SurFF: Universal Model for Surface Exposure and Synthesizability Across Intermetallic Crystals

SurFF: Universal Model for Surface Exposure and Synthesizability Across Intermetallic Crystals | 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 SurFF: Universal Model for Surface Exposure and Synthesizability Across Intermetallic Crystals Xiaonan Wang, Jun Yin, Honghao Chen, Jiangjie Qiu, Wentao Li, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4863775/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 09 Sep, 2025 Read the published version in Nature Computational Science → Version 1 posted You are reading this latest preprint version Abstract Catalysts are crucial in industrial processes, significantly enhancing reaction efficiency. With approximately 90% of industrial reactions occurring on surfaces, the role of heterogeneous catalysts is paramount. Accurate surface exposure prediction is vital for heterogeneous catalyst design but is hindered by the high costs of experimental and computational methods. Here, we introduce a universal force field-based model for predicting surface exposure and synthesizability (SurFF) across intermetallic crystals, essential materials for heterogeneous catalysts. We created a comprehensive intermetallic surface database using a data-efficient active learning method and high-throughput density functional theory (DFT) calculations, encompassing 12,553 unique surfaces and 344,200 single points. SurFF achieves DFT-level precision with a prediction error of 3.0 meV/Ų and enables large-scale surface exposure prediction, an impractical task for DFT methods, through a 10 5 -fold acceleration. Validation against computational and experimental data both shows strong alignment. We applied SurFF for large-scale predictions on over 6,000 intermetallic crystals, providing valuable data for the community. Demonstrating transferability to diverse crystal properties, SurFF is a robust tool for advancing catalyst design, representing a significant step toward large-scale catalyst discovery models. Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Main The development of high-performance catalytic materials is vital for advancing modern science and industry, impacting fields such as energy conversion and storage, environmental protection, and industrial manufacturing 1 , 2 . With approximately 90 percent of industrial reactions occurring on catalyst surfaces, the significance of heterogeneous catalysts cannot be overstated. A critical step in designing novel catalytic materials is the performance evaluation of potential candidates. Traditionally, this process is time-consuming, often taking weeks, which restricts the number of candidates that can be examined. However, the recent integration of high-throughput quantum chemistry computations and machine learning (ML) methods has revolutionized this field, dramatically accelerating the evaluation process 3 – 9 . These approaches typically correlate catalyst performance with computational properties like energy 10 and band gap 11 . By leveraging high-throughput computational data and advanced ML models, researchers can now efficiently screen a vast array of candidate materials, paving the way for innovative catalyst design. For typical heterogeneous catalysts, the two most critical properties influencing catalyst performance are the surface activity and exposure of surfaces on a crystal material. The former determines the reaction rate on a specific surface, while the latter determines whether the surface exists and the extent of its exposure (i.e., synthesizability). Theoretically, a crystal could possess an infinite number of unique surfaces, each characterized by different Miller indices and catalytic properties. While computational methods can predict the hypothetical activity of all these surfaces, thermodynamic and kinetic constraints significantly limit the number of unique surfaces that materialize during crystal growth. Despite numerous unique surfaces on crystals, typically only those with lower surface energies have higher exposure and synthesizability 12 , 13 . By understanding and predicting surface exposure, we can identify top surfaces with high exposure and synthesizability in large-scale screenings. This approach accelerates catalyst design by enabling researchers to focus on evaluating the properties of synthesizable and exposed surfaces. Conventional methods to obtain surface exposure information are costly and unsuitable for large-scale applications. Experimental methods usually takes weeks and involves characterization techniques such as X-ray diffraction (XRD) and high resolution transmission electron microscope (HR-TEM) 14 , 15 . A widely accepted computational method involves calculating the surface energies of a crystal and applying the Wulff construction to determine the morphology of catalyst nanoparticles and surface exposure 16 – 18 . Surface energy is a crucial crystal property for catalyst discovery, as it directly relates to surface exposure and nanoparticle morphology 16 , 19 . This property can be derived from the difference between the energies of the relaxed crystal surface and the crystal bulk. However, computing that difference for a single crystal using density function theory (DFT) can take several days 12 . To enable large-scale assessments on surface exposure, ML models could be developed to replace costly DFT calculations 20 – 23 . By efficiently predicting surface energies of a wide range of crystal materials, surface exposure and synthesizability information could be obtained at a large scale and low cost. This work introduces SurFF, a universal model for fast and accurate prediction of surface exposure directly from cell structures across intermetallic crystal materials. It is built on a comprehensive surface database 24 that features 50 metal elements, 12,000 unique intermetallic surfaces, and 344,000 frames of DFT single points. We showed that it achieved DFT-level precision 25 with a computational speed 10 5 times faster than conventional DFT methods, so that millions of crystal structures can be screened within days. To validate the accuracy of SurFF's predictions, we compared its results with both DFT predictions and experimental observations from the literature. SurFF accurately predicted both of them, which demonstrates its utility for real-world catalyst design. Following this validation, we used SurFF to predict the surface energy and surface exposure for six thousand binary and ternary intermetallic crystals with known cell structures and catalytic functionality. This has generated essential and comprehensive data for catalyst design, performance evaluation, and optimization. Lastly, we demonstrated SurFF’s transferability to unseen dataset with different crystal properties, showing its potential to extend to all other crystal systems. Our development of SurFF showcases an emerging approach in materials science research, illustrating how data-driven methods can enable large-scale screening and significantly accelerate material discovery—a process that traditionally requires extensive time and effort. This advancement not only enhances the efficiency of catalyst design but also opens new avenues for the rapid discovery of high-performance materials. Results Overall framework The overall framework of SurFF is depicted in Fig. 1 . SurFF integrates three functional modules: (1) a surface generation module to enumerate unique surfaces and generate corresponding surface slab structures of a given crystal structure; (2) a surface relaxation module to perform accurate and rapid structural relaxation for each slab structure to obtain the surface energies of all enumerated surfaces using a machine learning force field (MLFF); and, (3) a Wulff construction module to determine the morphology of thermodynamically stable crystal nanoparticles, where surface exposure information could be extracted. The key to SurFF's accuracy lies in its precise surface energy prediction. Therefore, it is essential to develop a deep MLFF applicable to all intermetallic surfaces and to construct a comprehensive surface database as the foundation. Dataset development - Design Space For a comprehensive surface database, the design space should cover intermetallic surfaces spanning various compositions, Miller indices, and crystal systems. Hence, we retrieved a wide array of thermodynamically stable metallic crystals from the Material Project 26 for surface generation (S2.1). These include pure, bimetallic, and trimetallic crystals from 49 metal or semimetal elements, all seven crystal systems and hundreds of composition systems. The retrieved crystals were first optimized using DFT to ensure uniformity and reliability 22 (S2.2). Then, multiple structures of oriented unit cells (OUCs) and surfaces slabs 12 are generated for each unique surface with miller index up to 2 (Method, S2.4 and S3.1). This methodical generation resulted in a total of 284,134 intermetallic surfaces, each uniquely identified by a crystal label, Miller index, and shift. The broad coverage of intermetallic surfaces makes the design space suitable for generating a comprehensive database to develop a MLFF for intermetallic surfaces. Dataset development - active learning Given the extensive design space of 284,134 surfaces, direct DFT calculations for all surfaces would be prohibitively expensive. As shown in Fig. 2 (a), to reduce computational effort, we adopted a data-efficient active learning strategy for dataset generation (Method and S3.3) 27 – 29 . We first used diversity sampling to obtain small batches of bimetallic and trimetallic surfaces respectively from the design space, and then computed their surface energies to form active learning (AL) test sets (Fig. 2 (b), S3.5). To ensure the reliability of the surface energy calculations, we performed convergence tests and benchmarked the results against higher-level DFT methods before dataset generation (S2.3). This AL test sets allowed us to continuously monitor model accuracy, ensure the predictive capabilities across the design space. During the active learning iteration, we generated the bimetallic surfaces first until the model reached a reasonable accuracy and then repeated the same for trimetallic surfaces. In each iteration of the active learning loop, a probabilistic ML model was trained or updated using all the available data. An uncertainty-based and diversity-based acquisition function was employed to identify and select the most informative surfaces from the design space for subsequent DFT data generation (S3.4). This iterative process was repeated until the model reached satisfactory accuracy on the AL test sets. Figure 2 (c) and S3.4 show detailed statistics on how the model accuracy increased as more data is generated. The active learning cycle concluded after ten iterations, where the model demonstrated reasonable accuracy and further data addition showed diminishing returns in improving model accuracy. Figure 2 (d) and S3.5 show the distribution of composition systems of surfaces in the final dataset (train set), which includes 12,000 surface energy data and 344,000 DFT single points. The entire process takes a total of 155,612 CPU-hours for DFT calculations. MLFF development After developing the surface database, we trained a large equivariant deep graph convolutional neural network 30 , 31 as MLFF on the trajectory data of DFT relaxation from our generated train set. Each trajectory frame was represented as a graph with atoms as vertices, atom connectivity information as edges, and DFT forces and energies as vertex outputs (Method and S4.1). The MLFF was designed and developed based on the training set to predict the forces and energies for given structures during crystal surface relaxation. As shown in Fig. 3 (a-b), we first trained the model on the train set, optimized hyper-parameters, and then assessed on the AL test sets (S4.2 and S4.4). We achieved a low mean absolute error (MAE) of 3.8 meV/Å 2 on the AL test set, indicating that the MLFF achieved the DFT-level precision 25 and accurately predicted the relaxed surface energies across the design space. With a highly accurate MLFF available, we marked the completion of SurFF development. Validation with Computational Results To assess SurFF’s performance on predicting surface exposure, we generated another in-distribution (ID) test set (S3.5), which contains sampled crystals from the design space and all their enumerated surfaces with miller indices of 2 or lower. Then, we used SurFF to perform surface relaxations and obtained final relaxed energies by providing only the initial structure of surfaces (S4.6). As shown in Fig. 3 (c), SurFF accurately predicted surface energies of the crystals in the ID test set with an MAE of 3.0 meV/Å 2 . We then compared the Wulff construction results obtained from DFT and MLFF relaxed surface energies for all the crystals in the ID test set (see Fig. 3 (d) and (g)). For synthesizability prediction, we categorized surface synthesizability into three levels based on exposed area: “Low” ( \(\:area\le\:0.01\) ), “Medium” ( \(\:0.010.1\) ). As shown in Fig. 3 (g), SurFF accurately predicted 80.0% of surface with high synthesizability, with an overall accuracy of 73.4%. Since the most exposed surfaces of a crystal are also of interest, we also show SurFF’s accuracy in predicting them (“Top-3” and “Top-5” in Fig. 3 (g)). These results show that it can successfully predict surface synthesizability and filter out low-synthesizability surfaces. It should also be highlighted that SurFF is 10 5 times faster than DFT (S4.3), hence it is highly efficient for large-scale applications. Based on these results, we conclude that SurFF is highly effective in ML relaxations and accurately predicts both surface energy and synthesizability across intermetallic surfaces in the design space. To further assess SurFF’s performance on more general intermetallic scenarios, we generated another out-of-distribution (OOD) test set (S3.5). This set included thermodynamically unstable yet experimentally validated crystals, and all their surfaces with Miller indices of 2 or lower. These crystals, which fall outside the initial design space and possess distinct properties, presented a significant challenge. We show the difference in surface energy distributions between ID and OOD test sets in S3.5. As shown in Fig. 3 (e), SurFF predicts the surface energies of crystals in the OOD test set with a MAE error of 10.5 meV/Å 2 . Although higher than the ID test set, it is still reasonably accurate for predicting surface synthesizability as surface energy is usually of the magnitude of 100 meV/Å 2 . We then performed Wulff construction for all the crystals in the OOD test set (Fig. 3 (f)). The results for Wulff construction and final surface synthesizability are summarized in Fig. 3 (g). Despite a higher error in surface energies, surface synthesizability has a “Top-5” accuracy of 0.820 and “High” accuracy of 0.744. These results demonstrate that SurFF could deliver useful synthesizability information for unseen OOD crystals with significantly different properties. We elaborate on this observation in S4.7, where we explain how SurFF’s low variance assures that the relative magnitudes of the predicted surface energies within a crystal remain comparable to those of the true surface energies. Consequently, despite the higher MAE in surface energy predictions, the accuracy in predicting surface synthesizability remains reliably high. The single point accuracy of the trained MLFF could be found in S4.6. Validation with Experimental Observations & Large-Scale Predictions Thus far, we have demonstrated that SurFF aligns with DFT results, offering a DFT-level precision in predicting surface energy and exposure. To further validate its relevance and utility in guiding actual experimental catalyst design, it is crucial to examinate SurFF’s predictions against experimental results. For this purpose, we gathered data of experimentally characterized intermetallic crystals from both existing literature and our original experiments. As delineated in Fig. 4 (a), we would confirm experimentally observed surfaces by both XRD-identified crystal structures and TEM-identified facets, which is currently the standard method for surface characterization in this field. For literature data, we screened over 10,000 research articles from four leading journals in the field of catalysis, utilizing a large language model (LLM) 33 . For original data, we conducted actual experiments to synthesize and characterize three intermetallics, namely ZnRh, ZnPd, and ZnPt (S5.3) 34 . Subsequently, we compared the surface exposures predicted by SurFF with the experimentally observed facets on the same crystal structures, as depicted in Fig. 4 (b) and S5.2. Remarkably, SurFF successfully predicted 73.1% of the experimentally observed facets, despite variations between experimental conditions and DFT-derived settings. This high rate of predictive success might be attributed to the fact that surface exposure is primarily influenced by the relative magnitudes of surface energies across different surfaces within crystal. Although the absolute values of surface energies may fluctuate under different environmental conditions, their relative values remain comparatively stable. Therefore, the predictions of surface exposure by SurFF also hold significant relevance for real-world experimental scenarios. Further details on the LLM screening and the collection of literature data are provided in S5.1. Given a good alignment with both experimental and computational results, we then applied SurFF to predict the surface exposure for a wide range of intermetallic crystals with catalytic functionality and known structures. The scope includes bimetallic and trimetallic crystals with a low energy-above-hull (less than 0.2 eV/atom) from a crystal structure database. This gave us more than 6,000 intermetallic crystals and 140 thousand unique intermetallic surfaces. All this predicted data would be available via table searching for community use. The prediction takes only 115 GPU hours in total for more than 6,000 crystals. More details about the workflow and results are provided in S6.1 and S6.2. Finetuning and Transferring Finally, we demonstrated the transferability of SurFF. Noticing that SurFF has a higher MAE in predicted surface energies in the unseen OOD test set because of different crystal properties, we used the OOD test set as an example to show that SurFF could be finetuned and transferred to other unseen datasets with minimal additional surface data. As shown in Fig. 5 (a), we created a new OOD finetuning dataset by randomly selecting and calculating only one surface from each crystal in the OOD test set (S3.5). Using this additional dataset, we finetuned SurFF for the OOD test set. Given that the task requires predicting multiple surfaces of the same crystal, SurFF could learn essential force field information from a single surface relaxation and apply this knowledge to all other surfaces of the same crystal due to their similarities in composition and force field. This capability, combined with the underlying knowledge in SurFF’s backbone, allowed for significant improvements in prediction accuracy with just a small amount of additional data. SurFF’s prediction results after transferring are summarized in Fig. 5 (b). The accuracy improved significantly by 45% in single point energy, 53% in single points force, 35% in surface energies, and 5.1% in Top-3 accuracy (S4.5). These results demonstrate that SurFF can be readily transferred to other unseen crystal materials with different properties using minimal data, showcasing its potential to extend to other crystal materials such as oxides, carbides, nitrides, or crystal materials in reaction environments. Discussion In this work, we developed SurFF, a universal model for fast and accurate prediction of surface exposure directly from cell structures across intermetallic crystal materials. By comparing both computational predictions and experimental observations from the literature, we validated its accuracy and applicability in real-world scenarios. Following this validation, we applied SurFF to predict the surface exposure for six thousand intermetallic crystals with catalytic functionality and known cell structures for community use. Lastly, we also demonstrated SurFF’s transferability to unseen dataset with different crystal properties, showing its potential to extend to all other crystal systems, including oxides 35 , nitrides 36 and carbides 37 . Despite SurFF’s high accuracy, we also acknowledge that the current dataset as well as model predictions do not yet consider various crystal preparation conditions, such as temperature and pressure 38 . A more comprehensive model could be prepared by finetuning with surface energy data under actual experimental conditions. The ability of SurFF to predict surface exposure rapidly and accurately at a large scale makes it a potent and robust tool for enhancing both computational and experimental approaches to catalyst design, marking a significant step toward large-scale models for catalyst discovery. Methods Surface Energy Calculation The typical slab approach for performing surface energy calculations requires the use of large supercells with high k-point density to ensure convergence, which makes such calculations computationally intensive. Here we adopted an efficient method which requires only one oriented unit cell (OUC) as bulk and one relatively thin slab calculation 12 , 39 . The calculated results of this method were validated with other literature values from both computation and experiment. We generated all required structures with PyMatgen package 40 . The surface energy can be calculated from the total energy of the crystal slab and crystal bulk: $$\:{E}_{ijk}^{surf}=\frac{{E}_{ijk}^{slab}-N\times\:{E}_{ijk}^{bulk,OUC}}{2{A}^{slab}}$$ 1 where \(\:{E}_{ijk}^{surf}\) is the surface energy of the surface with miller index \(\:(i,j,k)\) ; \(\:{E}_{ijk}^{slab}\) the total energy of the slab model with miller index \(\:(i,j,k)\) ; \(\:{E}_{ijk}^{bulk,OUC}\) the energy per atom of the bulk oriented unit cell (OUC) with miller index \(\:(i,j,k)\) ; \(\:N\) the number of atoms in the slab model; and, \(\:{A}^{slab}\) the cross-section area of the slab model. This efficient surface energy calculation method was validated on elemental crystals 12 , 39 , we also performed an additional convergence check of this method on intermetallic crystals to ensure this accuracy of our results (S3.2). DFT method All DFT energy calculations were performed using the Vienna Ab initio Simulation Package (VASP) within the projector augmented wave (PAW) approach. The exchange-correlation effects were modeled using the Perdew-Berke-Ernzerhof (PBE) generalized gradient approximation (GGA) functional, and all calculations were spin-polarized with a plane wave cutoff energy of 520 eV. The Methfessel Paxton method was employed for smearing, the blocked Davidson iteration scheme for electron minimization and the conjugated gradient algorithm for ion updates. Convergence was for energy, and atomic forces were set to be 10 − 6 eV and 0.02 eV/Å, respectively. Γ-centered k-point meshes of 35/a×35/b×35/c and 35/a×35/b×1 were used for OUC and slab calculations respectively, with non-integer values rounded up to the nearest integer. To ensure the accuracy of the calculation results obtained from the PBE GGA, we also calculated a batch of results using R2SCAN meta-GGA. The comparison results are shown in (S2.3). Wulff Construction Wulff Construction estimates the surface area fraction of each facet on a catalyst nanoparticle based on surface energies and surface orientations 16 . It is a geometric method used in the study of crystal growth and equilibrium crystal shapes developed by the German mathematician Gustav Wulff based on the idea that crystals grow in a way that minimizes their surface energy. Given direction-dependent surface energy information, including facet miller index and associated surface energy, the Wulff construction provides the lowest energy crystal shape by minimizing the surface energy of the crystal \(\:\varDelta\:G\) defined as: $$\:\varDelta\:\varvec{G}=\sum\:{\varvec{E}}_{\varvec{i}\varvec{j}\varvec{k}}^{\varvec{s}\varvec{u}\varvec{r}\varvec{f}}{\varvec{S}}_{\varvec{i}\varvec{j}\varvec{k}}$$ 2 where \(\:{\varvec{E}}_{\varvec{i}\varvec{j}\varvec{k}}^{\varvec{s}\varvec{u}\varvec{r}\varvec{f}}\) is the surface energy of the \(\:\left(i,j,k\right)\) surface, and \(\:{\varvec{S}}_{\varvec{i}\varvec{j}\varvec{k}}\) is the surface area of the \(\:\left(i,j,k\right)\) surface. The Wulff shape can then find the area fraction of each facet. Active learning Given an enormous design space of 284,134 crystal surfaces, a comprehensive dataset that contains all necessary information of the entire design space is required for the MLFF model to learn the underlying correlations and give accurate predictions. It should be noted that calculating all 284,134 crystal surfaces could be inefficient to construct a database for model development. To minimize the computational cost and increase data efficiency, active learning strategies can be adopted to add most informative data to the database iteratively and stop calculations when desired model accuracy is achieved 27 , 41 . In this work, we first use diversity sampling to generate 2,000 surface energy data, 1,000 from bimetallic surfaces and 1,000 from trimetallic surfaces, for constructing an AL test set. At each iteration, a probabilistic ML model of ensembles would be trained and updated on existing dataset 42 , 43 . The probabilistic model could take surface structures as input and predict their surface energies and uncertainties directly on current dataset and uncalculated surfaces in the design space (S3.3). After the model is updated, the model accuracy on the AL test set will be evaluated and recorded. To generate the next batch of data, the model uncertainties on the surfaces of the remaining design space would be calculated, and 1,000 surfaces would be chosen based on uncertainty and diversity sampling. Uncertainty sampling allows batches to have most informative surfaces with high uncertainties where model trained on current dataset does not have enough information. Diversity sampling avoids data unbalance issues by limiting the number of surfaces from the same compositional systems to at most three in each batch. The sampled batch would be sent for DFT calculations and then added to the dataset. Any failed calculations would be discarded. Since both bimetallic and trimetallic surfaces exist in the design space, we generate bimetallic data and test on the bimetallic data in the AL test set first, and then start to generate trimetallic data and test on the entire active learning test set. The final dataset is in in Fig. 2 and S3.5. MLFF model architecture A three-dimensional equivariant graph convolutional neural network (GNN), EquiformerV2 22,30 , is used as the model architecture for the MLFF in this work. EquiformerV2 is currently the state-of-the-art model for many quantum chemistry simulation datasets. It adapts eSCN 44 convolutions and Euclidean neural networks (e3nn) 45 to efficiently incorporate higher-degree tensors and 3-dimensional vectors to better model interatomic interactions. Similar to other GNNs for atomic modelling such as GemNet 46 , Graphormer 47 , SCN 31 and eSCN 44 , EquiformerV2 takes the 3D coordinates of a target structure as inputs and predicts its properties, which are forces and energies in this case. Each structure is first converted into graph representation \(\:G=\left(V,E\right)\) , where \(\:G\) is the graph data, \(\:V\) is the node set that contains atom type information, and \(\:E\) is the edge set that contains bond lengths and directions of all neighboring atoms. The atom features at each node are first embedded in an embedding layer. A few layers of eSCN convolutions and equivariant graph attention then iteratively update the atoms features based on their corresponding neighboring environments. Finally, the target properties, forces, and energies, will be predicted by the output heads based on the final atom features of each node. More details of model architecture are in S4.2. The model is trained in a supervised manner by the loss between predicted properties and ground true properties given in the training set. Optimization on the main model hyperparameters is conducted to maximize model performance. During the evaluation stage, the trained model would be used as MLFF for surface structure relaxation. Similar to a conventional force field model, it predicts the forces on each atom and the total energy of a structure. A relaxation algorithm moves atoms downwards the predicted potential energy hill and sends a new structure to the MLFF for prediction iteratively until the maximum force is below a certain threshold. More details of model training and evaluation are in S4.4. Model transferring The trained EquiformerV2 model as an MLFF can finetuned on additional data to improve performance on the OOD data (e.g., unseen crystal compositions). After the finetuning dataset is generated (Fig. 5 ), we finetuned the trained model by freezing the low-level layers and training with a small learning rate. Experimentations on the finetuning performance with different unfrozen output heads and convolutional layers were also performed to obtain the optimal finetuning configuration. The finetuned model was then tested on the same OOD test set to compare with the base model without finetuning. More details of model transferring are in S4.5. Declarations Data and Codes availability All data and codes in this work could be retrieved from S1.1 or GitHub repository https://github.com/Long1Corn/SurFF , where a step-by-step guide to use SurFF for prediction and a web UI are also provided. Acknowledgements This work is supported by the National Key R&D Program of China (No. 2022ZD0117501) and Tsinghua University Initiative Scientific Research Program. References Nørskov, J. K. & Bligaard, T. The Catalyst Genome. 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Y., Heras-Domingo, J., Kitchin, J. R. & Ulissi, Z. WhereWulff: A Semiautonomous Workflow for Systematic Catalyst Surface Reactivity under Reaction Conditions. Journal of Chemical Information and Modeling 63, 2427–2437 (2023). Sun, W. & Ceder, G. Efficient creation and convergence of surface slabs. Surface Science 617, 53–59 (2013). Ong, S. P. et al. Python Materials Genomics (pymatgen): A robust, open-source python library for materials analysis. Computational Materials Science 68, 314–319 (2013). Konyushkova, K., Sznitman, R. & Fua, P. Learning active learning from data. Advances in neural information processing systems 30 (2017). Lakshminarayanan, B., Pritzel, A. & Blundell, C. Simple and scalable predictive uncertainty estimation using deep ensembles. Advances in neural information processing systems 30 (2017). Yang, Y., Ma, Z., Nie, F., Chang, X. & Hauptmann, A. G. Multi-class active learning by uncertainty sampling with diversity maximization. International Journal of Computer Vision 113, 113–127 (2015). Passaro, S. & Zitnick, C. L. Reducing SO(3) convolutions to SO(2) for efficient equivariant GNNs. in Proceedings of the 40th International Conference on Machine Learning. (2023). Geiger, M. & Smidt, T. e3nn: Euclidean neural networks. arXiv preprint arXiv:2207.09453 (2022). Klicpera, J., Becker, F. & Günnemann, S. GemNet: Universal Directional Graph Neural Networks for Molecules. in Neural Information Processing Systems. (2021). Ying, C. et al. Do Transformers Really Perform Badly for Graph Representation? in The Thirty-Fifth Conference on Neural Information Processing Systems. (2021). Additional Declarations There is NO Competing Interest. Supplementary Files NATCOMPUTSCI241592SupplementaryInformationR1cleanKM.docx Supplementary Information Cite Share Download PDF Status: Published Journal Publication published 09 Sep, 2025 Read the published version in Nature Computational Science → Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-4863775","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":397429455,"identity":"033130ba-7e28-4ef1-82e6-f7f02a34f729","order_by":0,"name":"Xiaonan Wang","email":"data:image/png;base64,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","orcid":"https://orcid.org/0000-0001-9775-2417","institution":"Tsinghua University","correspondingAuthor":true,"prefix":"","firstName":"Xiaonan","middleName":"","lastName":"Wang","suffix":""},{"id":397429456,"identity":"e2228e52-4ded-4d6b-8d8e-8d68f8c72ece","order_by":1,"name":"Jun Yin","email":"","orcid":"https://orcid.org/0000-0002-8993-3178","institution":"Natinoal University of Singapore","correspondingAuthor":false,"prefix":"","firstName":"Jun","middleName":"","lastName":"Yin","suffix":""},{"id":397429457,"identity":"1a7ef9cf-a57f-419c-af7d-c6a0d0ae8e45","order_by":2,"name":"Honghao Chen","email":"","orcid":"","institution":"Tsinghua University","correspondingAuthor":false,"prefix":"","firstName":"Honghao","middleName":"","lastName":"Chen","suffix":""},{"id":397429458,"identity":"0640e126-c7e1-4d02-9a10-b3c2a99dd5ed","order_by":3,"name":"Jiangjie Qiu","email":"","orcid":"","institution":"Tsinghua University","correspondingAuthor":false,"prefix":"","firstName":"Jiangjie","middleName":"","lastName":"Qiu","suffix":""},{"id":397429459,"identity":"9c0dc7e0-57b6-4f80-9d17-5790cc675cdd","order_by":4,"name":"Wentao Li","email":"","orcid":"https://orcid.org/0009-0000-3002-7536","institution":"Tsinghua University","correspondingAuthor":false,"prefix":"","firstName":"Wentao","middleName":"","lastName":"Li","suffix":""},{"id":397429460,"identity":"1678c8d7-821f-4b89-8331-02567e172a1f","order_by":5,"name":"Peng He","email":"","orcid":"","institution":"National University of Singapore","correspondingAuthor":false,"prefix":"","firstName":"Peng","middleName":"","lastName":"He","suffix":""},{"id":397429461,"identity":"65b8e9f8-600f-4669-a47a-1d53beddb7c5","order_by":6,"name":"Jiali Li","email":"","orcid":"","institution":"National University of Singapore","correspondingAuthor":false,"prefix":"","firstName":"Jiali","middleName":"","lastName":"Li","suffix":""},{"id":397429462,"identity":"96d32ae0-2603-4190-b202-9461cfa9c32b","order_by":7,"name":"Iftekhar Karimi","email":"","orcid":"","institution":"National University of Singapore","correspondingAuthor":false,"prefix":"","firstName":"Iftekhar","middleName":"","lastName":"Karimi","suffix":""}],"badges":[],"createdAt":"2024-08-05 18:05:20","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4863775/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4863775/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s43588-025-00839-0","type":"published","date":"2025-09-09T04:00:00+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":73149183,"identity":"01472831-e9a0-447f-9639-018cecf4745a","added_by":"auto","created_at":"2025-01-07 08:09:19","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":431887,"visible":true,"origin":"","legend":"\u003cp\u003eThe overall framework of SurFF for predicting surface exposure. Surface generation module first enumerates unique surfaces given an input crystal structure. The surface energy of each surface is from the structural relaxation results facilitated by a deep MLFF. The MLFF is built on a comprehensive intermetallic surface database using data-efficient active learning methods. The predicted surface energies along with surface orientations are sent to Wulff construction module to obtain the final surface exposure.\u003c/p\u003e","description":"","filename":"image1.png","url":"https://assets-eu.researchsquare.com/files/rs-4863775/v1/01712cad22e9340aa57c5b18.png"},{"id":73149426,"identity":"4f8c4fe5-f7e3-45f5-9170-a81add63f89a","added_by":"auto","created_at":"2025-01-07 08:09:25","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":804708,"visible":true,"origin":"","legend":"\u003cp\u003elearning strategy used for dataset development. Surface energy data are iteratively generated by DFT calculation in small batches based on uncertainty and diversity sampling acquisition function and a probabilistic ML model. The loop concludes when the model achieves reasonable accuracy on the test sets. (b) The visualization of the generated relaxation trajectory data. (c) The visualization of crystal composition distribution of the active learning test sets. The total count of a composition in figure equals to the total number of surfaces in the active learning test sets that contains the two elements in the corresponding horizontal and vertical axis. A wide and balanced data coverage from diversity sampling makes it representative of the entire design space and suitable for testing purposes. (d) The plot of quantity of surface energy data in the dataset and model accuracy during the whole active learning progress. Batch 2-2 to 2-4 generated bimetallic surface energy data and tested on the bimetallic active learning test set. Batch 3-1 to 3-7 generated trimetallic surface energy data and tested on the entire test set active learning test sets. (e) The visualization of crystal composition distribution of the final generated dataset. The total count of a composition in figure equals to the total number of surfaces in the active learning test sets that contains the two elements in the corresponding horizontal and vertical axis.\u003c/p\u003e","description":"","filename":"image2.png","url":"https://assets-eu.researchsquare.com/files/rs-4863775/v1/82c1c67129542f1a71e01de8.png"},{"id":73149179,"identity":"4562f1dc-07ff-4514-afc5-05e75d6e40d1","added_by":"auto","created_at":"2025-01-07 08:09:18","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":558714,"visible":true,"origin":"","legend":"\u003cp\u003eMLFF training and testing results. (a) The accuracy of relaxed surface energy in the active learning test set. (b) The accuracy of energy and force predictions of single point in the training set. (c) The accuracy of relaxed surface energies of crystal surfaces in the ID testing set, calculated by relaxed surface slab energy minus crystal bulk energy divided by surface area. (d) The illustration of the Wulff shape and surface synthesizability obtained from both SurFF prediction and DFT calculated surface energies for crystals in the ID testing set. (e) The accuracy of relaxed surface energies of crystal surfaces in the OOD testing set. (f) The illustration of the Wulff shape and surface synthesizability obtained from both predicted and DFT calculated surface energies for crystals in the OOD testing set. (g) The comparison between DFT and SurFF in terms of surface exposure prediction. Metrics “Low”, “Medium”, “High” refers to the percentage of correctly predicted surfaces with low, medium, and high synthesizability, respectively. Additionally, the metrics “Top-3” and “Top-5” indicate the percentage of correctly predicted surfaces belonging to the highest 3 or 5 exposures within a crystal. (h) The comparison between DFT and SurFF in terms of Computational Time.\u003c/p\u003e","description":"","filename":"image3.png","url":"https://assets-eu.researchsquare.com/files/rs-4863775/v1/14e60be0236fa1511f903cba.png"},{"id":73149182,"identity":"88fc1727-9543-4a74-8bae-fd80b4824b18","added_by":"auto","created_at":"2025-01-07 08:09:19","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":1002536,"visible":true,"origin":"","legend":"\u003cp\u003eEvaluation of existing intermetallic crystals of known structures by the pre-train model and comparison with literature experimental results. (a) Method to obtain experimental observed surfaces, using CuPd data as an example \u003csup\u003e32\u003c/sup\u003e. Crystal phases and exposed surface indices are strictly determined by reported XRD patterns and d-spacing of TEM images. Any literature result with uncertain XRD pattern or TEM image are not included. (b) Visualization and tabulating 3 original experimental data and 8 arbitrarily selected literature experimental data for comparison. Each box shows the composition, space group, predicted Wulff shape, and predicted surface area fraction of a selected crystal. Experimentally observed surfaces that are also predicted are labelled on the Wulff plots. Experimentally observed surfaces that are not predicted are shown on the lower left corner of each box.\u003c/p\u003e","description":"","filename":"image4.png","url":"https://assets-eu.researchsquare.com/files/rs-4863775/v1/f7f6f9253763860d5ac146c3.png"},{"id":73149472,"identity":"dd9c9b6c-2154-4b0d-bf4c-6fccf54f0f07","added_by":"auto","created_at":"2025-01-07 08:09:26","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":364454,"visible":true,"origin":"","legend":"\u003cp\u003eModel finetuning and transferring. (a) Illustration of model finetuning and transferring learning to improve predictive accuracy for unseen crystal materials. An additional surface dataset is generated by DFT calculating only one surface of the target crystals. SurFF finetuned by the generated dataset gives rapid and more accurate predictions of the remaining dozens of surfaces, and thus more accurate surface exposure and synthesizability. (b) Comparison of SurFF’s performance before and after the finetuning on the OOD finetuning dataset.\u003c/p\u003e","description":"","filename":"image5.png","url":"https://assets-eu.researchsquare.com/files/rs-4863775/v1/e762e7669bcbc295d2d554b1.png"},{"id":91149385,"identity":"826a2a45-7122-4444-a308-fa358b7dec1c","added_by":"auto","created_at":"2025-09-12 06:49:14","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3645668,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4863775/v1/5f0a199b-2c58-402b-92e2-bd97331c66fd.pdf"},{"id":73149187,"identity":"088ab63a-4817-40cd-9825-626c5cc06421","added_by":"auto","created_at":"2025-01-07 08:09:20","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":32079035,"visible":true,"origin":"","legend":"\u003cp\u003eSupplementary Information\u003c/p\u003e","description":"","filename":"NATCOMPUTSCI241592SupplementaryInformationR1cleanKM.docx","url":"https://assets-eu.researchsquare.com/files/rs-4863775/v1/01b33b0745b4e02e58c08f67.docx"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"SurFF: Universal Model for Surface Exposure and Synthesizability Across Intermetallic Crystals","fulltext":[{"header":"Main","content":"\u003cp\u003eThe development of high-performance catalytic materials is vital for advancing modern science and industry, impacting fields such as energy conversion and storage, environmental protection, and industrial manufacturing \u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e,\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e. With approximately 90 percent of industrial reactions occurring on catalyst surfaces, the significance of heterogeneous catalysts cannot be overstated. A critical step in designing novel catalytic materials is the performance evaluation of potential candidates. Traditionally, this process is time-consuming, often taking weeks, which restricts the number of candidates that can be examined. However, the recent integration of high-throughput quantum chemistry computations and machine learning (ML) methods has revolutionized this field, dramatically accelerating the evaluation process \u003csup\u003e\u003cspan additionalcitationids=\"CR4 CR5 CR6 CR7 CR8\" citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e. These approaches typically correlate catalyst performance with computational properties like energy \u003csup\u003e\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e and band gap \u003csup\u003e\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/sup\u003e. By leveraging high-throughput computational data and advanced ML models, researchers can now efficiently screen a vast array of candidate materials, paving the way for innovative catalyst design.\u003c/p\u003e \u003cp\u003eFor typical heterogeneous catalysts, the two most critical properties influencing catalyst performance are the surface activity and exposure of surfaces on a crystal material. The former determines the reaction rate on a specific surface, while the latter determines whether the surface exists and the extent of its exposure (i.e., synthesizability). Theoretically, a crystal could possess an infinite number of unique surfaces, each characterized by different Miller indices and catalytic properties. While computational methods can predict the hypothetical activity of all these surfaces, thermodynamic and kinetic constraints significantly limit the number of unique surfaces that materialize during crystal growth. Despite numerous unique surfaces on crystals, typically only those with lower surface energies have higher exposure and synthesizability \u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e,\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u003c/sup\u003e. By understanding and predicting surface exposure, we can identify top surfaces with high exposure and synthesizability in large-scale screenings. This approach accelerates catalyst design by enabling researchers to focus on evaluating the properties of synthesizable and exposed surfaces.\u003c/p\u003e \u003cp\u003eConventional methods to obtain surface exposure information are costly and unsuitable for large-scale applications. Experimental methods usually takes weeks and involves characterization techniques such as X-ray diffraction (XRD) and high resolution transmission electron microscope (HR-TEM) \u003csup\u003e\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e,\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e. A widely accepted computational method involves calculating the surface energies of a crystal and applying the Wulff construction to determine the morphology of catalyst nanoparticles and surface exposure \u003csup\u003e\u003cspan additionalcitationids=\"CR17\" citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e. Surface energy is a crucial crystal property for catalyst discovery, as it directly relates to surface exposure and nanoparticle morphology \u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e,\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e. This property can be derived from the difference between the energies of the relaxed crystal surface and the crystal bulk. However, computing that difference for a single crystal using density function theory (DFT) can take several days \u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e. To enable large-scale assessments on surface exposure, ML models could be developed to replace costly DFT calculations \u003csup\u003e\u003cspan additionalcitationids=\"CR21 CR22\" citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e. By efficiently predicting surface energies of a wide range of crystal materials, surface exposure and synthesizability information could be obtained at a large scale and low cost.\u003c/p\u003e \u003cp\u003eThis work introduces SurFF, a universal model for fast and accurate prediction of surface exposure directly from cell structures across intermetallic crystal materials. It is built on a comprehensive surface database \u003csup\u003e\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e that features 50 metal elements, 12,000 unique intermetallic surfaces, and 344,000 frames of DFT single points. We showed that it achieved DFT-level precision \u003csup\u003e\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e with a computational speed 10\u003csup\u003e5\u003c/sup\u003e times faster than conventional DFT methods, so that millions of crystal structures can be screened within days. To validate the accuracy of SurFF's predictions, we compared its results with both DFT predictions and experimental observations from the literature. SurFF accurately predicted both of them, which demonstrates its utility for real-world catalyst design. Following this validation, we used SurFF to predict the surface energy and surface exposure for six thousand binary and ternary intermetallic crystals with known cell structures and catalytic functionality. This has generated essential and comprehensive data for catalyst design, performance evaluation, and optimization. Lastly, we demonstrated SurFF\u0026rsquo;s transferability to unseen dataset with different crystal properties, showing its potential to extend to all other crystal systems. Our development of SurFF showcases an emerging approach in materials science research, illustrating how data-driven methods can enable large-scale screening and significantly accelerate material discovery\u0026mdash;a process that traditionally requires extensive time and effort. This advancement not only enhances the efficiency of catalyst design but also opens new avenues for the rapid discovery of high-performance materials.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"Results","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eOverall framework\u003c/h2\u003e \u003cp\u003eThe overall framework of SurFF is depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. SurFF integrates three functional modules: (1) a surface generation module to enumerate unique surfaces and generate corresponding surface slab structures of a given crystal structure; (2) a surface relaxation module to perform accurate and rapid structural relaxation for each slab structure to obtain the surface energies of all enumerated surfaces using a machine learning force field (MLFF); and, (3) a Wulff construction module to determine the morphology of thermodynamically stable crystal nanoparticles, where surface exposure information could be extracted. The key to SurFF's accuracy lies in its precise surface energy prediction. Therefore, it is essential to develop a deep MLFF applicable to all intermetallic surfaces and to construct a comprehensive surface database as the foundation.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eDataset development - Design Space\u003c/h3\u003e\n\u003cp\u003eFor a comprehensive surface database, the design space should cover intermetallic surfaces spanning various compositions, Miller indices, and crystal systems. Hence, we retrieved a wide array of thermodynamically stable metallic crystals from the Material Project \u003csup\u003e\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/sup\u003e for surface generation (S2.1). These include pure, bimetallic, and trimetallic crystals from 49 metal or semimetal elements, all seven crystal systems and hundreds of composition systems. The retrieved crystals were first optimized using DFT to ensure uniformity and reliability \u003csup\u003e\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e (S2.2). Then, multiple structures of oriented unit cells (OUCs) and surfaces slabs \u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e are generated for each unique surface with miller index up to 2 (Method, S2.4 and S3.1). This methodical generation resulted in a total of 284,134 intermetallic surfaces, each uniquely identified by a crystal label, Miller index, and shift. The broad coverage of intermetallic surfaces makes the design space suitable for generating a comprehensive database to develop a MLFF for intermetallic surfaces.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\n\u003ch3\u003eDataset development - active learning\u003c/h3\u003e\n\u003cp\u003eGiven the extensive design space of 284,134 surfaces, direct DFT calculations for all surfaces would be prohibitively expensive. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(a), to reduce computational effort, we adopted a data-efficient active learning strategy for dataset generation (Method and S3.3) \u003csup\u003e\u003cspan additionalcitationids=\"CR28\" citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e. We first used diversity sampling to obtain small batches of bimetallic and trimetallic surfaces respectively from the design space, and then computed their surface energies to form active learning (AL) test sets (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(b), S3.5). To ensure the reliability of the surface energy calculations, we performed convergence tests and benchmarked the results against higher-level DFT methods before dataset generation (S2.3). This AL test sets allowed us to continuously monitor model accuracy, ensure the predictive capabilities across the design space. During the active learning iteration, we generated the bimetallic surfaces first until the model reached a reasonable accuracy and then repeated the same for trimetallic surfaces. In each iteration of the active learning loop, a probabilistic ML model was trained or updated using all the available data. An uncertainty-based and diversity-based acquisition function was employed to identify and select the most informative surfaces from the design space for subsequent DFT data generation (S3.4).\u003c/p\u003e \u003cp\u003eThis iterative process was repeated until the model reached satisfactory accuracy on the AL test sets. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(c) and S3.4 show detailed statistics on how the model accuracy increased as more data is generated. The active learning cycle concluded after ten iterations, where the model demonstrated reasonable accuracy and further data addition showed diminishing returns in improving model accuracy. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(d) and S3.5 show the distribution of composition systems of surfaces in the final dataset (train set), which includes 12,000 surface energy data and 344,000 DFT single points. The entire process takes a total of 155,612 CPU-hours for DFT calculations.\u003c/p\u003e\n\u003ch3\u003eMLFF development\u003c/h3\u003e\n\u003cp\u003e \u003c/p\u003e \u003cp\u003eAfter developing the surface database, we trained a large equivariant deep graph convolutional neural network \u003csup\u003e\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e,\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e\u003c/sup\u003e as MLFF on the trajectory data of DFT relaxation from our generated train set. Each trajectory frame was represented as a graph with atoms as vertices, atom connectivity information as edges, and DFT forces and energies as vertex outputs (Method and S4.1). The MLFF was designed and developed based on the training set to predict the forces and energies for given structures during crystal surface relaxation. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(a-b), we first trained the model on the train set, optimized hyper-parameters, and then assessed on the AL test sets (S4.2 and S4.4). We achieved a low mean absolute error (MAE) of 3.8 meV/\u0026Aring;\u003csup\u003e2\u003c/sup\u003e on the AL test set, indicating that the MLFF achieved the DFT-level precision \u003csup\u003e\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e and accurately predicted the relaxed surface energies across the design space. With a highly accurate MLFF available, we marked the completion of SurFF development.\u003c/p\u003e\n\u003ch3\u003eValidation with Computational Results\u003c/h3\u003e\n\u003cp\u003eTo assess SurFF\u0026rsquo;s performance on predicting surface exposure, we generated another in-distribution (ID) test set (S3.5), which contains sampled crystals from the design space and all their enumerated surfaces with miller indices of 2 or lower. Then, we used SurFF to perform surface relaxations and obtained final relaxed energies by providing only the initial structure of surfaces (S4.6). As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(c), SurFF accurately predicted surface energies of the crystals in the ID test set with an MAE of 3.0 meV/\u0026Aring;\u003csup\u003e2\u003c/sup\u003e. We then compared the Wulff construction results obtained from DFT and MLFF relaxed surface energies for all the crystals in the ID test set (see Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(d) and (g)). For synthesizability prediction, we categorized surface synthesizability into three levels based on exposed area: \u0026ldquo;Low\u0026rdquo; (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:area\\le\\:0.01\\)\u003c/span\u003e\u003c/span\u003e), \u0026ldquo;Medium\u0026rdquo; (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:0.01\u0026lt;area\\le\\:0.1\\)\u003c/span\u003e\u003c/span\u003e), and \u0026ldquo;High\u0026rdquo; (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:area\u0026gt;0.1\\)\u003c/span\u003e\u003c/span\u003e). As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(g), SurFF accurately predicted 80.0% of surface with high synthesizability, with an overall accuracy of 73.4%. Since the most exposed surfaces of a crystal are also of interest, we also show SurFF\u0026rsquo;s accuracy in predicting them (\u0026ldquo;Top-3\u0026rdquo; and \u0026ldquo;Top-5\u0026rdquo; in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(g)). These results show that it can successfully predict surface synthesizability and filter out low-synthesizability surfaces. It should also be highlighted that SurFF is 10\u003csup\u003e5\u003c/sup\u003e times faster than DFT (S4.3), hence it is highly efficient for large-scale applications. Based on these results, we conclude that SurFF is highly effective in ML relaxations and accurately predicts both surface energy and synthesizability across intermetallic surfaces in the design space.\u003c/p\u003e \u003cp\u003eTo further assess SurFF\u0026rsquo;s performance on more general intermetallic scenarios, we generated another out-of-distribution (OOD) test set (S3.5). This set included thermodynamically unstable yet experimentally validated crystals, and all their surfaces with Miller indices of 2 or lower. These crystals, which fall outside the initial design space and possess distinct properties, presented a significant challenge. We show the difference in surface energy distributions between ID and OOD test sets in S3.5. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(e), SurFF predicts the surface energies of crystals in the OOD test set with a MAE error of 10.5 meV/\u0026Aring;\u003csup\u003e2\u003c/sup\u003e. Although higher than the ID test set, it is still reasonably accurate for predicting surface synthesizability as surface energy is usually of the magnitude of 100 meV/\u0026Aring;\u003csup\u003e2\u003c/sup\u003e. We then performed Wulff construction for all the crystals in the OOD test set (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(f)). The results for Wulff construction and final surface synthesizability are summarized in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(g). Despite a higher error in surface energies, surface synthesizability has a \u0026ldquo;Top-5\u0026rdquo; accuracy of 0.820 and \u0026ldquo;High\u0026rdquo; accuracy of 0.744. These results demonstrate that SurFF could deliver useful synthesizability information for unseen OOD crystals with significantly different properties. We elaborate on this observation in S4.7, where we explain how SurFF\u0026rsquo;s low variance assures that the relative magnitudes of the predicted surface energies within a crystal remain comparable to those of the true surface energies. Consequently, despite the higher MAE in surface energy predictions, the accuracy in predicting surface synthesizability remains reliably high. The single point accuracy of the trained MLFF could be found in S4.6.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003eValidation with Experimental Observations \u0026amp; Large-Scale Predictions\u003c/h2\u003e \u003cp\u003eThus far, we have demonstrated that SurFF aligns with DFT results, offering a DFT-level precision in predicting surface energy and exposure. To further validate its relevance and utility in guiding actual experimental catalyst design, it is crucial to examinate SurFF\u0026rsquo;s predictions against experimental results. For this purpose, we gathered data of experimentally characterized intermetallic crystals from both existing literature and our original experiments. As delineated in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e(a), we would confirm experimentally observed surfaces by both XRD-identified crystal structures and TEM-identified facets, which is currently the standard method for surface characterization in this field. For literature data, we screened over 10,000 research articles from four leading journals in the field of catalysis, utilizing a large language model (LLM) \u003csup\u003e\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u003c/sup\u003e. For original data, we conducted actual experiments to synthesize and characterize three intermetallics, namely ZnRh, ZnPd, and ZnPt (S5.3) \u003csup\u003e\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e\u003c/sup\u003e. Subsequently, we compared the surface exposures predicted by SurFF with the experimentally observed facets on the same crystal structures, as depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e(b) and S5.2. Remarkably, SurFF successfully predicted 73.1% of the experimentally observed facets, despite variations between experimental conditions and DFT-derived settings. This high rate of predictive success might be attributed to the fact that surface exposure is primarily influenced by the relative magnitudes of surface energies across different surfaces within crystal. Although the absolute values of surface energies may fluctuate under different environmental conditions, their relative values remain comparatively stable. Therefore, the predictions of surface exposure by SurFF also hold significant relevance for real-world experimental scenarios. Further details on the LLM screening and the collection of literature data are provided in S5.1.\u003c/p\u003e \u003cp\u003eGiven a good alignment with both experimental and computational results, we then applied SurFF to predict the surface exposure for a wide range of intermetallic crystals with catalytic functionality and known structures. The scope includes bimetallic and trimetallic crystals with a low energy-above-hull (less than 0.2\u0026nbsp;eV/atom) from a crystal structure database. This gave us more than 6,000 intermetallic crystals and 140 thousand unique intermetallic surfaces. All this predicted data would be available via table searching for community use. The prediction takes only 115 GPU hours in total for more than 6,000 crystals. More details about the workflow and results are provided in S6.1 and S6.2.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eFinetuning and Transferring\u003c/h3\u003e\n\u003cp\u003eFinally, we demonstrated the transferability of SurFF. Noticing that SurFF has a higher MAE in predicted surface energies in the unseen OOD test set because of different crystal properties, we used the OOD test set as an example to show that SurFF could be finetuned and transferred to other unseen datasets with minimal additional surface data.\u003c/p\u003e \u003cp\u003eAs shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e (a), we created a new OOD finetuning dataset by randomly selecting and calculating only one surface from each crystal in the OOD test set (S3.5). Using this additional dataset, we finetuned SurFF for the OOD test set. Given that the task requires predicting multiple surfaces of the same crystal, SurFF could learn essential force field information from a single surface relaxation and apply this knowledge to all other surfaces of the same crystal due to their similarities in composition and force field. This capability, combined with the underlying knowledge in SurFF\u0026rsquo;s backbone, allowed for significant improvements in prediction accuracy with just a small amount of additional data. SurFF\u0026rsquo;s prediction results after transferring are summarized in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e (b). The accuracy improved significantly by 45% in single point energy, 53% in single points force, 35% in surface energies, and 5.1% in Top-3 accuracy (S4.5).\u003c/p\u003e \u003cp\u003eThese results demonstrate that SurFF can be readily transferred to other unseen crystal materials with different properties using minimal data, showcasing its potential to extend to other crystal materials such as oxides, carbides, nitrides, or crystal materials in reaction environments.\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eIn this work, we developed SurFF, a universal model for fast and accurate prediction of surface exposure directly from cell structures across intermetallic crystal materials. By comparing both computational predictions and experimental observations from the literature, we validated its accuracy and applicability in real-world scenarios. Following this validation, we applied SurFF to predict the surface exposure for six thousand intermetallic crystals with catalytic functionality and known cell structures for community use. Lastly, we also demonstrated SurFF\u0026rsquo;s transferability to unseen dataset with different crystal properties, showing its potential to extend to all other crystal systems, including oxides \u003csup\u003e\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e\u003c/sup\u003e, nitrides \u003csup\u003e\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e\u003c/sup\u003e and carbides \u003csup\u003e\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e\u003c/sup\u003e. Despite SurFF\u0026rsquo;s high accuracy, we also acknowledge that the current dataset as well as model predictions do not yet consider various crystal preparation conditions, such as temperature and pressure \u003csup\u003e\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e\u003c/sup\u003e. A more comprehensive model could be prepared by finetuning with surface energy data under actual experimental conditions. The ability of SurFF to predict surface exposure rapidly and accurately at a large scale makes it a potent and robust tool for enhancing both computational and experimental approaches to catalyst design, marking a significant step toward large-scale models for catalyst discovery.\u003c/p\u003e "},{"header":"Methods","content":"\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003cdiv id=\"Sec12\" class=\"Section3\"\u003e \u003ch2\u003eSurface Energy Calculation\u003c/h2\u003e \u003cp\u003eThe typical slab approach for performing surface energy calculations requires the use of large supercells with high k-point density to ensure convergence, which makes such calculations computationally intensive. Here we adopted an efficient method which requires only one oriented unit cell (OUC) as bulk and one relatively thin slab calculation \u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e,\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e\u003c/sup\u003e. The calculated results of this method were validated with other literature values from both computation and experiment. We generated all required structures with PyMatgen package \u003csup\u003e\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e\u003c/sup\u003e. The surface energy can be calculated from the total energy of the crystal slab and crystal bulk:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:{E}_{ijk}^{surf}=\\frac{{E}_{ijk}^{slab}-N\\times\\:{E}_{ijk}^{bulk,OUC}}{2{A}^{slab}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{E}_{ijk}^{surf}\\)\u003c/span\u003e\u003c/span\u003e is the surface energy of the surface with miller index \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:(i,j,k)\\)\u003c/span\u003e\u003c/span\u003e; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{E}_{ijk}^{slab}\\)\u003c/span\u003e\u003c/span\u003e the total energy of the slab model with miller index \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:(i,j,k)\\)\u003c/span\u003e\u003c/span\u003e; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{E}_{ijk}^{bulk,OUC}\\)\u003c/span\u003e\u003c/span\u003e the energy per atom of the bulk oriented unit cell (OUC) with miller index \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:(i,j,k)\\)\u003c/span\u003e\u003c/span\u003e; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:N\\)\u003c/span\u003e\u003c/span\u003e the number of atoms in the slab model; and, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{A}^{slab}\\)\u003c/span\u003e\u003c/span\u003e the cross-section area of the slab model.\u003c/p\u003e \u003cp\u003eThis efficient surface energy calculation method was validated on elemental crystals \u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e,\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e\u003c/sup\u003e, we also performed an additional convergence check of this method on intermetallic crystals to ensure this accuracy of our results (S3.2).\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003eDFT method\u003c/h2\u003e \u003cp\u003eAll DFT energy calculations were performed using the Vienna Ab initio Simulation Package (VASP) within the projector augmented wave (PAW) approach. The exchange-correlation effects were modeled using the Perdew-Berke-Ernzerhof (PBE) generalized gradient approximation (GGA) functional, and all calculations were spin-polarized with a plane wave cutoff energy of 520 eV. The Methfessel Paxton method was employed for smearing, the blocked Davidson iteration scheme for electron minimization and the conjugated gradient algorithm for ion updates. Convergence was for energy, and atomic forces were set to be 10\u003csup\u003e\u0026minus;\u0026thinsp;6\u003c/sup\u003e eV and 0.02 eV/\u0026Aring;, respectively. Γ-centered k-point meshes of 35/a\u0026times;35/b\u0026times;35/c and 35/a\u0026times;35/b\u0026times;1 were used for OUC and slab calculations respectively, with non-integer values rounded up to the nearest integer.\u003c/p\u003e \u003cp\u003eTo ensure the accuracy of the calculation results obtained from the PBE GGA, we also calculated a batch of results using R2SCAN meta-GGA. The comparison results are shown in (S2.3).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003eWulff Construction\u003c/h2\u003e \u003cp\u003eWulff Construction estimates the surface area fraction of each facet on a catalyst nanoparticle based on surface energies and surface orientations \u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e. It is a geometric method used in the study of crystal growth and equilibrium crystal shapes developed by the German mathematician Gustav Wulff based on the idea that crystals grow in a way that minimizes their surface energy.\u003c/p\u003e \u003cp\u003eGiven direction-dependent surface energy information, including facet miller index and associated surface energy, the Wulff construction provides the lowest energy crystal shape by minimizing the surface energy of the crystal \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varDelta\\:G\\)\u003c/span\u003e\u003c/span\u003e defined as:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:\\varDelta\\:\\varvec{G}=\\sum\\:{\\varvec{E}}_{\\varvec{i}\\varvec{j}\\varvec{k}}^{\\varvec{s}\\varvec{u}\\varvec{r}\\varvec{f}}{\\varvec{S}}_{\\varvec{i}\\varvec{j}\\varvec{k}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{E}}_{\\varvec{i}\\varvec{j}\\varvec{k}}^{\\varvec{s}\\varvec{u}\\varvec{r}\\varvec{f}}\\)\u003c/span\u003e\u003c/span\u003e is the surface energy of the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\left(i,j,k\\right)\\)\u003c/span\u003e\u003c/span\u003e surface, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{S}}_{\\varvec{i}\\varvec{j}\\varvec{k}}\\)\u003c/span\u003e\u003c/span\u003e is the surface area of the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\left(i,j,k\\right)\\)\u003c/span\u003e\u003c/span\u003e surface. The Wulff shape can then find the area fraction of each facet.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003eActive learning\u003c/h2\u003e \u003cp\u003eGiven an enormous design space of 284,134 crystal surfaces, a comprehensive dataset that contains all necessary information of the entire design space is required for the MLFF model to learn the underlying correlations and give accurate predictions. It should be noted that calculating all 284,134 crystal surfaces could be inefficient to construct a database for model development. To minimize the computational cost and increase data efficiency, active learning strategies can be adopted to add most informative data to the database iteratively and stop calculations when desired model accuracy is achieved \u003csup\u003e\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e,\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eIn this work, we first use diversity sampling to generate 2,000 surface energy data, 1,000 from bimetallic surfaces and 1,000 from trimetallic surfaces, for constructing an AL test set. At each iteration, a probabilistic ML model of ensembles would be trained and updated on existing dataset \u003csup\u003e\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e,\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e\u003c/sup\u003e. The probabilistic model could take surface structures as input and predict their surface energies and uncertainties directly on current dataset and uncalculated surfaces in the design space (S3.3). After the model is updated, the model accuracy on the AL test set will be evaluated and recorded. To generate the next batch of data, the model uncertainties on the surfaces of the remaining design space would be calculated, and 1,000 surfaces would be chosen based on uncertainty and diversity sampling. Uncertainty sampling allows batches to have most informative surfaces with high uncertainties where model trained on current dataset does not have enough information. Diversity sampling avoids data unbalance issues by limiting the number of surfaces from the same compositional systems to at most three in each batch. The sampled batch would be sent for DFT calculations and then added to the dataset. Any failed calculations would be discarded. Since both bimetallic and trimetallic surfaces exist in the design space, we generate bimetallic data and test on the bimetallic data in the AL test set first, and then start to generate trimetallic data and test on the entire active learning test set. The final dataset is in in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e and S3.5.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec16\" class=\"Section2\"\u003e \u003ch2\u003eMLFF model architecture\u003c/h2\u003e \u003cp\u003eA three-dimensional equivariant graph convolutional neural network (GNN), EquiformerV2 \u003csup\u003e22,30\u003c/sup\u003e, is used as the model architecture for the MLFF in this work. EquiformerV2 is currently the state-of-the-art model for many quantum chemistry simulation datasets. It adapts eSCN \u003csup\u003e\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e\u003c/sup\u003e convolutions and Euclidean neural networks (e3nn) \u003csup\u003e\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e\u003c/sup\u003e to efficiently incorporate higher-degree tensors and 3-dimensional vectors to better model interatomic interactions.\u003c/p\u003e \u003cp\u003eSimilar to other GNNs for atomic modelling such as GemNet \u003csup\u003e\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e\u003c/sup\u003e, Graphormer \u003csup\u003e\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e\u003c/sup\u003e, SCN \u003csup\u003e\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e\u003c/sup\u003e and eSCN \u003csup\u003e\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e\u003c/sup\u003e, EquiformerV2 takes the 3D coordinates of a target structure as inputs and predicts its properties, which are forces and energies in this case. Each structure is first converted into graph representation \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:G=\\left(V,E\\right)\\)\u003c/span\u003e\u003c/span\u003e, where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:G\\)\u003c/span\u003e\u003c/span\u003e is the graph data, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:V\\)\u003c/span\u003e\u003c/span\u003e is the node set that contains atom type information, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:E\\)\u003c/span\u003e\u003c/span\u003e is the edge set that contains bond lengths and directions of all neighboring atoms. The atom features at each node are first embedded in an embedding layer. A few layers of eSCN convolutions and equivariant graph attention then iteratively update the atoms features based on their corresponding neighboring environments. Finally, the target properties, forces, and energies, will be predicted by the output heads based on the final atom features of each node. More details of model architecture are in S4.2.\u003c/p\u003e \u003cp\u003eThe model is trained in a supervised manner by the loss between predicted properties and ground true properties given in the training set. Optimization on the main model hyperparameters is conducted to maximize model performance. During the evaluation stage, the trained model would be used as MLFF for surface structure relaxation. Similar to a conventional force field model, it predicts the forces on each atom and the total energy of a structure. A relaxation algorithm moves atoms downwards the predicted potential energy hill and sends a new structure to the MLFF for prediction iteratively until the maximum force is below a certain threshold. More details of model training and evaluation are in S4.4.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec17\" class=\"Section2\"\u003e \u003ch2\u003eModel transferring\u003c/h2\u003e \u003cp\u003eThe trained EquiformerV2 model as an MLFF can finetuned on additional data to improve performance on the OOD data (e.g., unseen crystal compositions). After the finetuning dataset is generated (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e), we finetuned the trained model by freezing the low-level layers and training with a small learning rate. Experimentations on the finetuning performance with different unfrozen output heads and convolutional layers were also performed to obtain the optimal finetuning configuration. The finetuned model was then tested on the same OOD test set to compare with the base model without finetuning. More details of model transferring are in S4.5.\u003c/p\u003e \u003c/div\u003e "},{"header":"Declarations","content":"\u003cdiv id=\"Sec18\" class=\"Section2\"\u003e \u003ch2\u003eData and Codes availability\u003c/h2\u003e \u003cp\u003eAll data and codes in this work could be retrieved from S1.1 or GitHub repository \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://github.com/Long1Corn/SurFF\u003c/span\u003e\u003cspan address=\"https://github.com/Long1Corn/SurFF\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e, where a step-by-step guide to use SurFF for prediction and a web UI are also provided.\u003c/p\u003e \u003c/div\u003e\n\u003ch2\u003eAcknowledgements\u003c/h2\u003e \u003cp\u003eThis work is supported by the National Key R\u0026amp;D Program of China (No. 2022ZD0117501) and Tsinghua University Initiative Scientific Research Program.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eN\u0026oslash;rskov, J. 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(2021).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYing, C. \u003cem\u003eet al.\u003c/em\u003e Do Transformers Really Perform Badly for Graph Representation? in \u003cem\u003eThe Thirty-Fifth Conference on Neural Information Processing Systems.\u003c/em\u003e (2021).\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"nature-portfolio","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Nature Portfolio","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"ejp","reportingPortfolio":"","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-4863775/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4863775/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eCatalysts are crucial in industrial processes, significantly enhancing reaction efficiency. With approximately 90% of industrial reactions occurring on surfaces, the role of heterogeneous catalysts is paramount. Accurate surface exposure prediction is vital for heterogeneous catalyst design but is hindered by the high costs of experimental and computational methods. Here, we introduce a universal force field-based model for predicting surface exposure and synthesizability (SurFF) across intermetallic crystals, essential materials for heterogeneous catalysts. We created a comprehensive intermetallic surface database using a data-efficient active learning method and high-throughput density functional theory (DFT) calculations, encompassing 12,553 unique surfaces and 344,200 single points. SurFF achieves DFT-level precision with a prediction error of 3.0 meV/\u0026Aring;\u0026sup2; and enables large-scale surface exposure prediction, an impractical task for DFT methods, through a 10\u003csup\u003e5\u003c/sup\u003e-fold acceleration. Validation against computational and experimental data both shows strong alignment. We applied SurFF for large-scale predictions on over 6,000 intermetallic crystals, providing valuable data for the community. Demonstrating transferability to diverse crystal properties, SurFF is a robust tool for advancing catalyst design, representing a significant step toward large-scale catalyst discovery models.\u003c/p\u003e","manuscriptTitle":"SurFF: Universal Model for Surface Exposure and Synthesizability Across Intermetallic Crystals","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-01-07 08:08:35","doi":"10.21203/rs.3.rs-4863775/v1","editorialEvents":[],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"nature-computational-science","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"natcomputsci","sideBox":"Learn more about [Nature Computational Science](http://www.nature.com/natcomputsci/)","snPcode":"","submissionUrl":"","title":"Nature Computational Science","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Nature Research","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"b183b294-0f05-4a32-961d-b50398c2e14b","owner":[],"postedDate":"January 7th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-09-12T06:46:28+00:00","versionOfRecord":{"articleIdentity":"rs-4863775","link":"https://doi.org/10.1038/s43588-025-00839-0","journal":{"identity":"nature-computational-science","isVorOnly":false,"title":"Nature Computational Science"},"publishedOn":"2025-09-09 04:00:00","publishedOnDateReadable":"September 9th, 2025"},"versionCreatedAt":"2025-01-07 08:08:35","video":"","vorDoi":"10.1038/s43588-025-00839-0","vorDoiUrl":"https://doi.org/10.1038/s43588-025-00839-0","workflowStages":[]},"version":"v1","identity":"rs-4863775","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4863775","identity":"rs-4863775","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}