893), it still lagged behind DNN-based approaches, particularly in terms of error minimisation. This suggests that while XGBoost remains a strong contender in traditional settings, its performance may be somewhat poorer when tasked with complex NLP tasks. The design automation for the remaining parameters is detailed in the supplementary file. 3.3 Learning curve of DNN models The learning curve is a foundational tool for optimizing deep neural networks, offering a clear, dynamic view of model performance across epochs. It provides critical insights into how well a model learns from the training data and generalizes to unseen data by plotting metrics such as training and validation loss or accuracy over time. Monitoring the learning curve is especially crucial for determining the optimal number of training epochs, a key factor in balancing underfitting and overfitting. Underfitting is indicated by persistently high training and validation losses, suggesting the model has not learned sufficiently from the data. Overfitting, in contrast, occurs when training loss continues to decrease while validation loss plateaus or rises, signaling the model is excessively tuned to the training data and failing to generalize. The minimum validation loss often signifies the optimal epoch for stopping training. This principle is integral to techniques like early stopping, which aim to prevent overfitting. Careful interpretation of the curve not only informs epoch selection but also guides iterative adjustments to the learning rate, batch size, regularization strength, and other optimization parameters. Consequently, the learning curve is indispensable for systematically refining training processes to achieve optimal performance and robust generalization. The learning curve of a DNN combined with SentenceTransformer for droplet diameter, depicting the training and validation loss trends over 500 epochs, is illustrated in Fig. 7 . Initially, both metrics show a steep decline, indicating rapid convergence, followed by stabilization at lower loss values. Notably, the rapid convergence within the first 100 epochs highlights the importance of monitoring early training phases to avoid overtraining. Importantly, the validation loss generally aligns with the training loss, suggesting minimal overfitting. In this case, the plateau in validation loss suggests that training could be halted earlier, around 80–100 epochs, to optimize computational resources while maintaining model performance. These observations reinforce the importance of closely monitoring the learning curve to determine the proper epoch range for training, ensuring a balance between minimizing training loss and achieving robust generalization. Additional selected learning curves are provided in Supplementary Fig. 42–44. 4. Conclusion In this paper, we present µ-Fluidic-LLMs, an innovative framework designed to process tabular data associated with droplet microfluidics by transforming it into a text-based representation that effectively incorporates essential contextual information, including column descriptions. Our findings underscore the critical role of model selection and language model integration in achieving optimal efficiency of performance prediction and design automation. We emphasise the superior performance of DNN models, particularly when integrated with advanced NLP models such as DistilBERT and GPT-2. In comparison, traditional ensemble methods like LightGBM and XGBoost, even when incorporating state-of-the-art NLP approaches, may struggle to achieve comparable performance levels. Multiple research directions can be pursued to further advance and optimise our framework. For example, exploration of various text serialisation methods, regularisation techniques, dataset augmentation, or advanced optimisation algorithms could provide means to enhance model performance and reduce error rates. Furthermore, given the flexibility of our framework to accommodate different language models, it can be utilised with the latest LLMs, such as GPT-4, 45 , 46 PaLM 2, 47 Gemini 1.5, 48 and LLaMA 3, 49 to assess variations in overall performance. Moreover, µ-Fluidic-LLMs is a general framework that can be adapted for use with other microfluidic components, such as micromixers, 50 and extended to non-microfluidic structures like 3D-printed lattices 51 , thereby enabling the automation of intricate design processes. In addition, µ-Fluidic-LLMs can be seamlessly integrated with existing microfluidic computer-aided design tools 52 – 60 to enable more sophisticated and advanced design automation. We anticipate that this work will inspire further research into the application of language technologies across a broader range of microfluidic applications. Declarations Conflicts of interest There are no conflicts to declare. Acknowledgments We gratefully acknowledge the funding provided by the Research Grant Council of Hong Kong, General Research Fund (Ref No. 14211223). Data availability https://github.com/duydinhlab/MicrofluidicLLMs References G. M. Whitesides, Nat. 2006 4427101, 2006, 442, 368–373. Y. Ding, P. D. Howes and A. J. Demello, Anal. Chem., 2020, 92, 132–149. E. Y. u. Basova and F. Foret, Analyst , 2014, 140, 22–38. S. H. Han, Y. Choi, J. Kim and D. Lee, ACS Appl. Mater. Interfaces, 2020, 12, 3936–3944. T. Moragues, D. Arguijo, T. Beneyton, C. Modavi, K. Simutis, A. R. Abate, J. C. Baret, A. J. deMello, D. Densmore and A. D. Griffiths, Nat. Rev. Methods Prim. 2023 31 , 2023, 3, 1–22. R. Zilionis, J. Nainys, A. Veres, V. Savova, D. Zemmour, A. M. Klein and L. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6282521","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":433112986,"identity":"45cf1d9c-d25d-4cbd-b878-13d781b0ce07","order_by":0,"name":"NGOC-DUY DINH","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA9UlEQVRIiWNgGAWjYLACHgYGxjYGHsYHDAwHDIB8AwbGhgSitDAbkKalgYGHTYIoLeb8iw9+eNt2WLZPuvdYxc+2O8YM7M3bJBh3pOHUYjnjWbLk3LbDxm0y59Ju9rY9M2PgOVYmwXgmB6cWgxtnzJh52w4ntknkmN1mbDtswwBkSDC2VRCnpRisRf4NAS3nexBamIFazBgkeEBa8DmMLVlyzrl0Y6AWY8mec4eN2XjSii0S23B73+D84YMf3pRZy86fkWP44UfZYcN+9sMbb3xsS8aphUEiAUQ2IwTYQEQCbg0MDPwHQGQdPiWjYBSMglEw0gEAi6ZWxY8T/EAAAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0002-4964-7038","institution":"The Chinese University of Hong Kong","correspondingAuthor":true,"prefix":"","firstName":"NGOC-DUY","middleName":"","lastName":"DINH","suffix":""},{"id":433112987,"identity":"a12e2520-74f4-42d1-a616-f264e349aeb4","order_by":1,"name":"Nguyen Nguyen","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Nguyen","middleName":"","lastName":"Nguyen","suffix":""},{"id":433112988,"identity":"824da02e-6faa-4296-8690-d8c34abbd112","order_by":2,"name":"Raymond Tong","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Raymond","middleName":"","lastName":"Tong","suffix":""}],"badges":[],"createdAt":"2025-03-22 09:00:12","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6282521/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6282521/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":79405789,"identity":"3e28ff36-6aae-4245-b25b-7d138c085edc","added_by":"auto","created_at":"2025-03-28 04:00:45","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":196712,"visible":true,"origin":"","legend":"\u003cp\u003eμ-Fluidic-LLMs framework. Regarding performance prediction, μ-Fluidic-LLMs transforms input design parameters from tabular structures into natural language sentences, which are then processed \u003cstrong\u003eby LLMs to generate embeddings from the final layer\u003c/strong\u003e. These embeddings are subsequently used as input for traditional machine learning models. In the context of design automation, μ-Fluidic-LLMs follows the same steps; however, the output design parameters serve as the input parameters.\u003c/p\u003e","description":"","filename":"image1.png","url":"https://assets-eu.researchsquare.com/files/rs-6282521/v1/22edea96e84aecbe40bf0346.png"},{"id":79405112,"identity":"70da43b1-95a6-47be-987e-3c961e88df88","added_by":"auto","created_at":"2025-03-28 03:52:45","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":579084,"visible":true,"origin":"","legend":"\u003cp\u003eSummary of the overall methodology. Fig. 2A illustrates the process of converting each row of tabular data into a paragraph that includes the eight column headers and their corresponding values. This paragraph is then input into large language models to generate embeddings \u003cstrong\u003efrom the final layer\u003c/strong\u003e, which are subsequently used in machine learning models for performance prediction. Fig. 2B demonstrates a similar procedure for design automation, with the paragraph containing only three column headers and their corresponding values.\u003c/p\u003e","description":"","filename":"image2.png","url":"https://assets-eu.researchsquare.com/files/rs-6282521/v1/c27419fa3081faaef9cdf109.png"},{"id":79405113,"identity":"0bdac976-57b4-4ff7-a39f-e59dc8eadee3","added_by":"auto","created_at":"2025-03-28 03:52:45","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":684591,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of mean absolute error (MAE) across models for droplet diameter, with the repetition label indicating iterations of 10-fold cross-validation.\u003c/p\u003e","description":"","filename":"image3.png","url":"https://assets-eu.researchsquare.com/files/rs-6282521/v1/0fb0e30ed9a89b18f8b7bdb8.png"},{"id":79405794,"identity":"f99fc42d-1202-41bd-a559-5071ab9cef96","added_by":"auto","created_at":"2025-03-28 04:00:45","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":707322,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of MAE across models for droplet generation rate, with the repetition label indicating iterations of 10-fold cross-validation.\u003c/p\u003e","description":"","filename":"image4.png","url":"https://assets-eu.researchsquare.com/files/rs-6282521/v1/d5db12bf8a0ccfdaf7c29c95.png"},{"id":79405131,"identity":"5fda0f59-75bf-43a3-b089-7858c30c978c","added_by":"auto","created_at":"2025-03-28 03:52:45","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":684630,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of accuracy across models for droplet regime, with the repetition label indicating iterations of 10-fold cross-validation.\u003c/p\u003e","description":"","filename":"image5.png","url":"https://assets-eu.researchsquare.com/files/rs-6282521/v1/cd6f3764a073df6af991d761.png"},{"id":79405796,"identity":"2fe54cd1-d36e-46fe-9707-e78b8b4853e6","added_by":"auto","created_at":"2025-03-28 04:00:45","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":666714,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of MAE across models for droplet capillary number, with the repetition label indicating iterations of 10-fold cross-validation.\u003c/p\u003e","description":"","filename":"image6.png","url":"https://assets-eu.researchsquare.com/files/rs-6282521/v1/fac82d677668df35f12e1128.png"},{"id":79405114,"identity":"95f3d088-ac8c-485c-948c-28f03aab21b4","added_by":"auto","created_at":"2025-03-28 03:52:45","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":51116,"visible":true,"origin":"","legend":"\u003cp\u003eLearning curve for DNN-SentenceTransformer model for droplet diameter\u003c/p\u003e","description":"","filename":"image7.png","url":"https://assets-eu.researchsquare.com/files/rs-6282521/v1/96d5e9eb48a9327e6f9f5b68.png"},{"id":79564567,"identity":"5c8727e9-8e37-4b9a-925c-9d15be896535","added_by":"auto","created_at":"2025-03-31 09:18:54","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":4736310,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6282521/v1/c220b4be-fa69-4e32-8aae-4b824cf5ea3c.pdf"},{"id":79405116,"identity":"62919417-1662-4ba6-8d30-1230b872895b","added_by":"auto","created_at":"2025-03-28 03:52:45","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":3879770,"visible":true,"origin":"","legend":"Supporting Information","description":"","filename":"SupportingInformation.docx","url":"https://assets-eu.researchsquare.com/files/rs-6282521/v1/0d96fa71a8f64c775cb6abbc.docx"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Autonomous Droplet Microfluidic Design Framework with Large Language Models","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eDroplet-based microfluidics has been recognised as a groundbreaking technology for miniaturising biological and chemical experiments. It has significantly advanced biotechnology\u003csup\u003e\u003cspan additionalcitationids=\"CR2 CR3 CR4\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e by enabling techniques such as next-generation sequencing,\u003csup\u003e\u003cspan additionalcitationids=\"CR7\" citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e single-cell RNA sequencing,\u003csup\u003e\u003cspan additionalcitationids=\"CR9\" citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e droplet digital PCR,\u003csup\u003e\u003cspan additionalcitationids=\"CR12 CR13\" citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u003c/sup\u003e and liquid biopsies diagnostics.\u003csup\u003e\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e However, the impact of microfluidics remains largely confined to single-use cartridges, integrated bench-top devices, and specialised lab setups.\u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e,\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e In addition, the complex design and fabrication of custom microfluidic devices have limited their widespread adoption and general use.\u003csup\u003e\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e,\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e Moreover, microfluidic design and operation can take months or years of iterative testing to optimise, even if fabrication is outsourced at a high cost.\u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e To overcome these limitations, machine learning, which predicts patterns and behaviour, has been employed.\u003c/p\u003e \u003cp\u003eMachine learning models are becoming more popular for predicting performance and automating design in microfluidic droplet generation. For instance, Mahdi \u003cem\u003eet al\u003c/em\u003e.\u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e used machine learning to predict the size of water droplets in glycerine oil from a T-junction setup. The model, trained with 742 data points, accurately predicted droplet size using Reynolds and capillary numbers across different flow rates and fluid properties within one geometry. Furthermore, in Lashkaripour \u003cem\u003eet al\u003c/em\u003e.,\u003csup\u003e\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e neural networks were used to predict droplet size, generation rate, and flow regime based on design geometry and flow conditions. The neural networks, which were trained on 888 data points with varying capillary numbers, flow rate ratio, and six geometric parameters, accurately predicted the droplet generation regime (95.1% accuracy), size (error\u0026thinsp;\u0026lt;\u0026thinsp;10 \u0026micro;m), and generation rate (error\u0026thinsp;\u0026lt;\u0026thinsp;20 Hz) for droplets ranging from 25 to 250 \u0026micro;m in size and 5 to 500 Hz in rate. Elsewhere, in Damiati \u003cem\u003eet al\u003c/em\u003e.,\u003csup\u003e\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e a machine learning model predicted the size of poly(lactic-co-glycolic acid) (PLGA) microparticles produced by flow-focusing droplet generators and dichloromethane solvent evaporation. The model was trained on data from 223 combinations of flow rates, PLGA concentrations, device types, and sizes to predict PLGA particle size (R\u0026sup2; \u0026gt; 0.94) accurately. Furthermore, Hong \u003cem\u003eet al\u003c/em\u003e.\u003csup\u003e\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e applied machine learning models to automate the design of concentration gradient generators. A neural network trained on 9\u0026nbsp;million data points from a verified physics model was able to map desired concentration profiles to inlet settings, achieving an 8.5% error rate. Meanwhile, \u003cem\u003eJi et al\u003c/em\u003e.\u003csup\u003e\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e applied machine learning to automate the iterative design of grid micromixers. Neural networks were trained on 4,320 simulated chips to map channel lengths to output concentrations. The designs met outlet concentration targets within 0.01 mol/m\u0026sup3;, compared with simulations, for 91.5% of benchmarks. \u003cb\u003eMoreover, Dressler\u003c/b\u003e \u003cb\u003eet al\u003c/b\u003e.\u003csup\u003e\u003cb\u003e\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/b\u003e\u003c/sup\u003e \u003cb\u003ecompared two reinforcement learning algorithms, Deep-Q Networks (DQNs) and model-free episodic controllers (MFECs), in controlling laminar flow between fluids and droplet generation in water-in-oil emulsions. Both models achieved or exceeded superhuman performance and can be adapted to optimize complex systems, such as double emulsions or liposome formation\u003c/b\u003e. However, these machine learning models are limited to processing the explicit content within tables, without considering the surrounding contextual information, such as column headers and accompanying descriptions. Furthermore, the data processing becomes more complex when inconsistencies in units of measurement or data types are present across varying tabular data systems. These challenges could be mitigated by harnessing the power of language-based approaches, because language is a highly versatile data modality capable of representing information across diverse data points without the need for structural consistency. Additionally, recent advancements in large language models (LLMs) utilising Transformer architecture\u003csup\u003e\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u003c/sup\u003e have enabled state-of-the-art performance across a diverse array of language tasks, including translation, sentence completion, and question answering. These pre-trained models are frequently built using vast and diverse datasets, which allows them to leverage prior knowledge and make accurate predictions even with minimal training data. Some LLMs are specifically trained to address domain-specific knowledge and technical complexities, enhancing their utility in relevant applications. For instance, LLMs including ClinicalBERT,\u003csup\u003e\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e\u003c/sup\u003e BioBERT,\u003csup\u003e\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e and BioGPT\u003csup\u003e\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u003c/sup\u003e have been used to fine-tune medical records and biomedical datasets, providing substantial benefits for healthcare-related tasks.\u003c/p\u003e \u003cp\u003eIn this study, we establish \u003cem\u003e\u0026micro;-Fluidic-LLMs\u003c/em\u003e, a systematic framework that utilises linguistic techniques to derive contextual information related to droplet microfluidic design parameters within tabular structures. This approach produces more comprehensive data representations. We handle tabular data by converting each data sample into a corresponding textual representation. This representation is integrated into the column attributes with their respective values while incorporating any relevant contextual information that may be present. \u003cb\u003eSubsequently, the complete text is fed into a pre-trained LLM, which generates fixed-dimensional embeddings from its final layer\u003c/b\u003e. These embeddings are then utilised as input for standard machine learning models to perform downstream tasks. Then, we evaluate the effect on final task performance by comparing the performance when inputting the embeddings into standard machine learning models against the performance when inputting the original tabular features into the same models. Finally, we demonstrate that integrating deep neural networks (DNNs) with LLMs substantially enhances performance on downstream tasks. We also demonstrate the adaptability of this framework, enabling it to incorporate new LLMs as they become available. An overview of this study is illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"2. Experimental","content":"\u003cp\u003e \u003c/p\u003e \u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Data and Tasks\u003c/h2\u003e \u003cp\u003eWe utilised a dataset on flow-focusing droplet microfluidics,\u003csup\u003e\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e structured in tabular form and comprising 998 data points. This dataset includes 11 features: orifice width, normalised orifice length, normalised water inlet width, normalised oil inlet width, expansion ratio, aspect ratio, flow rate ratio, capillary number, droplet diameter, generation rate, and regime. Using this dataset, we conducted two regression tasks and one classification task focused on performance prediction, as well as eight regression tasks related to design automation. For the design automation aspect, we present the results of one regression task, with the remaining results in the supplementary file.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Text Serialisation for Performance Prediction and Design Automation\u003c/h2\u003e \u003cp\u003eText serialisation is the process of converting structured data into a linear, text-based format that can be easily stored, transmitted, and reconstructed. In LLMs, text serialisation plays a vital role in processing and managing vast amounts of data\u003csup\u003e\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e\u003c/sup\u003e. These models rely on serialised text data to train on diverse datasets, often including a mix of natural language, structured information, and metadata. By converting complex input data into a serialised text format, LLMs can uniformly process this information, enabling them to generate meaningful predictions, responses, or completions based on the input. Furthermore, the serialised text is essential for fine-tuning models with specific data, allowing the LLMs to adapt to new tasks or domains by processing serialised input and output pairs.\u003csup\u003e\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e,\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u003c/sup\u003e Our framework implements manual text serialisation for individual data samples, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. By leveraging the column headers of tabular data, the framework systematically transforms each table row into a sequence of key\u0026ndash;value pairs, with the keys originating from the column headers and the values corresponding to the respective data entries. For performance prediction, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eA, the eight column headers and their corresponding values are transformed into a paragraph. This text is then input into pre-trained LLMs to generate embeddings \u003cb\u003efrom the final layer\u003c/b\u003e. These embeddings are subsequently used as input for baseline machine learning models, which predict output values such as droplet diameter, generation rate, and regime. For design automation, as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eB, the three column headers droplet diameter, generation rate, and regime, along with their respective values, are transformed into a paragraph. This paragraph is processed by pre-trained LLMs to produce \u003cb\u003eembeddings from the final layer\u003c/b\u003e, which are then utilised as inputs for the baseline machine learning models to predict the remaining eight design parameters. This strategy is designed to maintain both the integrity and the contextual meaning of the original tabular data during serialisation.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Text Embeddings\u003c/h2\u003e \u003cp\u003eText embedding is a technique used to convert textual data into a dense, fixed-size vector representation. These vectors capture the semantic meaning of the text by mapping words, phrases, or entire documents into a continuous vector space, where similar pieces of text are represented by vectors that are close to each other. The primary advantage of text embedding lies in its ability to represent complex linguistic relationships and contextual meanings in a numerical format that can be efficiently processed by machine learning algorithms. This makes text embedding an essential component in various natural language processing (NLP) tasks, such as sentiment analysis, text classification, and machine translation.\u003csup\u003e\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e2.4 Large Language Model Selection\u003c/h2\u003e \u003cp\u003eLLMs play a pivotal role in generating high-quality text embeddings by leveraging their understanding of linguistic patterns and contextual relationships. Pre-trained language models, such as BERT,\u003csup\u003e\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e\u003c/sup\u003e GPT-2,\u003csup\u003e\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e\u003c/sup\u003e and their variants, are particularly effective in producing embeddings because they are trained on vast text corpora and can capture nuanced semantic information. These models transform input text into embeddings by processing it through multiple layers of neural networks, where each layer refines the representation by focusing on different aspects of the language, such as syntax, semantics, and context. The resulting embeddings are highly informative and can be used as input for downstream NLP tasks, enhancing the performance of models in applications like question-answering document retrieval and text summarisation.\u003c/p\u003e \u003cp\u003eIn our study, it was essential to carefully select the language model backbones that would be employed. While there are many potential options, we focused on DistilBERT,\u003csup\u003e\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e\u003c/sup\u003e SentenceTransformer, and GPT-2 for generating text embeddings in downstream tasks. DistilBERT, a more compact version of BERT, is particularly suitable for scenarios where computational efficiency is paramount, as it effectively balances speed and accuracy. SentenceTransformer\u003csup\u003e\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e\u003c/sup\u003e is specifically designed for creating sentence-level embeddings, making it ideal for tasks such as semantic similarity, clustering, and information retrieval. This model builds upon the BERT architecture, which has been fine-tuned for these particular applications. Finally, GPT-2, although more computationally demanding, produces contextually rich embeddings by considering a broader contextual scope. This makes it a robust choice for tasks that require deep comprehension and generative capabilities, such as text generation and complex language understanding. The choice of these three language models highlights the versatility of our framework, as it can be adapted to integrate any available language model.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e2.5 Baseline Machine Learning Models\u003c/h2\u003e \u003cp\u003eTo assess the effectiveness of text embeddings compared with non-text embeddings in downstream tasks, we employed a range of standard machine learning models, including XGBoost,\u003csup\u003e\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e\u003c/sup\u003e LightGBM,\u003csup\u003e\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e\u003c/sup\u003e and support vector machine (SVM).\u003csup\u003e\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e\u003c/sup\u003e Additionally, DNNs, an advanced form of traditional neural networks characterised by the addition of multiple hidden layers,\u003csup\u003e\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e\u003c/sup\u003e were designed and applied in this study. Subsequently, we optimised the hyperparameters for all baseline models, as well as for their respective combinations with pre-trained language models.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e2.6 Evaluation Metrics\u003c/h2\u003e \u003cp\u003eAfter finalising the models, we performed 10-fold cross-validation 15 times to obtain more robust and reliable mean performance estimates, thereby reducing the variability introduced by random data partitioning.\u003csup\u003e\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e\u003c/sup\u003e For regression tasks, the evaluation utilised four metrics: mean absolute error (MAE), mean squared error (MSE), root mean squared error (RMSE), and the coefficient of determination (R\u0026sup2;), along with their associated standard errors. For the classification task, five metrics were employed: accuracy, F1 score, precision, recall, and area under the receiver operating characteristic curve (ROC AUC), each accompanied by standard errors. Here, we present line graphs comparing MAE across models for regression and accuracy across models for classification. Line graphs for the remaining metrics are included in the supplementary file. In addition, we provide tables in the \u0026lsquo;Results \u0026amp; discussion\u0026rsquo; section demonstrating the minimisation of standard error and the stabilisation of mean estimated performance for metrics across different models. Specifically, the values presented in the table are those obtained from repetitions in which the discrepancy between the mean and median of the corresponding metric is minimised, indicating that the data likely follows a normal distribution.\u003csup\u003e\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e,\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Results \u0026 discussion","content":"\u003cp\u003eTo verify the effectiveness of our \u0026micro;-Fluidic-LLMs framework, we highlight selected results in this section, with the remaining findings provided in the supplementary file.\u003c/p\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Enhanced Efficiency for Performance Prediction\u003c/h2\u003e \u003cdiv id=\"Sec11\" class=\"Section3\"\u003e \u003ch2\u003e3.1.1 Performance in Prediction of Droplet Diameter\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo assess the trends in accuracy in droplet diameter prediction across different models, a detailed comparison of 16 models over 15 repetitions was conducted, using MAE as the performance metric, as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. DNNs integrated with DistilBERT and GPT-2 exhibited the most substantial improvement, with MAE decreasing from approximately 7.5 to around 2.5, demonstrating their adaptability and accuracy. In contrast, XGBoost and LightGBM, when paired with DistilBERT, consistently displayed high MAE values, approaching 20, indicating persistent inefficiencies and minimal improvement in performance. However, XGBoost and LightGBM achieved moderate performance, with MAE stabilising between 10 and 12.5 after initial reductions. This variability in model performance highlights the critical need for iterative testing and careful model selection to optimise predictive accuracy and reliability. Across the remaining metrics, the combination of DNNs with DistilBERT and GPT-2 consistently showed the best performance (see Supplementary Figs.\u0026nbsp;1, 2, and 3).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eMetrics of evaluation for droplet diameter prediction, compared across models\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"5\" nameend=\"c5\" namest=\"c1\"\u003e \u003cp\u003eDroplet Diameter (\u0026micro;m)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eModel\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"4\" nameend=\"c5\" namest=\"c2\"\u003e \u003cp\u003eMetrics\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMAE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMSE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eRMSE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eR\u0026sup2;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDNN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e6.9375\u0026thinsp;\u0026plusmn;\u0026thinsp;0.1782\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e98.6397\u0026thinsp;\u0026plusmn;\u0026thinsp;6.5203\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e10.4152\u0026thinsp;\u0026plusmn;\u0026thinsp;0.3664\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9675\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0025\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDNN\u0026ndash;DistilBERT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2.9814\u0026thinsp;\u0026plusmn;\u0026thinsp;0.1623\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e22.6262\u0026thinsp;\u0026plusmn;\u0026thinsp;3.5155\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3.9286\u0026thinsp;\u0026plusmn;\u0026thinsp;0.219\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9619\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0063\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDNN\u0026ndash;GPT-2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2.3941\u0026thinsp;\u0026plusmn;\u0026thinsp;0.1159\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e12.8634\u0026thinsp;\u0026plusmn;\u0026thinsp;1.3313\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3.512\u0026thinsp;\u0026plusmn;\u0026thinsp;0.1573\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9966\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0004\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDNN\u0026ndash;SentenceTransformer\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e12.1736\u0026thinsp;\u0026plusmn;\u0026thinsp;1.147\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e98.5915\u0026thinsp;\u0026plusmn;\u0026thinsp;6.2758\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e15.112\u0026thinsp;\u0026plusmn;\u0026thinsp;1.384\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.978\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0023\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLightGBM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e11.344\u0026thinsp;\u0026plusmn;\u0026thinsp;0.217\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e399.2599\u0026thinsp;\u0026plusmn;\u0026thinsp;13.8805\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e19.489\u0026thinsp;\u0026plusmn;\u0026thinsp;0.5123\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9019\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0031\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLightGBM\u0026ndash;DistilBERT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e18.6042\u0026thinsp;\u0026plusmn;\u0026thinsp;0.3312\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e835.1644\u0026thinsp;\u0026plusmn;\u0026thinsp;52.8888\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e28.1189\u0026thinsp;\u0026plusmn;\u0026thinsp;0.3305\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.8028\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0032\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLightGBM\u0026ndash;GPT-2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e15.8265\u0026thinsp;\u0026plusmn;\u0026thinsp;0.2479\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e642.6034\u0026thinsp;\u0026plusmn;\u0026thinsp;17.0149\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e25.0282\u0026thinsp;\u0026plusmn;\u0026thinsp;0.3484\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.8436\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0034\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLightGBM\u0026ndash;SentenceTransformer\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e17.2428\u0026thinsp;\u0026plusmn;\u0026thinsp;0.3663\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e752.7167\u0026thinsp;\u0026plusmn;\u0026thinsp;20.0303\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e27.1305\u0026thinsp;\u0026plusmn;\u0026thinsp;0.3931\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.8161\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0033\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSVM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e20.4542\u0026thinsp;\u0026plusmn;\u0026thinsp;0.3696\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1136.2003\u0026thinsp;\u0026plusmn;\u0026thinsp;35.1405\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e33.309\u0026thinsp;\u0026plusmn;\u0026thinsp;0.4373\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.7203\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0058\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSVM\u0026ndash;DistilBERT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e16.8047\u0026thinsp;\u0026plusmn;\u0026thinsp;0.9945\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e851.9856\u0026thinsp;\u0026plusmn;\u0026thinsp;34.0729\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e28.7854\u0026thinsp;\u0026plusmn;\u0026thinsp;0.578\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.7916\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0059\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSVM\u0026ndash;GPT-2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e14.7982\u0026thinsp;\u0026plusmn;\u0026thinsp;0.3302\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e649.6983\u0026thinsp;\u0026plusmn;\u0026thinsp;18.0926\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e25.1214\u0026thinsp;\u0026plusmn;\u0026thinsp;0.368\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.8405\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0058\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSVM\u0026ndash;SentenceTransformer\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e17.3951\u0026thinsp;\u0026plusmn;\u0026thinsp;0.2184\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e908.6298\u0026thinsp;\u0026plusmn;\u0026thinsp;23.5036\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e29.7663\u0026thinsp;\u0026plusmn;\u0026thinsp;0.3882\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.7779\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0069\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eXGBoost\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e10.6225\u0026thinsp;\u0026plusmn;\u0026thinsp;0.1797\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e307.5357\u0026thinsp;\u0026plusmn;\u0026thinsp;13.8743\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e17.3687\u0026thinsp;\u0026plusmn;\u0026thinsp;0.3621\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9233\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0019\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eXGBoost\u0026ndash;DistilBERT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e19.0411\u0026thinsp;\u0026plusmn;\u0026thinsp;0.2699\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e742.1614\u0026thinsp;\u0026plusmn;\u0026thinsp;17.4954\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e27.1867\u0026thinsp;\u0026plusmn;\u0026thinsp;0.4374\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.8138\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0047\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eXGBoost\u0026ndash;GPT-2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e15.6338\u0026thinsp;\u0026plusmn;\u0026thinsp;0.1782\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e545.6909\u0026thinsp;\u0026plusmn;\u0026thinsp;12.6868\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e23.1538\u0026thinsp;\u0026plusmn;\u0026thinsp;0.2716\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.862\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0046\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eXGBoost\u0026ndash;SentenceTransformer\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e17.5008\u0026thinsp;\u0026plusmn;\u0026thinsp;0.1626\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e679.0781\u0026thinsp;\u0026plusmn;\u0026thinsp;13.921\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e25.8538\u0026thinsp;\u0026plusmn;\u0026thinsp;0.2868\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.8298\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0044\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTo demonstrate the minimal standard error and the stabilisation of mean estimated performance across metrics of droplet diameter prediction for different models, a comprehensive evaluation of various machine learning models combined with language models is provided. This evaluation focuses on MAE, MSE, RMSE, and R\u0026sup2;, along with their corresponding standard errors, as shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. The table presents values derived from the repetitions in which the discrepancy between the mean and median of the respective metric was minimised. The models assessed include DNNs, LightGBM, SVM, and XGBoost, each tested with DistilBERT, GPT-2, and SentenceTransformer. DNN paired with GPT-2 emerged as the most effective model across all metrics. It achieved the lowest MAE of 2.3941 \u0026ndash; approximately a factor of five smaller than the MAE of 10 reported in a previous study\u003csup\u003e\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e \u0026ndash; an MSE of 12.8634, and RMSE of 3.512, indicating minimal prediction error. Moreover, it recorded the highest R\u0026sup2; value of 0.9966, demonstrating an exceptionally strong correlation between predicted and actual values, with a very low standard error of 0.0004, underscoring its reliability and stability. This combination significantly outperformed other models, highlighting the potential of GPT-2 in enhancing predictive accuracy when integrated with DNNs. In contrast, SVM models, particularly when combined with SentenceTransformer and DistilBERT, displayed the weakest performance. The SVM model without any language model integration showed a notably high MAE of 20.4542 and MSE of 1136.2003, alongside a low R\u0026sup2; of 0.7203. Even with DistilBERT, the SVM model\u0026rsquo;s performance remained suboptimal, exhibiting considerable prediction errors. This suggests that SVM might not be as well-suited for the types of tasks or data considered in this evaluation, especially compared with other model and language model combinations. Another critical observation is the performance variability of LightGBM and XGBoost models when integrated with different language models. LightGBM showed poor performance with DistilBERT (MAE of 18.6042 and MSE of 835.1644) but significantly better results with GPT-2 (MAE of 15.8265 and MSE of 642.6034), although still not reaching the efficacy of DNN\u0026ndash;GPT-2. XGBoost, while generally outperforming LightGBM and SVM, still lagged behind DNN in accuracy, particularly in its combination with SentenceTransformer, where it registered an RMSE of 25.8538 and an R\u0026sup2; of 0.8298.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section3\"\u003e \u003ch2\u003e3.1.2 Performance in Prediction of Droplet Generation Rate\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo evaluate the trends in accuracy in droplet generation rate prediction across various models, a thorough comparison of the 16 models over 15 repetitions was carried out, utilising MAE as the performance metric, as depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. DNNs combined with DistilBERT and GPT-2 demonstrated outstanding performance, with MAE values of around 3, indicating high accuracy and effective learning. This reflects robust model architecture and well-optimised hyperparameters, which contribute to their stability and precision. In contrast, XGBoost, LightGBM, and SVM, when paired with GPT-2, consistently exhibited MAE values above 35, indicating significant limitations in predictive capability. DNN paired with SentenceTransformer, XGBoost paired with SentenceTransformer, and standalone DNN models showed moderate performance, with MAE values between 12 and 25. Across the remaining metrics, DNN integrated with DistilBERT and GPT-2 consistently outperformed other models, showing significant improvements (see Supplementary Figs.\u0026nbsp;4, 5, and 6).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eMetrics of evaluation for droplet generation rate, compared across models\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"5\" nameend=\"c5\" namest=\"c1\"\u003e \u003cp\u003eDroplet Generation Rate (Hz)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eModel\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"4\" nameend=\"c5\" namest=\"c2\"\u003e \u003cp\u003eMetrics\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMAE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMSE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eRMSE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eR\u0026sup2;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDNN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e25.3095\u0026thinsp;\u0026plusmn;\u0026thinsp;0.4555\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1624.4079\u0026thinsp;\u0026plusmn;\u0026thinsp;139.5017\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e44.6364\u0026thinsp;\u0026plusmn;\u0026thinsp;1.1816\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.8718\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0041\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDNN\u0026ndash;DistilBERT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3.478\u0026thinsp;\u0026plusmn;\u0026thinsp;0.2272\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e49.2167\u0026thinsp;\u0026plusmn;\u0026thinsp;11.2906\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e20.5089\u0026thinsp;\u0026plusmn;\u0026thinsp;2.09\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9969\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0008\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDNN\u0026ndash;GPT-2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3.1921\u0026thinsp;\u0026plusmn;\u0026thinsp;0.178\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e39.8099\u0026thinsp;\u0026plusmn;\u0026thinsp;7.8973\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e6.2534\u0026thinsp;\u0026plusmn;\u0026thinsp;0.4721\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9975\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0005\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDNN\u0026ndash;SentenceTransformer\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e12.4193\u0026thinsp;\u0026plusmn;\u0026thinsp;0.3476\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e509.0871\u0026thinsp;\u0026plusmn;\u0026thinsp;40.3895\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e21.3771\u0026thinsp;\u0026plusmn;\u0026thinsp;0.8071\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.968\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0015\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLightGBM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e20.1445\u0026thinsp;\u0026plusmn;\u0026thinsp;0.5134\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1559.2185\u0026thinsp;\u0026plusmn;\u0026thinsp;96.3836\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e38.9632\u0026thinsp;\u0026plusmn;\u0026thinsp;0.6701\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9089\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0089\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLightGBM\u0026ndash;DistilBERT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e34.531\u0026thinsp;\u0026plusmn;\u0026thinsp;1.023\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4156.6292\u0026thinsp;\u0026plusmn;\u0026thinsp;337.1268\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e63.9626\u0026thinsp;\u0026plusmn;\u0026thinsp;1.2642\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.747\u0026thinsp;\u0026plusmn;\u0026thinsp;0.016\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLightGBM\u0026ndash;GPT-2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e33.3094\u0026thinsp;\u0026plusmn;\u0026thinsp;0.72\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3954.8462\u0026thinsp;\u0026plusmn;\u0026thinsp;142.4064\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e61.8214\u0026thinsp;\u0026plusmn;\u0026thinsp;1.1531\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.7634\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0055\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLightGBM\u0026ndash;SentenceTransformer\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e36.9546\u0026thinsp;\u0026plusmn;\u0026thinsp;0.7657\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e5373.4073\u0026thinsp;\u0026plusmn;\u0026thinsp;253.7448\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e71.6789\u0026thinsp;\u0026plusmn;\u0026thinsp;2.0648\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.6851\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0066\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSVM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e39.6055\u0026thinsp;\u0026plusmn;\u0026thinsp;0.9626\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4613.4453\u0026thinsp;\u0026plusmn;\u0026thinsp;131.3044\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e67.0637\u0026thinsp;\u0026plusmn;\u0026thinsp;1.2258\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.7132\u0026thinsp;\u0026plusmn;\u0026thinsp;0.035\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSVM\u0026ndash;DistilBERT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e42.7807\u0026thinsp;\u0026plusmn;\u0026thinsp;1.2286\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e7303.8329\u0026thinsp;\u0026plusmn;\u0026thinsp;477.9589\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e84.2248\u0026thinsp;\u0026plusmn;\u0026thinsp;1.8198\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.5687\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0102\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSVM\u0026ndash;GPT-2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e41.7472\u0026thinsp;\u0026plusmn;\u0026thinsp;0.5623\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e6699.5807\u0026thinsp;\u0026plusmn;\u0026thinsp;226.8325\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e80.7062\u0026thinsp;\u0026plusmn;\u0026thinsp;1.8152\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.6032\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0061\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSVM\u0026ndash;SentenceTransformer\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e38.0529\u0026thinsp;\u0026plusmn;\u0026thinsp;0.4146\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4218.9963\u0026thinsp;\u0026plusmn;\u0026thinsp;337.7307\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e63.8702\u0026thinsp;\u0026plusmn;\u0026thinsp;2.6419\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.7398\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0299\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eXGBoost\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e17.9172\u0026thinsp;\u0026plusmn;\u0026thinsp;0.3871\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1105.9582\u0026thinsp;\u0026plusmn;\u0026thinsp;56.9718\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e32.3535\u0026thinsp;\u0026plusmn;\u0026thinsp;0.5636\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9325\u0026thinsp;\u0026plusmn;\u0026thinsp;0.002\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eXGBoost\u0026ndash;DistilBERT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e35.2952\u0026thinsp;\u0026plusmn;\u0026thinsp;0.4083\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3444.8867\u0026thinsp;\u0026plusmn;\u0026thinsp;100.9941\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e57.8354\u0026thinsp;\u0026plusmn;\u0026thinsp;0.845\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.7891\u0026thinsp;\u0026plusmn;\u0026thinsp;0.006\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eXGBoost\u0026ndash;GPT-2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e34.3704\u0026thinsp;\u0026plusmn;\u0026thinsp;0.9647\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3319.7046\u0026thinsp;\u0026plusmn;\u0026thinsp;113.926\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e57.1386\u0026thinsp;\u0026plusmn;\u0026thinsp;0.7216\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.792\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0052\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eXGBoost\u0026ndash;SentenceTransformer\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e37.622\u0026thinsp;\u0026plusmn;\u0026thinsp;0.6225\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4099.8887\u0026thinsp;\u0026plusmn;\u0026thinsp;359.9063\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e63.5527\u0026thinsp;\u0026plusmn;\u0026thinsp;1.0436\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.7529\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0169\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTo illustrate the minimal standard error and the stabilisation of mean estimated performance across metrics of droplet generation rate prediction for different models, we present a comprehensive evaluation of the various machine learning models integrated with LLMs. This assessment again uses MAE, MSE, RMSE, and R\u0026sup2;, along with their associated standard errors, as presented in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. The table displays values obtained from the repetitions in which the difference between the mean and median of the corresponding metric was minimised. The DNN models integrated with NLP models\u0026mdash;particularly DistilBERT and GPT-2\u0026mdash;consistently outperformed other models, achieving significantly lower error metrics and higher R\u0026sup2; values. For example, the DNN\u0026ndash;GPT-2 model exhibited an MAE of 3.1921, roughly a factor of seven smaller than the MAE of 20 reported in a previous study,\u003csup\u003e\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e and an R\u0026sup2; of 0.9975, indicating an exceptional fit to the data with minimal prediction error. This strong performance underscores the effectiveness of combining deep learning with advanced NLP models in enhancing predictive accuracy. In contrast, traditional machine learning models such as SVM and LightGBM showed substantially higher error rates and lower R\u0026sup2; values, particularly when combined with NLP models. For instance, the SVM\u0026ndash;DistilBERT model, with an MAE of 42.7807 and an R\u0026sup2; of 0.5687, demonstrated inadequate predictive power, suggesting that the integration of DistilBERT with SVM does not yield substantial improvements. Similarly, the LightGBM\u0026ndash;SentenceTransformer combination resulted in a high MAE of 36.9546 and a relatively low R\u0026sup2; of 0.6851, reflecting its limited efficacy. The analysis also reveals notable inconsistencies in the performance of models when combined with NLP techniques. While DNN-based models saw significant improvements when integrated with NLP models, traditional models like XGBoost and SVM did not consistently benefit from such integration. For instance, the XGBoost\u0026ndash;GPT-2 combination, despite achieving a respectable R\u0026sup2; of 0.792, showed only marginal improvement over XGBoost alone, indicating that the choice of model architecture plays a crucial role in determining the success of NLP integration.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section3\"\u003e \u003ch2\u003e3.1.3 Performance in Prediction of Droplet Regime\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo evaluate the trends in accuracy in droplet regime predictions across various models, a detailed comparison of 16 models across 15 repetitions was performed, with accuracy serving as the primary performance metric, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. DNNs paired with DistilBERT, GPT-2, and SentenceTransformer consistently demonstrated exceptional accuracy, with values approaching 1.00. This indicates that these models are highly effective, likely due to advanced algorithms or well-optimised training processes. Their consistent performance across repetitions suggests robustness and reliability, making them well-suited for tasks requiring high precision. In contrast, XGBoost paired with DistilBERT consistently showed lower accuracy, around 0.93. Meanwhile, DNN and LightGBM paired with SentenceTransformer, SVM paired with DistilBERT, and XGBoost exhibited moderate accuracy, generally ranging from 0.95 to 0.98, with slight improvements observed over repetitions. Across the remaining metrics, the combination of DNN and DistilBERT consistently outperformed other models, exhibiting superior predictive performance (see Supplementary Figs.\u0026nbsp;7, 8, 9, and 10).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eMetrics of evaluation for droplet regime, compared across models\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"6\" nameend=\"c6\" namest=\"c1\"\u003e \u003cp\u003eDroplet Regime\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eModel\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"5\" nameend=\"c6\" namest=\"c2\"\u003e \u003cp\u003eMetrics\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAccuracy\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eF1 Score\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003ePrecision\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eRecall\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eROC AUC\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDNN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.9801\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0014\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.9778\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0016\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.9778\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0024\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9756\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0022\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.9682\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0034\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDNN\u0026ndash;DistilBERT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.9999\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.9998\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0002\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.0\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9997\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0002\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.9998\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0002\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDNN\u0026ndash;GPT-2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.99\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0022\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.9886\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0025\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.9969\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0007\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9964\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0009\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.9908\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0019\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDNN\u0026ndash;SentenceTransformer\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.9905\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0024\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.9892\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0027\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.9975\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0007\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.997\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0007\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.9904\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0024\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLightGBM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.9653\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0027\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.9594\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0033\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.9767\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0026\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9441\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0055\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.9628\u0026thinsp;\u0026plusmn;\u0026thinsp;0.003\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLightGBM\u0026ndash;DistilBERT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.9444\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0051\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.9337\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0021\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.9419\u0026thinsp;\u0026plusmn;\u0026thinsp;0.004\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9303\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0055\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.9422\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0029\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLightGBM\u0026ndash;GPT-2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.9449\u0026thinsp;\u0026plusmn;\u0026thinsp;0.007\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.9368\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0079\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.95\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0028\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9317\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0115\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.9459\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0027\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLightGBM\u0026ndash;SentenceTransformer\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.9509\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0046\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.9438\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0026\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.9572\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0065\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9318\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0042\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.9504\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0031\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSVM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.965\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0017\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.9599\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0026\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.9761\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0034\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.947\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0029\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.9635\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0023\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSVM\u0026ndash;DistilBERT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.9549\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0061\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.9545\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0049\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.9546\u0026thinsp;\u0026plusmn;\u0026thinsp;0.005\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9566\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0056\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.9596\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0042\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSVM\u0026ndash;GPT-2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.9647\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0023\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.9597\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0026\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.9567\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0075\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9554\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0059\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.9642\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0024\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSVM\u0026ndash;SentenceTransformer\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.95\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0016\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.9432\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0019\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.9377\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0032\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9453\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0117\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.948\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0026\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eXGBoost\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.9685\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0017\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.9633\u0026thinsp;\u0026plusmn;\u0026thinsp;0.002\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.977\u0026thinsp;\u0026plusmn;\u0026thinsp;0.003\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9521\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0094\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.9657\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0023\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eXGBoost\u0026ndash;DistilBERT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.9351\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0034\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.9247\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0041\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.9384\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0043\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9072\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0111\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.9327\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0036\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eXGBoost\u0026ndash;GPT-2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.9449\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0072\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.937\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0028\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.9434\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0042\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9317\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0143\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.944\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0029\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eXGBoost\u0026ndash;SentenceTransformer\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.9429\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0057\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.9339\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0066\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.9536\u0026thinsp;\u0026plusmn;\u0026thinsp;0.003\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9224\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0036\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.9407\u0026thinsp;\u0026plusmn;\u0026thinsp;0.006\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTo demonstrate the minimal standard error and the stabilisation of mean estimated performance across metrics of droplet regime prediction for various models, we present an extensive comparative analysis of DNNs, LightGBM, SVM, and XGBoost. The performance of each model was evaluated when integrated with advanced NLP models, as outlined in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. Key metrics of accuracy, F1 score, precision, recall, and ROC AUC are employed to examine the efficacy of these models. The table reports values obtained from the repetitions in which the difference between the mean and median of the corresponding metric was minimised. DNN models, particularly when combined with DistilBERT, GPT-2, and SentenceTransformer, demonstrated superior performance across all metrics. Notably, the DNN\u0026ndash;DistilBERT model achieved an exceptional accuracy of 0.9999 \u0026ndash; representing an improvement of more than 4% over the accuracy of 0.951 reported in a previous study\u003csup\u003e\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e \u0026ndash; and an F1 score of 0.9998 and precision of 1.0, underscoring its exceptional ability to correctly classify instances with minimal error. This model also achieved a recall of 0.9997, reflecting its high sensitivity in detecting true positives. In contrast, other model combinations, such as LightGBM with DistilBERT and GPT-2, underperformed relative to DNN-based models. For instance, LightGBM\u0026ndash;DistilBERT achieved a lower accuracy of 0.9444 and F1 score of 0.9337, indicating weaker overall performance and a greater likelihood of misclassifications. Similarly, SVM models paired with various NLP techniques exhibited varying degrees of performance, with the SVM\u0026ndash;DistilBERT combination showing an accuracy of 0.9549 and an F1 score of 0.9545, but with increased variability in precision and recall, suggesting instability in classification consistency. XGBoost, although traditionally strong in structured data scenarios, did not perform as well when integrated with these NLP models, particularly in comparison with DNN-based approaches. For example, XGBoost\u0026ndash;DistilBERT yielded an accuracy of 0.9351 and an F1 score of 0.9247, lower than the best-performing DNN combinations. Additionally, the larger standard errors observed in models like LightGBM\u0026ndash;GPT-2 (e.g., recall standard error of 0.0115) indicate higher uncertainty.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Enhanced Efficiency for Design Automation\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo analyse the trends in accuracy in droplet capillary number predictions across various models, a detailed comparison of 16 models was conducted over 15 repetitions, employing MAE as the performance metric, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e. The DNN paired with DistilBERT exhibited exceptional accuracy, with MAE decreasing significantly from approximately 0.04 to below 0.02, indicating robust learning and adaptability. Similarly, the DNN paired with GPT-2 and the DNN paired with SentenceTransformer showed improvements, although their MAE levels stabilised at higher values, around 0.03 to 0.05, suggesting moderate effectiveness. In contrast, SVM paired with DistilBERT, XGBoost paired with DistilBERT, LightGBM paired with DistilBERT, and SVM paired with SentenceTransformer consistently displayed high MAE values near 0.12. DNN and LightGBM maintained stable MAE values around 0.08, indicating average performance. DNN integrated with DistilBERT demonstrated exceptional performance across all metrics (Supplementary Figs.\u0026nbsp;11, 12, and 13).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eMetrics of evaluation for droplet capillary number, compared across models\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"5\" nameend=\"c5\" namest=\"c1\"\u003e \u003cp\u003eDroplet Capillary Number\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eModel\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"4\" nameend=\"c5\" namest=\"c2\"\u003e \u003cp\u003eMetrics\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMAE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMSE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eRMSE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eR\u0026sup2;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDNN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0828\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0012\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0185\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0004\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.1327\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0014\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.8301\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0042\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDNN\u0026ndash;DistilBERT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0115\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0009\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0005\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0002\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0163\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0016\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9947\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0023\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDNN\u0026ndash;GPT-2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0663\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0057\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0017\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0003\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0354\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0017\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9842\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0025\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDNN\u0026ndash;SentenceTransformer\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.092\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0086\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0041\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0003\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0603\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0018\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9611\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0034\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLightGBM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0819\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0010\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0249\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0005\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.1565\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0016\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.7714\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0042\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLightGBM\u0026ndash;DistilBERT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.1161\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0014\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0341\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0006\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.1839\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0016\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.686\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0049\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLightGBM\u0026ndash;GPT-2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0945\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0016\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0265\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0005\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.162\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0016\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.7546\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0107\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLightGBM\u0026ndash;SentenceTransformer\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.1061\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0021\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0307\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0006\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.1741\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0016\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.7182\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0043\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSVM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0918\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0020\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0223\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0009\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.1487\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0030\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.7919\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0042\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSVM\u0026ndash;DistilBERT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.1218\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0012\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0316\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0006\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.1771\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0020\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.7061\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0055\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSVM\u0026ndash;GPT-2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.1137\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0015\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0296\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0007\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.1717\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0018\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.7289\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0073\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSVM\u0026ndash;SentenceTransformer\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.1267\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0022\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0325\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0009\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.1795\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0026\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.6995\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0094\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eXGBoost\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0936\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0009\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0234\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0004\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.1522\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0013\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.7929\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0122\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eXGBoost\u0026ndash;DistilBERT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.1194\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0025\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0341\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0007\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.1832\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0022\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.6893\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0083\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eXGBoost\u0026ndash;GPT-2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0995\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0011\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0269\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0015\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.1642\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0031\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.7479\u0026thinsp;\u0026plusmn;\u0026thinsp;0.012\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eXGBoost\u0026ndash;SentenceTransformer\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.1108\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0011\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0308\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0011\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.1748\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0033\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.7151\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0051\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTo highlight the low standard error and the stabilisation of mean estimation performance across metrics of prediction for droplet capillary number for different models, we present an extensive comparative analysis of DNN, LightGBM, SVM, and XGBoost paired with the various NLP models, i.e., DistilBERT, GPT-2, and SentenceTransformer, as detailed in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. The performances of the models are rigorously evaluated using MAE, MSE, RMSE, and R\u0026sup2;. The table presents values derived from the repetitions in which the difference between the mean and median of the respective metric was minimised. This analysis provides key insights into the efficacy of these models in handling complex predictive tasks. The DNN model combined with DistilBERT emerged as the most effective, achieving an MAE of 0.0115, MSE of 0.0005, RMSE of 0.0163, and an R\u0026sup2; value of 0.9947. These results indicate that DNN\u0026ndash;DistilBERT has a remarkable ability to minimise error and maximise predictive accuracy, suggesting a strong synergy between deep learning architectures and transformer-based embeddings. The high R\u0026sup2; value of almost 1 implies that the model can explain nearly all the variability in the data, making it highly reliable for predictive tasks. In contrast, other model\u0026ndash;embedding combinations showed significant weaknesses in performance. For instance, LightGBM, while known for its efficiency in handling structured data, showed limitations when paired with NLP embeddings. The combination of LightGBM and SentenceTransformer resulted in a relatively high MAE of 0.1061 and a low R\u0026sup2; of 0.7182, reflecting a less accurate prediction capability. Similarly, SVM, a model traditionally strong in classification tasks, demonstrated suboptimal performance with DistilBERT (MAE: 0.1218, R\u0026sup2;: 0.7061), indicating that SVM may not fully capitalise on the rich semantic features offered by transformers. A critical observation is the consistent underperformance of SentenceTransformer across all models. Despite its theoretical promise, SentenceTransformer consistently yielded higher error rates and lower R\u0026sup2; values than DistilBERT and GPT-2. This suggests that SentenceTransformer may not capture the linguistic nuances required for high-accuracy predictions in these scenarios. The underperformance of the models with this embedding highlights the importance of choosing the right embedding based on the specific task and dataset characteristics. Moreover, the data reveals that advanced transformers like DistilBERT and GPT-2 significantly enhance model performance, especially in deep learning contexts. For instance, the DNN model with GPT-2 achieved a competitive MAE of 0.0663 and an R\u0026sup2; of 0.9842, although slightly inferior to DNN\u0026ndash;DistilBERT. This reinforces the idea that the architecture of the embedding model plays a crucial role in determining the overall performance, with simpler embeddings potentially lacking the depth needed for nuanced predictions. XGBoost, often favoured for its robustness and speed in structured data tasks, also showed variability depending on the embedding used. While XGBoost\u0026ndash;DistilBERT achieved a reasonable performance (MAE: 0.1194, R\u0026sup2;: 0.6893), it still lagged behind DNN-based approaches, particularly in terms of error minimisation. This suggests that while XGBoost remains a strong contender in traditional settings, its performance may be somewhat poorer when tasked with complex NLP tasks. The design automation for the remaining parameters is detailed in the supplementary file.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Learning curve of DNN models\u003c/h2\u003e \u003cp\u003eThe learning curve is a foundational tool for optimizing deep neural networks, offering a clear, dynamic view of model performance across epochs. It provides critical insights into how well a model learns from the training data and generalizes to unseen data by plotting metrics such as training and validation loss or accuracy over time. Monitoring the learning curve is especially crucial for determining the optimal number of training epochs, a key factor in balancing underfitting and overfitting. Underfitting is indicated by persistently high training and validation losses, suggesting the model has not learned sufficiently from the data. Overfitting, in contrast, occurs when training loss continues to decrease while validation loss plateaus or rises, signaling the model is excessively tuned to the training data and failing to generalize. The minimum validation loss often signifies the optimal epoch for stopping training. This principle is integral to techniques like early stopping, which aim to prevent overfitting. Careful interpretation of the curve not only informs epoch selection but also guides iterative adjustments to the learning rate, batch size, regularization strength, and other optimization parameters. Consequently, the learning curve is indispensable for systematically refining training processes to achieve optimal performance and robust generalization.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe learning curve of a DNN combined with SentenceTransformer for droplet diameter, depicting the training and validation loss trends over 500 epochs, is illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e. Initially, both metrics show a steep decline, indicating rapid convergence, followed by stabilization at lower loss values. Notably, the rapid convergence within the first 100 epochs highlights the importance of monitoring early training phases to avoid overtraining. Importantly, the validation loss generally aligns with the training loss, suggesting minimal overfitting. In this case, the plateau in validation loss suggests that training could be halted earlier, around 80\u0026ndash;100 epochs, to optimize computational resources while maintaining model performance. These observations reinforce the importance of closely monitoring the learning curve to determine the proper epoch range for training, ensuring a balance between minimizing training loss and achieving robust generalization. Additional selected learning curves are provided in Supplementary Fig.\u0026nbsp;42\u0026ndash;44.\u003c/p\u003e \u003c/div\u003e"},{"header":"4. Conclusion","content":"\u003cp\u003eIn this paper, we present \u0026micro;-Fluidic-LLMs, an innovative framework designed to process tabular data associated with droplet microfluidics by transforming it into a text-based representation that effectively incorporates essential contextual information, including column descriptions. Our findings underscore the critical role of model selection and language model integration in achieving optimal efficiency of performance prediction and design automation. We emphasise the superior performance of DNN models, particularly when integrated with advanced NLP models such as DistilBERT and GPT-2. In comparison, traditional ensemble methods like LightGBM and XGBoost, even when incorporating state-of-the-art NLP approaches, may struggle to achieve comparable performance levels.\u003c/p\u003e \u003cp\u003eMultiple research directions can be pursued to further advance and optimise our framework. For example, exploration of various text serialisation methods, regularisation techniques, dataset augmentation, or advanced optimisation algorithms could provide means to enhance model performance and reduce error rates. Furthermore, given the flexibility of our framework to accommodate different language models, it can be utilised with the latest LLMs, such as GPT-4,\u003csup\u003e\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e,\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e\u003c/sup\u003e PaLM 2,\u003csup\u003e\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e\u003c/sup\u003e Gemini 1.5,\u003csup\u003e\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e\u003c/sup\u003e and LLaMA 3,\u003csup\u003e\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e\u003c/sup\u003e to assess variations in overall performance. Moreover, \u0026micro;-Fluidic-LLMs is a general framework that can be adapted for use with other microfluidic components, such as micromixers,\u003csup\u003e\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e\u003c/sup\u003e and extended to non-microfluidic structures like 3D-printed lattices\u003csup\u003e\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e51\u003c/span\u003e\u003c/sup\u003e, thereby enabling the automation of intricate design processes. In addition, \u0026micro;-Fluidic-LLMs can be seamlessly integrated with existing microfluidic computer-aided design tools\u003csup\u003e\u003cspan additionalcitationids=\"CR53 CR54 CR55 CR56 CR57 CR58 CR59\" citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e60\u003c/span\u003e\u003c/sup\u003e to enable more sophisticated and advanced design automation. We anticipate that this work will inspire further research into the application of language technologies across a broader range of microfluidic applications.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eConflicts of interest\u003c/h2\u003e \u003cp\u003eThere are no conflicts to declare.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eAcknowledgments\u003c/h2\u003e \u003cp\u003eWe gratefully acknowledge the funding provided by the Research Grant Council of Hong Kong, General Research Fund (Ref No. 14211223).\u003c/p\u003e\u003ch2\u003eData availability\u003c/h2\u003e \u003cp\u003e \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://github.com/duydinhlab/MicrofluidicLLMs\u003c/span\u003e\u003cspan address=\"https://github.com/duydinhlab/MicrofluidicLLMs\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e \u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eG. 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Commun.\u003c/em\u003e 2024 \u003cem\u003e151\u003c/em\u003e, 2024, 15, 1\u0026ndash;16.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Droplet Microfluidics, Large Language models, Machine Learning, Autonomous Design, Artificial Intelligence ","lastPublishedDoi":"10.21203/rs.3.rs-6282521/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6282521/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eDroplet-based microfluidic devices have substantial promise as cost-effective alternatives to current assessment tools in biological research. Moreover, machine learning models that leverage tabular data, including input design parameters and their corresponding efficiency outputs, are increasingly utilised to automate the design process of these devices and to predict their performance. However, these models fail to fully leverage the data presented in the tables, neglecting crucial contextual information, including column headings and their associated descriptions. This study presents \u0026micro;-Fluidic-LLMs, a framework designed for processing and feature extraction, which effectively captures contextual information from tabular data formats. \u0026micro;-Fluidic-LLMs overcomes processing challenges by transforming the content into a linguistic format and leveraging pre-trained large language models (LLMs) for analysis. We evaluate our \u0026micro;-Fluidic-LLMs framework on 11 prediction tasks, covering aspects such as geometry, flow conditions, regimes, and performance, utilising a publicly available dataset on flow-focusing droplet microfluidics. We demonstrate that our \u0026micro;-Fluidic-LLMs framework can empower deep neural network models to be highly effective and straightforward while minimising the need for extensive data preprocessing. Moreover, the exceptional performance of deep neural network models, particularly when combined with advanced natural language processing models such as DistilBERT and GPT-2, \u003cem\u003ereduces the mean absolute error in the droplet diameter and generation rate by nearly 5- and 7-fold\u003c/em\u003e, respectively, and enhances the regime classification accuracy by \u003cem\u003eover 4%\u003c/em\u003e, compared with the performance reported in a previous study. This study lays the foundation for the huge potential applications of LLMs and machine learning in a wider spectrum of microfluidic applications.\u003c/p\u003e","manuscriptTitle":"Autonomous Droplet Microfluidic Design Framework with Large Language Models","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-03-28 03:52:40","doi":"10.21203/rs.3.rs-6282521/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"49d94e50-ce7b-41f0-bb31-a71aebb8a095","owner":[],"postedDate":"March 28th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":46117812,"name":"Physical sciences/Engineering/Biomedical engineering"},{"id":46117813,"name":"Biological sciences/Biological techniques/Lab-on-a-chip"}],"tags":[],"updatedAt":"2025-03-31T09:10:42+00:00","versionOfRecord":[],"versionCreatedAt":"2025-03-28 03:52:40","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6282521","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6282521","identity":"rs-6282521","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}