AI-Based Multivariate Analysis of Environmental Radiation Dose Trends in Taiwan

AI-Based Multivariate Analysis of Environmental Radiation Dose Trends in Taiwan | 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 Research Article AI-Based Multivariate Analysis of Environmental Radiation Dose Trends in Taiwan Chuan-Pin Lee, Wei-Hsiang Tseng, Yu-Hung Wang, Yu-Cheng Tsai, and 5 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8736433/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 Nuclear energy is considered a key low-carbon energy source for sustainable development; however, the potential risks of nuclear accidents necessitate effective environmental radiation dose monitoring. This study integrates radiation dose rate and precipitation data from 63 monitoring stations across Taiwan, incorporating spatial relationships among stations. A Variational Autoencoder architecture was employed to predict site-specific radiation dose rates using approximately 300 consecutive days of time-series data from 2024. Based on radiation observations from the preceding 10 minutes, the model achieved a mean absolute error below 0.0005 (µSv/h) for 7-minute-ahead predictions. The results demonstrate strong predictive performance, while also indicating sensitivity to low radiation thresholds, which may induce periodic oscillations and increase prediction errors. Environmental Radiation Dose Artificial intelligence Variational Autoencoder Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Introduction With the official decommissioning of Taiwan’s last nuclear power plant in May 2025, the country has formally entered a nuclear-free era. Nevertheless, nuclear safety remains a critical issue of public concern. To enhance information transparency and ensure the public’s right to be informed about radiological safety, the Taiwan Nuclear Safety Commission (NSC) has established a nationwide Environmental Radiation Monitoring Network [ 1 , 2 ]. Each monitoring station is equipped with a fixed gamma dose-rate detector, and real-time measurement data are continuously transmitted and periodically uploaded to open-access platforms. Based on the temporal variation of radiation dose rates at different locations, the NSC regularly publishes the Monthly Automatic Monitoring Report on Radiation Safety Alerts [ 3 ], which serves as an important reference for policy evaluation and risk management. In addition, for areas of heightened concern—such as nuclear power plants, radioactive waste storage facilities, and their surrounding regions [ 4 , 5 ]—the NSC has implemented sampling and analytical mechanisms and provides historical monitoring data for public access and academic use [ 6 ]. To further improve accessibility and interpretability, visualization techniques have been adopted through the development of an environmental radiation map platform [ 1 ]. This platform integrates data from the air quality monitoring network and marine data systems, thereby establishing a cross-disciplinary, multi-parameter environmental monitoring framework [ 7 , 8 ]. However, rapid technological advances, including improvements in detector resolution and the increasing number of monitored parameters, have significantly increased data volume and complexity. In practice, challenges such as data loss, instrument replacement, and inconsistent sampling frequencies frequently arise, posing substantial difficulties for future data management and analytical applications. In recent years, advances in artificial intelligence (AI) technologies have demonstrated considerable potential for processing and predicting outcomes from large-scale, multi-parameter datasets. By extracting key features from vast amounts of unstructured data, AI-based approaches can effectively identify critical information and support anomaly detection and early warning decision-making. Currently, nuclear safety–related institutions have made environmental dose-rate information publicly available, including real-time and historical dose rates, station GPS locations, and monitoring metadata. These open datasets provide a feasible foundation for the introduction of AI-driven intelligent monitoring methodologies. Against this background, the present study aims to integrate big data processing, data cleansing, and deep learning techniques to develop an intelligent radiation dose-rate data processing and prediction system. Given that radiation dose-rate variations are influenced by multiple environmental factors and are often closely associated with meteorological conditions—such as precipitation, wind speed, wind direction, atmospheric pressure, and aerosol concentration—this study further integrates heterogeneous data sources, including the NSC environmental radiation map and the national air quality monitoring network [ 1 , 2 , 6 – 8 ]. By incorporating multiple environmental variables, the feature space of the predictive model is expanded to enhance its forecasting capability. To address discrepancies in observation scales and sampling frequencies among different data sources, multivariate analytical methods are employed for variable screening and feature selection. Correlation analysis is subsequently conducted to evaluate the direction and magnitude of the influence of each environmental parameter on radiation dose rates. Through these approaches, this study not only improves the accuracy and stability of radiation dose-rate prediction models but also deepens the understanding of the underlying mechanisms governing dose-rate variability. Furthermore, it strengthens early warning capabilities and provides a more robust scientific basis for emergency response and decision-making during anomalous radiological events. Figure 1 illustrates a simplified schematic of the environmental radiation monitoring system. The system consists of multiple in situ radiation monitoring stations, each equipped with a radiation detector. Radiation dose-rate data collected from various environments—including urban areas, natural background radiation zones, and key monitoring sites near nuclear facilities—are transmitted wirelessly to a central monitoring center for real-time processing and storage. Through centralized management, continuous surveillance of environmental radiation dose rates is achieved, enabling timely decision support in the event of radiological anomalies. Literature Review With the increasing global emphasis on sustainable development and green energy transition, nuclear safety and environmental radiation monitoring have become critical research priorities. In the context of natural radiation exposure, long-term observations from Canada’s Fixed Point Surveillance (FPS) network indicate that population annual effective doses are dominated by cosmic radiation and naturally occurring terrestrial radionuclides, with approximately 89% of exposure occurring indoors, highlighting the strong influence of natural background radiation on everyday exposure [ 9 ]. China has implemented a hierarchical monitoring framework for research reactors, although further technological upgrades and institutional reinforcement remain necessary [ 10 ]. The National Academy of Sciences of Ukraine has developed advanced radiation monitoring systems, including real-time airborne platforms, solid-state detectors, and portable workstations, enhancing spatial flexibility and enabling rapid post-accident risk assessment [ 11 ]. Following the Fukushima Daiichi accident, global efforts have increasingly focused on mobile radiation detection systems integrating sensor networks and artificial intelligence, such as unmanned platforms equipped with silicon photomultipliers for radioactive material search, border inspection, and nuclear facility security monitoring [ 12 ]. Subsequent studies further demonstrated that plutonium (Pu) contamination from the Fukushima accident exhibits pronounced regional heterogeneity and that isotopic ratios can serve as reliable source fingerprints for risk mapping and geochemical baseline construction [ 13 ]. Atmospheric radiation processes represent a major source of uncertainty in climate system modeling. The complex interactions among clouds, aerosols, and radiation are particularly challenging in remote regions such as the Southern Ocean, where excessive supercooled liquid water and strong small-scale variability substantially affect radiative transfer [ 14 ]. Low-level clouds have been identified as a dominant contributor to shortwave radiation biases, motivating the use of high-resolution observations and advanced radiative parameterizations. At the global scale, ISCCP-H cloud optical thickness and cloud-top pressure datasets support cloud classification and weather state analysis; however, current climate models, including CMIP6, systematically underestimate mid- and high-level clouds and shallow cumulus clouds, resulting in weakened shortwave radiative cooling [ 15 ]. Observations from the Yeonggwang region in South Korea further reveal a significant association between heavy precipitation events and elevated environmental radiation dose rates, likely driven by rain-induced radionuclide washout and cloud microphysical changes [ 16 ]. These radiative and energetic imbalances are closely linked to large-scale climate variability, including polar processes and ENSO, underscoring the need for integrated observational, modeling, and AI-based approaches [ 17 ]. The rapid growth and high dimensionality of environmental monitoring data have established artificial intelligence (AI) as a key tool for data analysis and prediction. In nuclear applications, AI techniques have been widely adopted for system safety monitoring, operational support, and fault diagnosis. Hybrid supervised and reinforcement learning approaches have demonstrated improved operational efficiency in nuclear power plant maintenance and support integrated Nuclear Power Plant–Human–Cyber–Physical Systems (NPPHCPS) [ 18 , 19 ]. However, stringent safety requirements and limited data availability pose challenges related to model interpretability and reliability, leading to increasing interest in hybrid frameworks that incorporate expert knowledge and explainable AI (XAI) [ 18 ]. Bayesian methods, including Markov Chain Monte Carlo (MCMC), have also been integrated to quantify uncertainty and enhance decision robustness [ 20 ]. In climate science, the long-term rise in global surface temperature since the nineteenth century is widely recognized as a key indicator of anthropogenic influence and is often illustrated by the “hockey stick” curve. Statistical approaches complement physics-based models through trend estimation, change-point detection, and uncertainty quantification. Recent studies demonstrate that the apparent post-1998 “global warming hiatus” lacks robust statistical support and largely reflects data selection and uncertainty effects [ 21 ]. Machine learning techniques have also been increasingly applied to weather and climate prediction, achieving strong performance in short-term forecasting but remaining limited for medium- and long-term prediction due to system complexity and data constraints. This highlights the need for unified modeling frameworks across multiple temporal scales [ 22 ]. Machine learning has further been applied to source term inversion in nuclear accident scenarios, where rapid estimation of radionuclide release rates is critical for emergency response. LSTM-based inversion models reduce dependence on prior assumptions while maintaining stable performance across multiple radionuclides (e.g., Kr-88, Te-132, and I-131) and varying meteorological conditions [ 23 ]. Subsequent studies confirm their adaptability under more complex scenarios involving Kr-88, Sr-91, Te-132, and I-131, identifying gamma dose rate as a key factor influencing prediction accuracy [ 24 ]. Machine learning combined with Bayesian optimization techniques, such as Optuna, has also demonstrated robust performance under uncertain release durations and meteorological perturbations [ 25 ]. In broader environmental science applications, AI and statistical techniques have been increasingly integrated into climate change monitoring, water resource management, and pollution risk assessment [ 26 ]. Representative examples include groundwater quality prediction using RNN–GIS integration [ 27 ], crude oil price forecasting using multivariate support vector regression [ 28 ], hydraulic structure safety monitoring via Random Forest and SVM-based scour prediction [ 29 ], and real-time precipitation monitoring enabled by high-speed imaging and image processing techniques [ 30 ]. Multivariate analyses of atmospheric radionuclide Be-7 further elucidate its interactions with precipitation processes and atmospheric dynamics [ 31 ]. Advanced AI architectures for time-series analysis, including Transformers and graph neural networks (GNNs), have been widely applied to traffic flow, meteorology, healthcare, air quality prediction, and anomaly detection [ 32 – 37 ]. Spatio-temporal graph neural networks (STGNNs) explicitly model spatial and temporal dependencies and demonstrate strong predictive performance in sensor networks [ 38 ]. Transformer-based frameworks such as STTN enable dynamic attention and long-range dependency modeling for long-term forecasting [ 39 , 40 ], while models such as AirFormer improve prediction accuracy and uncertainty representation through staged spatio-temporal modeling [ 41 ]. These developments highlight the growing potential of AI-driven time-series modeling for complex environmental and safety-critical applications. Theory and Methods Radiation Dose Rate To evaluate the radiation intensity in a specific region over a given time period, we use the "Radiation Dose Rate" as the basis for assessment. The Radiation Dose Rate is defined as the amount of radiation received by the human body or measured in the environment within a unit of time, expressed in microsieverts per hour (µSv/h). In typical environmental conditions, background radiation usually ranges from approximately 0.02 to 0.2 µSv/h, though this range can vary depending on regional geological factors and altitude. Medical radiation dose rates are generally below 0.5 µSv/h, while the International Commission on Radiological Protection (ICRP) recommends a public annual dose limit of no more than 1 millisievert (1 mSv/a), which translates to an hourly dose rate of 0.1 µSv/h. Dataset and Detector In this study, we utilize the MERM-PE-HDB model plastic scintillation detector manufactured by SERVCOMPUTING INC. (Kaohsiung City, Taiwan). This instrument is designed for continuous all-weather monitoring, measuring the gamma radiation dose rate in the environment once per minute and outputting results in micro-Sieverts per hour (µSv/h). Such a design effectively reflects the real-time variations and sensitivity of environmental radiation. The recorded data are stored on servers at the Radiation Monitoring Center (RMC), containing historical dose rates, time information, and rainfall data from 63 monitoring stations across Taiwan. These datasets are then integrated to form the primary dataset for this research. Model Design In this study, we integrate rainfall data and radiation dose rates from various locations, and perform both spatial and temporal correlation analyses based on the structure of the Airformer model. The results from these analyses are then fed into the model, and the outputs are compared with our actual measurements. The model, which is inspired by Airformer, utilizes Variational Autoencoders (VAE) as its core framework and incorporates a Multi-Head Attention Mechanism [ 41 ]. The VAE allows for the reconstruction of inputs at each time point, which enhances the model's learning performance, as illustrated in Fig. 2 . In the Deterministic Stage of the AirFormer model, the architecture incorporates two major attention modules: a Spatial Attention module and a Temporal Attention module. These modules are designed to learn spatial correlations among monitoring stations and temporal dependencies within individual stations, respectively. When the data are fed into the model, the historical time-series observations X 1:T are first mapped into a feature space through a Multi-Layer Perceptron (MLP). The transformed features are then passed into multiple stacked AirFormer layers for spatiotemporal feature learning. Within this framework, the Spatial Attention module employs a linear-complexity multi-head attention mechanism to efficiently capture spatial interactions among stations, while the Temporal Attention module focuses on modeling temporal dependencies at each individual station. To prevent the model from accessing future information during training and thereby compromising prediction accuracy, a masking mechanism is introduced in the temporal attention to block future time steps. In the spatial attention module, this study designs a spatial relationship matrix for 63 radiation monitoring stations across Taiwan. Using a target-region partitioning strategy, the surrounding area of each station is divided into multiple regions based on predefined radii and quadrants. The distribution and density of neighboring stations within these regions are then computed to quantify the relative geographical relationships among stations. Through the spatial multi-head attention mechanism, the model is able to learn and enhance spatial dependencies across different monitoring stations. In contrast, the temporal attention module performs time-series learning based on historical observations from a single station. To avoid information leakage during training, a masking design is incorporated into the attention mechanism, ensuring that predictions are made solely based on current and past observations. This design enhances the robustness and stability of the model in real-world deployment scenarios. The overall model is built upon a Variational Autoencoder (VAE)-based core architecture, which enables effective feature extraction and dimensionality reduction while preserving continuity and generative capacity in the latent space. This property is advantageous for downstream tasks such as data reconstruction, forecasting, and data imputation under incomplete observation scenarios, as illustrated in Fig. 3 . The overall architecture draws inspiration from the concept of latent space in VAEs. In a standard VAE, the latent space is learned by modeling the probability distribution of the input data—typically assuming a Gaussian distribution—and introducing stochastic noise, which endows the model with generative capabilities. However, for the radiation dose rate time-series forecasting task considered in this study, the data inherently exhibit strong fluctuations and high variability. Introducing additional stochastic noise, as in conventional VAEs, may increase the difficulty of model convergence and adversely affect prediction stability. Therefore, this study proposes a deterministic modification to the VAE architecture by setting the noise term to zero. As a result, the latent space transitions from a probabilistic distribution to a high-dimensional deterministic feature representation. This adjustment allows the model to focus on precise reconstruction and feature extraction of the input data during training, rather than distributional generation. Through this strategy, the proposed approach aims to retain the deep feature extraction capability of the VAE framework while improving prediction stability and accuracy under high-variability time-series conditions. Integration of Spatial Features with Taiwan's Radiation Monitoring Stations In the AirFormer architecture, spatial information is utilized to assist the model in learning the spatial dependencies between the 63 radiation monitoring stations across Taiwan. To enable the model to capture finer spatial features, we have designed two matrices to support the learning process. One matrix quantifies the detailed positional relationships between stations, while the other is used solely to indicate whether other stations are present in the vicinity of each station. Currently, Taiwan has 63 radiation monitoring stations, which are distributed across various regions, based on the areas of monitoring focus. Each station has a clear GPS location. To transform this spatial information into features that can be learned by the model, we use each station i as the center and draw concentric circles with radii of 5 km and 10 km, respectively. These circles are then divided into four quadrants both horizontally and vertically, resulting in a total of 9 regions (with the center region being 1, and the surrounding regions extending outward in quadrant order up to region 9), forming a target-like region partitioning. This division effectively reflects the geographical relative positioning distribution of other stations around each station. One of the matrices is responsible for recording the number of neighboring stations within each region. Specifically, when the i-th station is considered the center, if other stations appear in a given region, the region is weighted based on the number of stations it contains: if one station appears in the region, it is marked as 1; if two stations appear, each receives a weight of 0.5; if three stations appear, each receives a weight of 1/3, and so on. This design ensures that the total weight in each region sums to 1 (the sum of the values in the red rectangle of Fig. 4 must equal 1), thus avoiding bias due to station density differences. If no other stations are present in a given region, its weight is set to 0. Once all stations have been processed, a 3D matrix of size 63×63×9 is generated, fully describing the detailed spatial relationships between the monitoring stations across Taiwan, as shown in Fig. 4 . where i and 𝑘 represent station IDs, and j represents the region within the concentric circles. Another matrix is a simplified version, primarily used in the model’s attention mechanism as a mask. During the training process, the model reads both past and future data. However, in actual prediction scenarios, future information is not accessible, so a mask is necessary to block future time steps' information, preventing the model from learning future-known data during training, which could distort performance during prediction. The spatial mask further restricts the model to focus only on spatial location information within a reasonable range in the attention mechanism. The construction of this matrix is as follows: for the i-th station, if any station appears in a given region, that region is labeled as 1; if no stations are present in the region, it is labeled as 0, without further subdividing the number of stations. Therefore, this matrix is a 63 × 9 two-dimensional matrix, reflecting only the presence or absence of neighboring stations in the surrounding area of each station, as shown in Fig. 4 . Through the design of these two matrices, one provides the model with complete spatial structural information to help the model learn the spatial dependencies between stations. The other, using the mask, controls the model’s learning scope, preventing the model from accessing future information that should not be available, thereby improving the model’s prediction stability and accuracy in real-world application scenarios. Integration of Temporal Features into the Model In addition to utilizing spatial features to help the model learn the interdependencies between stations, learning the temporal features of the historical data from individual stations is also an essential part of the model's predictive performance. Therefore, in this study, we specifically integrate time series information, enabling the model to learn the inherent temporal dynamics from the historical changes in radiation dose rates at each station. In the model design, the Window Size represents the length of historical time steps provided as input during each training and prediction phase. For example, the model may utilize historical observations from the past 24 or 48 hours as input features. In this study, window sizes corresponding to 10-minute to 60-minute intervals are adopted as experimental parameters. The Blocks parameter refers to the number of stacked Transformer blocks in the model, where each block employs a multi-head self-attention mechanism to capture temporal dependencies within the input sequence. Here, b denotes the index of the current Transformer block. Although the self-attention mechanism in Transformers theoretically allows each time step to attend to all positions within the input sequence, such unrestricted attention is inappropriate for time-series regression tasks, including radiation dose rate prediction. Specifically, allowing the model to access future time steps during training would lead to information leakage and result in overly optimistic performance estimates. To prevent this issue, a temporal masking mechanism is applied during the attention computation. This mechanism restricts each time step to attend only to the current and previous time steps, while completely blocking access to future information. As a result, the model generates predictions based solely on information that would be available in real-world forecasting scenarios. By integrating both spatial and temporal features, the proposed model is capable of simultaneously learning spatial dependencies among monitoring stations and temporal evolution patterns within individual stations. This joint modeling strategy enhances the model’s ability to capture complex radiation dose rate dynamics and improves prediction accuracy. Normalization Adjustment In the original model, Z-score normalization was applied to the dataset. The basic assumption of the Z-score is that the overall data approximately follows a Gaussian distribution. By calculating the deviation of each value from the mean and expressing it in terms of the standard deviation, the data with different scales are transformed to a common standard. After Z-score normalization, the data’s mean is shifted to 0, and the standard deviation becomes 1. The transformed values are centered around 0 and symmetrically distributed in the shape of a Gaussian distribution. Since the values in our dataset oscillate around 0, after applying Z-score normalization, the model might treat values less than 0 as noise. This could lead to better prediction performance for values greater than the mean, while values below the mean are processed as noise. As a result, the predictions may exhibit periodic oscillations. To address this issue, we adjusted the Z-score process by adding the maximum value from the dataset to all values. For example, if the radiation dose rate at the Aodi station is 0.04, and the maximum radiation dose rate in the dataset is 0.1 at Alishan, then after adjustment, the radiation dose rate at the Aodi station becomes 0.14, and the value at Alishan becomes 0.2. The following is the adjusted Z-score formula: $$\:\text{z}=\:\frac{\text{x}+\underset{\text{n}}{\text{max}}{\text{x}}_{\text{i}}-{\mu\:}}{{\sigma\:}}=\frac{\text{x}-{\mu\:}}{{\sigma\:}}+\frac{\underset{\text{n}}{\text{max}}{\text{x}}_{\text{i}}}{{\sigma\:}}$$ 1 Data Flow and Preprocessing In this study, the collected multi-dimensional data from various radiation monitoring stations (including radiation dose rates, timestamps, and the geographical locations of the stations) were first aggregated, along with external meteorological factors (primarily rainfall data) as auxiliary features. Through the preprocessing workflow, missing data, outlier correction, and format standardization were performed for each data type, ultimately converting the data into an input format suitable for heterogeneous data analysis and predictive modeling. For the prediction task, the model inputs include historical radiation dose rates, time-related information, meteorological factors, and spatial correlation features calculated based on the geographical locations of the monitoring stations. In the heterogeneous data analysis task, preprocessed time-series meteorological data and radiation monitoring data were used for statistical analysis and feature exploration to further investigate the potential impact mechanisms of environmental factors on the variations in radiation dose rates, as shown in Fig. 5 . The experimental dataset consists of background radiation dose rate measurements collected by the Radiation Detection Center from radiation monitoring stations distributed across Taiwan. The data cover the period from 00:00 on January 1, 2024, to 23:59 on December 31, 2024, with a temporal resolution of one minute. The radiation dose rate is measured in microsieverts per hour (µSv/h). To ensure consistency in data scale across different datasets, data preprocessing was conducted prior to model training, including the removal of anomalous values, handling of missing data, and data imputation. Using the full-year dataset from January to December 2024 (2024/01/01 00:00 to 2024/12/31 23:59) as an example, stations with missing measurements during certain time intervals—presumably due to instrument malfunction or equipment replacement—were excluded for those periods. The remaining data were then split into training (2024/1/1 00:00 ~ 2024/10/17 07:35), validation (2024/10/17 07:36–2024/11/23 22:43), and testing sets (2024/11/23 22:44–2024/12/31 23:59) according to an 80% / 10% / 10% ratio. After partitioning the data into three subsets, the datasets are fed into the model in a stage-wise manner. The input to the model is structured as a three-dimensional tensor with dimensions representing the time length, the number of monitoring stations, and the feature channels, which include radiation dose rate, rainfall and temporal information. Taking the training set as an example, each sample has a dimensionality of 10 × 63 × (1 + 1 + 4) When the samples are constructed without overlapping time windows, a total of 40,450 samples can be obtained. In this study, overlapping sliding windows are adopted to improve data utilization, resulting in 57,785 samples, each with the same dimensionality of 10 × 63 × (1 + 1 + 4) After the aforementioned preprocessing steps, the data are further organized to match the input requirements of the proposed model. A batch dimension is appended to the front of each data sample, enabling the model to process multiple samples simultaneously during each training iteration and thereby improving learning efficiency. The resulting data format is (batch size, time length, number of stations, number of features), specifically 16×10×63×(1 + 1+14). The feature dimension consists of background radiation dose rate (1 dimension), rainfall data (1 dimension), and temporal information, which is transformed into a 14-dimensional representation through an embedding mechanism. This embedding design allows temporal features to attain compatible dimensionality after linear transformations within the model, facilitating effective extraction of temporal correlations. The model outputs comprise three main components. First, the model produces predictions for the target variable at the current time step. Second, it reconstructs the input data, enabling comparison between the reconstructed outputs and the original inputs to evaluate the model’s reconstruction capability. Third, the model directly computes the KL loss of the latent variables during training. The data types corresponding to each output are illustrated in Fig. 6 . Experimental Results and Analysis Experimental Environment The model development and training in this study were conducted on a hardware and software environment equipped with sufficient computational resources. The system operated on Windows 10, utilizing an Intel® Core™ i7-7700 processor and an NVIDIA GeForce RTX 4070 GPU as the primary computation cores, accompanied by 20 GB of RAM to ensure stable performance during model training and data processing. On the software side, Python 3.8.18 was employed as the main programming language, and PyTorch 2.2.1 served as the deep learning framework for implementing the model architecture and constructing the training pipeline. For deep learning computations, NVIDIA CUDA 12.1 was integrated to fully leverage hardware acceleration, enhancing the efficiency of large-scale data training and inference. The overall computing platform configuration is summarized in Table 1 . Table 1 Software and Hardware Setup for Experiments Operating System Windows 10 CPU Intel® Core™ i7-7700 GPU NVIDIA GeForce RTX 4070 Memory 20.0 GB RAM Programming Language: PYTHON 3.8.18 Deep Learning Framework CUDA 12.1 Torch 2.2.1 Model Prediction This chapter employs data collected from January to October 2024 as the primary experimental dataset, with the objective of validating whether the proposed model architecture can effectively enhance prediction stability and accuracy. In addition, the impacts of key model components and parameter configurations on predictive performance are systematically analyzed. To quantitatively evaluate the prediction performance of the proposed model, the Mean Absolute Error (MAE) is adopted as the primary evaluation metric, as it provides an intuitive and robust measure of the average magnitude of prediction errors without being overly sensitive to outliers. $$\:\text{M}\text{A}\text{E}=\:\frac{1}{N}{\sum\:}_{i=1}^{N}\left|\widehat{{y}_{i}}-{y}_{i}\right|$$ 2 Prior to model training, the statistical characteristics of the entire dataset are computed. The dataset exhibits a mean value of 0.049 and a standard deviation of 0.019, which are subsequently used as references for data normalization and input scaling. This section is organized as follows: (1) an investigation of the effects of normalization strategies and activation functions; (2) an analysis of the contributions of the key design elements of the proposed method to predictive performance; (3) an evaluation of the necessity of spatial dependency modeling; and (4) an assessment of the model’s robustness and generalization capability in practical application scenarios. Normalization Strategy First, the impact of adopting the proposed adjusted Z-score normalization on prediction performance is examined. The experimental results indicate that when the original data values fall below the overall dataset mean, failing to apply the adjustment leads to pronounced periodic oscillations in the model’s predictions. Moreover, the greater the deviation from the mean, the more severe the oscillations become. In contrast, this phenomenon is not evident when the data values exceed the mean. Figure 7 presents a comparison of prediction results with and without the adjusted Z-score normalization (using Aodi as an illustrative example). It can be observed that, in the absence of adjustment, the model exhibits unreasonable oscillatory behavior in low-value regions. After incorporating the adjusted Z-score normalization, the predicted curves become noticeably smoother and exhibit improved agreement with the ground truth. These results demonstrate that the proposed normalization strategy effectively mitigates prediction instability caused by imbalanced data distributions. Activation Function In the activation function experiments, Tanh and ReLU were adopted for comparative analysis. The primary differences between these two functions lie in their mathematical properties and their influence on the training process. Tanh is a smooth nonlinear function, and its zero-centered characteristic facilitates balanced gradient propagation in both positive and negative directions, thereby promoting parameter convergence. In contrast, ReLU is computationally efficient and simple to implement. However, compared with Tanh, ReLU is more prone to the “dying ReLU” phenomenon during the early stages of training, in which a portion of neurons output zero and fail to recover, consequently reducing the model’s representational capacity. Under the proposed experimental framework, the performance differences between the two activation functions were found to be marginal, as illustrated in Fig. 8 Nevertheless, considering that the input data exhibit an approximately Gaussian distribution and that Tanh is better suited for modeling nonlinear characteristics in such distributions, Tanh was ultimately selected as the primary activation function for subsequent experiments. Table 2 Activation function parameter comparison Training Results Comparison Activation function Tanh Tanh ReLU ReLU Dropout 0.4 0.3 0.4 0.3 Total epoch 21 12 14 8 Best_epoch 16 4 6 3 MAE 0.00029 0.00033 0.00041 0.00043 (a) Dropout = 0.3; (b) Dropout = 0.4 (First 1000 Minutes) Spatial Correlation Analysis This study considers both temporal and spatial correlations. To evaluate the necessity of incorporating spatial information, two model configurations were further compared: one using only temporal features and the other integrating spatial correlations. As illustrated in Fig. 9 , when spatial correlations are not included, the model is still able to capture the overall temporal trends; however, the prediction errors are noticeably higher. In contrast, after incorporating spatial correlations, both the mean absolute error (MAE) and the overall loss are significantly reduced, indicating that information from neighboring stations effectively enhances prediction accuracy and stability. These results demonstrate that, although the spatial correlation module is not strictly required for model operation, it serves as an important design component for improving overall model performance. With vs. Without Spatial Correlation (First 1000 Minutes) Hyperparameter Importance This study further evaluates the effects of several hyperparameters, including the hidden layer size, dropout rate, and the number of attention heads, on model performance. The overall experimental results indicate that, when other parameters are held constant, adjusting only the hidden layer size does not lead to significant differences in prediction performance. The results show that increasing the hidden layer size primarily increases model complexity and may amplify fluctuations in the predicted outputs. In contrast, smaller hidden layer configurations produce smoother predictions without a noticeable degradation in accuracy. The best training results for each experimental configuration are summarized in Tables 3 Table 3 Comparison of Models with Different Hyperparameter Settings Training Results Comparison Activation function Tanh Dropout 0.3 0.4 Number head 2 4 2 4 Hidden layer 128 128 128 128 valid_loss 0.0004 0.0003 0.0005 0.0003 MAE 0.000431 0.000326 0.000421 0.000291 To investigate the model's dependence on the length of historical data, this study also examined the impact of different window sizes on prediction performance. In the experiments, window sizes of 10, 20, 30, and 60 minutes were tested, while the model predicted data for the next 7 minutes, allowing a comparison of performance under different input lengths. As shown in Fig. 10 , the model is able to capture the overall trend regardless of the window size, although differences exist in how closely the predictions match the observed values. Specifically, Fig. 10 (a) shows that when the window size is 10 minutes, the model predictions align most closely with the actual data. This is because shorter input sequences reduce computational burden, allowing other hyperparameters to be increased to learn more complex features, thereby improving predictive accuracy. In contrast, increasing the window size to 60 minutes significantly increases computational load. To ensure stable model operation, some hyperparameters had to be reduced, resulting in slightly decreased prediction performance. (a) Window size = 10 minutes; (b) Window size = 60 minutes. Therefore, under the conditions of this experiment, a shorter window size (10 minutes) is more favorable for prediction performance. Simulation of Realistic Scenario Test Results To simulate potential sensor failures or communication errors in practical scenarios, this study set the outputs of certain stations to zero, thereby mimicking situations where one or multiple stations fail simultaneously. The experimental results indicate that, although the MAE at the anomalous stations increased significantly, the predictions at the remaining normal stations remained stable (Fig. 11 ). This demonstrates that the model possesses strong fault tolerance and robustness. (a) Aodi Station; (b) Kenting Station. In this study, data from January to October 2024 were used as the training set, November as the validation set, and December as the test set to evaluate the model’s generalization capability on unseen data. As shown in Fig. 12 , the model is able to accurately capture the trends during the period not included in the training set, demonstrating its strong and stable temporal learning ability. (a) Aodi Station; (b) Shuangxi Station. Based on these findings, a medium-sized hidden layer configuration that balances predictive performance and computational cost is adopted in the subsequent experiments. Conclusion and Future Work This study integrates deep learning techniques to analyze heterogeneous data, including environmental radiation dose rates with spatial and temporal dependencies. Future work may incorporate additional meteorological factors, such as cloud cover, wind direction, and wind speed, to further investigate their potential impact on radiation variations, thereby enhancing model accuracy and learning capability. Regarding input data, the current system simultaneously receives historical data from all 63 monitoring stations. Future optimization could focus on a localized and user-oriented approach, such as restricting data input and prediction to specific target areas (e.g., near nuclear power plants or waste storage sites). This strategy not only reduces computational costs but also improves model efficiency and real-time applicability. Moreover, to enhance the practical utility and interpretability of predictions, anomaly detection mechanisms could be integrated into the model framework. This would allow for the assessment of prediction reliability and the real-time reporting of deviations between predicted and observed values, including the corresponding time and location, thereby supporting subsequent decision-making and response strategies. In practical applications, the developed model is expected to be integrated into Taiwan’s environmental radiation monitoring system, providing more timely and accurate predictive support. Although the current model is capable of forecasting radiation dose rates only up to the next seven minutes, future development aims to extend the prediction horizon to 30 minutes or even one hour, offering greater lead time for emergency response, strengthening incident warning and protection mechanisms, and ultimately enabling effective monitoring and management of environmental radiation risks. Declarations Author Contribution ConceptualizationChuan-Pin Lee , Wei-Hsiang Tseng, Chi-Wen Hsieh, Shih-Chin Tsai.MethodologyChuan-Pin Lee, Wei-Hsiang Tseng, Chi-Wen Hsieh, Shih-Chin Tsai.SoftwareWei-Hsiang Tseng, Chi-Wen Hsieh.ValidationChuan-Pin Lee, Yu-Hung Wang, Shih-Chin Tsai.Formal analysisChuan-Pin Lee, Wei-Hsiang Tseng, Yu-Hung Wang, Yu-Cheng Tsai, Chi-Wen Hsieh, Shih-Chin Tsai.InvestigationChuan-Pin Lee, Wei-Hsiang Tseng, Yu-Jei Li, Chun-Yi Fang.ResourcesChuan-Pin Lee, Wei-Hsiang Tseng, Yu-Jei Li, Chun-Yi Fang.Data curationWei-Hsiang Tseng, Yu-Cheng Tsai, Chun-Liang Yeh.Writing – Original DraftYu-Hung Wang, Yu-Cheng Tsai.Writing – Review & EditingChuan-Pin Lee, Wei-Hsiang Tseng, Yu-Hung Wang, Yu-Cheng Tsai.VisualizationYu-Hung Wang, Yu-Cheng Tsai.SupervisionChuan-Pin Lee, Chi-Wen Hsieh, Shih-Chin Tsai.Project administrationChuan-Pin Lee, Chi-Wen Hsieh, Shih-Chin Tsai.Funding acquisitionChuan-Pin Lee, Chi-Wen Hsieh, Shih-Chin Tsai. Acknowledgement The authors sincerely thank the Radiation Monitoring Center, Nuclear Safety Commission, for their generous support. We are grateful for providing valuable environmental radiation monitoring data, which served as an important basis for this study and enhanced the reference value and empirical foundation of this work. We also appreciate the assistance and support from the Center’s staff during the research process, which enabled the smooth progress of the study. We also sincerely thank Zih-Shiuan Chiou and Wei-Min Li, graduate students from the Department of Electrical Engineering, National Chung Cheng University, for their valuable contributions to this research. This project was mainly supported by the NSTC (Taiwan, R.O.C.) through mutual fund programs under grant numbers NSTC 114-2623-E-007 -001 -NU, 115-2623-E-007 -006 -NU, 114-2622-E-194 -005 ,114‑2119‑M‑001‑007, NSTC 114‑2740‑M‑001‑002, and NSTC 114‑2111‑M‑001‑010, as well as by Academia Sinica under project AS‑IAIA‑114‑M03. Supplementary information This section will not appear in the printed version of your paper but it will contain a link; the webpage containing the electronic supplementary information will appear when one clicks on the hyperlink. Here you can list the details of your research which would be too long for the main text, e.g. a larger number of spectra etc . Start with 1 for Figure and Table numbers in this section. References Environmental Radiation Map of Taiwan. https://radmap.nusc.gov.tw/EBRM21/. Accessed 01 Jul 2025 Radiation Monitoring Center, Nuclear Safety Commission, National Environmental Radiation Monitoring. 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DOI 10.1609/aaai.v35i5.16523 Ma J, Zhao J, Hou Y (2024) Spatial–Temporal Transformer Networks for Traffic Flow Forecasting Using a Pre-Trained Language Model. Sensors 24:5502. DOI 10.3390/s24175502 Islam MK (2024) Temporal Dependencies and Spatio-Temporal Patterns of Time Series Models. Proc AAAI Conf Artif Intell 38:21. DOI 10.1609/aaai.v38i21.30396 Xu M, et al. (2021) Spatial-Temporal Transformer Networks for Traffic Flow Forecasting. arXiv:2001.02908. DOI 10.48550/arXiv.2001.02908. Liang Y, et al. (2023) AirFormer: Predicting Nationwide Air Quality in China with Transformers. Proc AAAI Conf Artif Intell 37:12. DOI 10.1609/aaai.v37i12.26676 Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted 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. 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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-8736433","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":604966096,"identity":"3ca7a04e-4a2f-42a7-8ebd-01e49ce783b8","order_by":0,"name":"Chuan-Pin Lee","email":"","orcid":"","institution":"National Tsing Hua University","correspondingAuthor":false,"prefix":"","firstName":"Chuan-Pin","middleName":"","lastName":"Lee","suffix":""},{"id":604966102,"identity":"2a1bc952-ce4e-4df3-91a2-668eb65bc146","order_by":1,"name":"Wei-Hsiang Tseng","email":"","orcid":"","institution":"National Chung Cheng 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4","display":"","copyAsset":false,"role":"figure","size":153935,"visible":true,"origin":"","legend":"\u003cp\u003eDiagram of the Relationship Matrix between Stations [41], \u0026nbsp;where i and 𝑘 represent station IDs, and j represents the region within the concentric circles.\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-8736433/v1/85929c279ce0ff51b33df57d.png"},{"id":104544661,"identity":"6fd18969-2b45-4bff-aa75-0a7ec6a37ee3","added_by":"auto","created_at":"2026-03-13 07:05:19","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":181713,"visible":true,"origin":"","legend":"\u003cp\u003eData Architecture 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normalization. \u003cbr\u003e\n(a) Prediction results obtained using the adjusted Z-score normalization.\u003cbr\u003e\n(b) Prediction results obtained without applying the adjusted Z-score normalization.\u003c/p\u003e","description":"","filename":"floatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-8736433/v1/95eb045d1c9536f58dc70ddf.png"},{"id":104781705,"identity":"825bc260-3d4e-4e11-9c5f-b253c2fc09b1","added_by":"auto","created_at":"2026-03-17 07:56:12","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":400336,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of Prediction Residuals between Tanh and ReLU at Aodi Station\u003cbr\u003e\n(a) Dropout = 0.3; (b) Dropout = 0.4 (First 1000 Minutes)\u003c/p\u003e","description":"","filename":"floatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-8736433/v1/ef749776fb9e131a5d97eb8a.png"},{"id":104544660,"identity":"ff960fa1-c885-4ef6-aef7-93a739f4ac5c","added_by":"auto","created_at":"2026-03-13 07:05:19","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":569644,"visible":true,"origin":"","legend":"\u003cp\u003ePrediction Residuals at Aodi Station: With vs. Without Spatial Correlation (First 1000 Minutes)\u003c/p\u003e","description":"","filename":"floatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-8736433/v1/f854230a851c3d8131995199.png"},{"id":104835210,"identity":"e8bacfba-0fa7-4fa1-8115-b8a0578b0722","added_by":"auto","created_at":"2026-03-17 17:42:14","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":397247,"visible":true,"origin":"","legend":"\u003cp\u003eComparison between predicted and observed values at Aodi Station.\u003cbr\u003e\n(a) Window size = 10 minutes; (b) Window size = 60 minutes.\u003c/p\u003e","description":"","filename":"floatimage10.png","url":"https://assets-eu.researchsquare.com/files/rs-8736433/v1/37890738054a9d8be17e9f53.png"},{"id":104782046,"identity":"e4730ed2-aff2-4bf9-b03c-4556889fa79b","added_by":"auto","created_at":"2026-03-17 07:56:45","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":502008,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of predicted and actual values for non-anomalous stations. \u003cbr\u003e\n(a) Aodi Station; (b) Kenting Station.\u003c/p\u003e","description":"","filename":"floatimage11.png","url":"https://assets-eu.researchsquare.com/files/rs-8736433/v1/a4035be33b88bd913988db4a.png"},{"id":104544665,"identity":"eb8db8c3-c06d-4426-9d1b-4c0e3912615b","added_by":"auto","created_at":"2026-03-13 07:05:19","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":451994,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of model generalization performance at different stations.\u003cbr\u003e\n(a) Aodi Station; (b) Shuangxi Station.\u003c/p\u003e","description":"","filename":"floatimage12.png","url":"https://assets-eu.researchsquare.com/files/rs-8736433/v1/2d0f32da351aa9caeb82693a.png"},{"id":104835896,"identity":"ce6a1b27-1051-4c97-8d1b-292b60a74e51","added_by":"auto","created_at":"2026-03-17 17:50:23","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3704702,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8736433/v1/5eabb393-e77e-42cf-9f08-06b28d1a4269.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"AI-Based Multivariate Analysis of Environmental Radiation Dose Trends in Taiwan","fulltext":[{"header":"Introduction","content":"\u003cp\u003eWith the official decommissioning of Taiwan\u0026rsquo;s last nuclear power plant in May 2025, the country has formally entered a nuclear-free era. Nevertheless, nuclear safety remains a critical issue of public concern. To enhance information transparency and ensure the public\u0026rsquo;s right to be informed about radiological safety, the Taiwan Nuclear Safety Commission (NSC) has established a nationwide Environmental Radiation Monitoring Network [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. Each monitoring station is equipped with a fixed gamma dose-rate detector, and real-time measurement data are continuously transmitted and periodically uploaded to open-access platforms. Based on the temporal variation of radiation dose rates at different locations, the NSC regularly publishes the Monthly Automatic Monitoring Report on Radiation Safety Alerts [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e], which serves as an important reference for policy evaluation and risk management.\u003c/p\u003e \u003cp\u003eIn addition, for areas of heightened concern\u0026mdash;such as nuclear power plants, radioactive waste storage facilities, and their surrounding regions [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]\u0026mdash;the NSC has implemented sampling and analytical mechanisms and provides historical monitoring data for public access and academic use [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. To further improve accessibility and interpretability, visualization techniques have been adopted through the development of an environmental radiation map platform [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. This platform integrates data from the air quality monitoring network and marine data systems, thereby establishing a cross-disciplinary, multi-parameter environmental monitoring framework [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. However, rapid technological advances, including improvements in detector resolution and the increasing number of monitored parameters, have significantly increased data volume and complexity. In practice, challenges such as data loss, instrument replacement, and inconsistent sampling frequencies frequently arise, posing substantial difficulties for future data management and analytical applications.\u003c/p\u003e \u003cp\u003eIn recent years, advances in artificial intelligence (AI) technologies have demonstrated considerable potential for processing and predicting outcomes from large-scale, multi-parameter datasets. By extracting key features from vast amounts of unstructured data, AI-based approaches can effectively identify critical information and support anomaly detection and early warning decision-making. Currently, nuclear safety\u0026ndash;related institutions have made environmental dose-rate information publicly available, including real-time and historical dose rates, station GPS locations, and monitoring metadata. These open datasets provide a feasible foundation for the introduction of AI-driven intelligent monitoring methodologies.\u003c/p\u003e \u003cp\u003eAgainst this background, the present study aims to integrate big data processing, data cleansing, and deep learning techniques to develop an intelligent radiation dose-rate data processing and prediction system. Given that radiation dose-rate variations are influenced by multiple environmental factors and are often closely associated with meteorological conditions\u0026mdash;such as precipitation, wind speed, wind direction, atmospheric pressure, and aerosol concentration\u0026mdash;this study further integrates heterogeneous data sources, including the NSC environmental radiation map and the national air quality monitoring network [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e, \u003cspan additionalcitationids=\"CR7\" citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. By incorporating multiple environmental variables, the feature space of the predictive model is expanded to enhance its forecasting capability. To address discrepancies in observation scales and sampling frequencies among different data sources, multivariate analytical methods are employed for variable screening and feature selection. Correlation analysis is subsequently conducted to evaluate the direction and magnitude of the influence of each environmental parameter on radiation dose rates.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThrough these approaches, this study not only improves the accuracy and stability of radiation dose-rate prediction models but also deepens the understanding of the underlying mechanisms governing dose-rate variability. Furthermore, it strengthens early warning capabilities and provides a more robust scientific basis for emergency response and decision-making during anomalous radiological events. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e illustrates a simplified schematic of the environmental radiation monitoring system. The system consists of multiple in situ radiation monitoring stations, each equipped with a radiation detector. Radiation dose-rate data collected from various environments\u0026mdash;including urban areas, natural background radiation zones, and key monitoring sites near nuclear facilities\u0026mdash;are transmitted wirelessly to a central monitoring center for real-time processing and storage. Through centralized management, continuous surveillance of environmental radiation dose rates is achieved, enabling timely decision support in the event of radiological anomalies.\u003c/p\u003e"},{"header":"Literature Review","content":"\u003cp\u003eWith the increasing global emphasis on sustainable development and green energy transition, nuclear safety and environmental radiation monitoring have become critical research priorities. In the context of natural radiation exposure, long-term observations from Canada\u0026rsquo;s Fixed Point Surveillance (FPS) network indicate that population annual effective doses are dominated by cosmic radiation and naturally occurring terrestrial radionuclides, with approximately 89% of exposure occurring indoors, highlighting the strong influence of natural background radiation on everyday exposure [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. China has implemented a hierarchical monitoring framework for research reactors, although further technological upgrades and institutional reinforcement remain necessary [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. The National Academy of Sciences of Ukraine has developed advanced radiation monitoring systems, including real-time airborne platforms, solid-state detectors, and portable workstations, enhancing spatial flexibility and enabling rapid post-accident risk assessment [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. Following the Fukushima Daiichi accident, global efforts have increasingly focused on mobile radiation detection systems integrating sensor networks and artificial intelligence, such as unmanned platforms equipped with silicon photomultipliers for radioactive material search, border inspection, and nuclear facility security monitoring [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. Subsequent studies further demonstrated that plutonium (Pu) contamination from the Fukushima accident exhibits pronounced regional heterogeneity and that isotopic ratios can serve as reliable source fingerprints for risk mapping and geochemical baseline construction [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eAtmospheric radiation processes represent a major source of uncertainty in climate system modeling. The complex interactions among clouds, aerosols, and radiation are particularly challenging in remote regions such as the Southern Ocean, where excessive supercooled liquid water and strong small-scale variability substantially affect radiative transfer [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. Low-level clouds have been identified as a dominant contributor to shortwave radiation biases, motivating the use of high-resolution observations and advanced radiative parameterizations. At the global scale, ISCCP-H cloud optical thickness and cloud-top pressure datasets support cloud classification and weather state analysis; however, current climate models, including CMIP6, systematically underestimate mid- and high-level clouds and shallow cumulus clouds, resulting in weakened shortwave radiative cooling [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. Observations from the Yeonggwang region in South Korea further reveal a significant association between heavy precipitation events and elevated environmental radiation dose rates, likely driven by rain-induced radionuclide washout and cloud microphysical changes [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. These radiative and energetic imbalances are closely linked to large-scale climate variability, including polar processes and ENSO, underscoring the need for integrated observational, modeling, and AI-based approaches [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe rapid growth and high dimensionality of environmental monitoring data have established artificial intelligence (AI) as a key tool for data analysis and prediction. In nuclear applications, AI techniques have been widely adopted for system safety monitoring, operational support, and fault diagnosis. Hybrid supervised and reinforcement learning approaches have demonstrated improved operational efficiency in nuclear power plant maintenance and support integrated Nuclear Power Plant\u0026ndash;Human\u0026ndash;Cyber\u0026ndash;Physical Systems (NPPHCPS) [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. However, stringent safety requirements and limited data availability pose challenges related to model interpretability and reliability, leading to increasing interest in hybrid frameworks that incorporate expert knowledge and explainable AI (XAI) [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. Bayesian methods, including Markov Chain Monte Carlo (MCMC), have also been integrated to quantify uncertainty and enhance decision robustness [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIn climate science, the long-term rise in global surface temperature since the nineteenth century is widely recognized as a key indicator of anthropogenic influence and is often illustrated by the \u0026ldquo;hockey stick\u0026rdquo; curve. Statistical approaches complement physics-based models through trend estimation, change-point detection, and uncertainty quantification. Recent studies demonstrate that the apparent post-1998 \u0026ldquo;global warming hiatus\u0026rdquo; lacks robust statistical support and largely reflects data selection and uncertainty effects [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. Machine learning techniques have also been increasingly applied to weather and climate prediction, achieving strong performance in short-term forecasting but remaining limited for medium- and long-term prediction due to system complexity and data constraints. This highlights the need for unified modeling frameworks across multiple temporal scales [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eMachine learning has further been applied to source term inversion in nuclear accident scenarios, where rapid estimation of radionuclide release rates is critical for emergency response. LSTM-based inversion models reduce dependence on prior assumptions while maintaining stable performance across multiple radionuclides (e.g., Kr-88, Te-132, and I-131) and varying meteorological conditions [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. Subsequent studies confirm their adaptability under more complex scenarios involving Kr-88, Sr-91, Te-132, and I-131, identifying gamma dose rate as a key factor influencing prediction accuracy [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. Machine learning combined with Bayesian optimization techniques, such as Optuna, has also demonstrated robust performance under uncertain release durations and meteorological perturbations [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIn broader environmental science applications, AI and statistical techniques have been increasingly integrated into climate change monitoring, water resource management, and pollution risk assessment [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]. Representative examples include groundwater quality prediction using RNN\u0026ndash;GIS integration [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e], crude oil price forecasting using multivariate support vector regression [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e], hydraulic structure safety monitoring via Random Forest and SVM-based scour prediction [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e], and real-time precipitation monitoring enabled by high-speed imaging and image processing techniques [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. Multivariate analyses of atmospheric radionuclide Be-7 further elucidate its interactions with precipitation processes and atmospheric dynamics [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eAdvanced AI architectures for time-series analysis, including Transformers and graph neural networks (GNNs), have been widely applied to traffic flow, meteorology, healthcare, air quality prediction, and anomaly detection [\u003cspan additionalcitationids=\"CR33 CR34 CR35 CR36\" citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e]. Spatio-temporal graph neural networks (STGNNs) explicitly model spatial and temporal dependencies and demonstrate strong predictive performance in sensor networks [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e]. Transformer-based frameworks such as STTN enable dynamic attention and long-range dependency modeling for long-term forecasting [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e, \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e], while models such as AirFormer improve prediction accuracy and uncertainty representation through staged spatio-temporal modeling [\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e]. These developments highlight the growing potential of AI-driven time-series modeling for complex environmental and safety-critical applications.\u003c/p\u003e "},{"header":"Theory and Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003cp\u003eRadiation Dose Rate\u003c/p\u003e \u003cp\u003eTo evaluate the radiation intensity in a specific region over a given time period, we use the \"Radiation Dose Rate\" as the basis for assessment. The Radiation Dose Rate is defined as the amount of radiation received by the human body or measured in the environment within a unit of time, expressed in microsieverts per hour (\u0026micro;Sv/h). In typical environmental conditions, background radiation usually ranges from approximately 0.02 to 0.2 \u0026micro;Sv/h, though this range can vary depending on regional geological factors and altitude. Medical radiation dose rates are generally below 0.5 \u0026micro;Sv/h, while the International Commission on Radiological Protection (ICRP) recommends a public annual dose limit of no more than 1 millisievert (1 mSv/a), which translates to an hourly dose rate of 0.1 \u0026micro;Sv/h.\u003c/p\u003e \u003cp\u003eDataset and Detector\u003c/p\u003e \u003cp\u003eIn this study, we utilize the MERM-PE-HDB model plastic scintillation detector manufactured by SERVCOMPUTING INC. (Kaohsiung City, Taiwan). This instrument is designed for continuous all-weather monitoring, measuring the gamma radiation dose rate in the environment once per minute and outputting results in micro-Sieverts per hour (\u0026micro;Sv/h). Such a design effectively reflects the real-time variations and sensitivity of environmental radiation. The recorded data are stored on servers at the Radiation Monitoring Center (RMC), containing historical dose rates, time information, and rainfall data from 63 monitoring stations across Taiwan. These datasets are then integrated to form the primary dataset for this research.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eModel Design\u003c/h3\u003e\n\u003cp\u003eIn this study, we integrate rainfall data and radiation dose rates from various locations, and perform both spatial and temporal correlation analyses based on the structure of the Airformer model. The results from these analyses are then fed into the model, and the outputs are compared with our actual measurements. The model, which is inspired by Airformer, utilizes Variational Autoencoders (VAE) as its core framework and incorporates a Multi-Head Attention Mechanism [\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e]. The VAE allows for the reconstruction of inputs at each time point, which enhances the model's learning performance, as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn the Deterministic Stage of the AirFormer model, the architecture incorporates two major attention modules: a Spatial Attention module and a Temporal Attention module. These modules are designed to learn spatial correlations among monitoring stations and temporal dependencies within individual stations, respectively. When the data are fed into the model, the historical time-series observations X\u003csub\u003e1:T\u003c/sub\u003e are first mapped into a feature space through a Multi-Layer Perceptron (MLP). The transformed features are then passed into multiple stacked AirFormer layers for spatiotemporal feature learning. Within this framework, the Spatial Attention module employs a linear-complexity multi-head attention mechanism to efficiently capture spatial interactions among stations, while the Temporal Attention module focuses on modeling temporal dependencies at each individual station. To prevent the model from accessing future information during training and thereby compromising prediction accuracy, a masking mechanism is introduced in the temporal attention to block future time steps.\u003c/p\u003e \u003cp\u003eIn the spatial attention module, this study designs a spatial relationship matrix for 63 radiation monitoring stations across Taiwan. Using a target-region partitioning strategy, the surrounding area of each station is divided into multiple regions based on predefined radii and quadrants. The distribution and density of neighboring stations within these regions are then computed to quantify the relative geographical relationships among stations. Through the spatial multi-head attention mechanism, the model is able to learn and enhance spatial dependencies across different monitoring stations. In contrast, the temporal attention module performs time-series learning based on historical observations from a single station. To avoid information leakage during training, a masking design is incorporated into the attention mechanism, ensuring that predictions are made solely based on current and past observations. This design enhances the robustness and stability of the model in real-world deployment scenarios.\u003c/p\u003e \u003cp\u003eThe overall model is built upon a Variational Autoencoder (VAE)-based core architecture, which enables effective feature extraction and dimensionality reduction while preserving continuity and generative capacity in the latent space. This property is advantageous for downstream tasks such as data reconstruction, forecasting, and data imputation under incomplete observation scenarios, as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe overall architecture draws inspiration from the concept of latent space in VAEs. In a standard VAE, the latent space is learned by modeling the probability distribution of the input data\u0026mdash;typically assuming a Gaussian distribution\u0026mdash;and introducing stochastic noise, which endows the model with generative capabilities. However, for the radiation dose rate time-series forecasting task considered in this study, the data inherently exhibit strong fluctuations and high variability. Introducing additional stochastic noise, as in conventional VAEs, may increase the difficulty of model convergence and adversely affect prediction stability. Therefore, this study proposes a deterministic modification to the VAE architecture by setting the noise term to zero. As a result, the latent space transitions from a probabilistic distribution to a high-dimensional deterministic feature representation. This adjustment allows the model to focus on precise reconstruction and feature extraction of the input data during training, rather than distributional generation. Through this strategy, the proposed approach aims to retain the deep feature extraction capability of the VAE framework while improving prediction stability and accuracy under high-variability time-series conditions.\u003c/p\u003e \u003cp\u003eIntegration of Spatial Features with Taiwan's Radiation Monitoring Stations\u003c/p\u003e \u003cp\u003eIn the AirFormer architecture, spatial information is utilized to assist the model in learning the spatial dependencies between the 63 radiation monitoring stations across Taiwan. To enable the model to capture finer spatial features, we have designed two matrices to support the learning process. One matrix quantifies the detailed positional relationships between stations, while the other is used solely to indicate whether other stations are present in the vicinity of each station. Currently, Taiwan has 63 radiation monitoring stations, which are distributed across various regions, based on the areas of monitoring focus. Each station has a clear GPS location. To transform this spatial information into features that can be learned by the model, we use each station i as the center and draw concentric circles with radii of 5 km and 10 km, respectively. These circles are then divided into four quadrants both horizontally and vertically, resulting in a total of 9 regions (with the center region being 1, and the surrounding regions extending outward in quadrant order up to region 9), forming a target-like region partitioning. This division effectively reflects the geographical relative positioning distribution of other stations around each station.\u003c/p\u003e \u003cp\u003eOne of the matrices is responsible for recording the number of neighboring stations within each region. Specifically, when the i-th station is considered the center, if other stations appear in a given region, the region is weighted based on the number of stations it contains: if one station appears in the region, it is marked as 1; if two stations appear, each receives a weight of 0.5; if three stations appear, each receives a weight of 1/3, and so on. This design ensures that the total weight in each region sums to 1 (the sum of the values in the red rectangle of Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e must equal 1), thus avoiding bias due to station density differences. If no other stations are present in a given region, its weight is set to 0. Once all stations have been processed, a 3D matrix of size 63\u0026times;63\u0026times;9 is generated, fully describing the detailed spatial relationships between the monitoring stations across Taiwan, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003ewhere i and \u0026#119896; represent station IDs,\u003c/p\u003e \u003cp\u003eand j represents the region within the concentric circles.\u003c/p\u003e \u003cp\u003eAnother matrix is a simplified version, primarily used in the model\u0026rsquo;s attention mechanism as a mask. During the training process, the model reads both past and future data. However, in actual prediction scenarios, future information is not accessible, so a mask is necessary to block future time steps' information, preventing the model from learning future-known data during training, which could distort performance during prediction. The spatial mask further restricts the model to focus only on spatial location information within a reasonable range in the attention mechanism.\u003c/p\u003e \u003cp\u003eThe construction of this matrix is as follows: for the i-th station, if any station appears in a given region, that region is labeled as 1; if no stations are present in the region, it is labeled as 0, without further subdividing the number of stations. Therefore, this matrix is a 63 \u0026times; 9 two-dimensional matrix, reflecting only the presence or absence of neighboring stations in the surrounding area of each station, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eThrough the design of these two matrices, one provides the model with complete spatial structural information to help the model learn the spatial dependencies between stations. The other, using the mask, controls the model\u0026rsquo;s learning scope, preventing the model from accessing future information that should not be available, thereby improving the model\u0026rsquo;s prediction stability and accuracy in real-world application scenarios.\u003c/p\u003e \u003cp\u003eIntegration of Temporal Features into the Model\u003c/p\u003e \u003cp\u003eIn addition to utilizing spatial features to help the model learn the interdependencies between stations, learning the temporal features of the historical data from individual stations is also an essential part of the model's predictive performance. Therefore, in this study, we specifically integrate time series information, enabling the model to learn the inherent temporal dynamics from the historical changes in radiation dose rates at each station.\u003c/p\u003e \u003cp\u003eIn the model design, the Window Size represents the length of historical time steps provided as input during each training and prediction phase. For example, the model may utilize historical observations from the past 24 or 48 hours as input features. In this study, window sizes corresponding to 10-minute to 60-minute intervals are adopted as experimental parameters.\u003c/p\u003e \u003cp\u003eThe Blocks parameter refers to the number of stacked Transformer blocks in the model, where each block employs a multi-head self-attention mechanism to capture temporal dependencies within the input sequence. Here, b denotes the index of the current Transformer block.\u003c/p\u003e \u003cp\u003eAlthough the self-attention mechanism in Transformers theoretically allows each time step to attend to all positions within the input sequence, such unrestricted attention is inappropriate for time-series regression tasks, including radiation dose rate prediction. Specifically, allowing the model to access future time steps during training would lead to information leakage and result in overly optimistic performance estimates.\u003c/p\u003e \u003cp\u003eTo prevent this issue, a temporal masking mechanism is applied during the attention computation. This mechanism restricts each time step to attend only to the current and previous time steps, while completely blocking access to future information. As a result, the model generates predictions based solely on information that would be available in real-world forecasting scenarios.\u003c/p\u003e \u003cp\u003eBy integrating both spatial and temporal features, the proposed model is capable of simultaneously learning spatial dependencies among monitoring stations and temporal evolution patterns within individual stations. This joint modeling strategy enhances the model\u0026rsquo;s ability to capture complex radiation dose rate dynamics and improves prediction accuracy.\u003c/p\u003e \u003cp\u003eNormalization Adjustment\u003c/p\u003e \u003cp\u003eIn the original model, Z-score normalization was applied to the dataset. The basic assumption of the Z-score is that the overall data approximately follows a Gaussian distribution. By calculating the deviation of each value from the mean and expressing it in terms of the standard deviation, the data with different scales are transformed to a common standard. After Z-score normalization, the data\u0026rsquo;s mean is shifted to 0, and the standard deviation becomes 1. The transformed values are centered around 0 and symmetrically distributed in the shape of a Gaussian distribution.\u003c/p\u003e \u003cp\u003eSince the values in our dataset oscillate around 0, after applying Z-score normalization, the model might treat values less than 0 as noise. This could lead to better prediction performance for values greater than the mean, while values below the mean are processed as noise. As a result, the predictions may exhibit periodic oscillations. To address this issue, we adjusted the Z-score process by adding the maximum value from the dataset to all values. For example, if the radiation dose rate at the Aodi station is 0.04, and the maximum radiation dose rate in the dataset is 0.1 at Alishan, then after adjustment, the radiation dose rate at the Aodi station becomes 0.14, and the value at Alishan becomes 0.2. The following is the adjusted Z-score formula:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:\\text{z}=\\:\\frac{\\text{x}+\\underset{\\text{n}}{\\text{max}}{\\text{x}}_{\\text{i}}-{\\mu\\:}}{{\\sigma\\:}}=\\frac{\\text{x}-{\\mu\\:}}{{\\sigma\\:}}+\\frac{\\underset{\\text{n}}{\\text{max}}{\\text{x}}_{\\text{i}}}{{\\sigma\\:}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\n\u003ch3\u003eData Flow and Preprocessing\u003c/h3\u003e\n\u003cp\u003eIn this study, the collected multi-dimensional data from various radiation monitoring stations (including radiation dose rates, timestamps, and the geographical locations of the stations) were first aggregated, along with external meteorological factors (primarily rainfall data) as auxiliary features. Through the preprocessing workflow, missing data, outlier correction, and format standardization were performed for each data type, ultimately converting the data into an input format suitable for heterogeneous data analysis and predictive modeling.\u003c/p\u003e \u003cp\u003eFor the prediction task, the model inputs include historical radiation dose rates, time-related information, meteorological factors, and spatial correlation features calculated based on the geographical locations of the monitoring stations. In the heterogeneous data analysis task, preprocessed time-series meteorological data and radiation monitoring data were used for statistical analysis and feature exploration to further investigate the potential impact mechanisms of environmental factors on the variations in radiation dose rates, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe experimental dataset consists of background radiation dose rate measurements collected by the Radiation Detection Center from radiation monitoring stations distributed across Taiwan. The data cover the period from 00:00 on January 1, 2024, to 23:59 on December 31, 2024, with a temporal resolution of one minute. The radiation dose rate is measured in microsieverts per hour (\u0026micro;Sv/h).\u003c/p\u003e \u003cp\u003eTo ensure consistency in data scale across different datasets, data preprocessing was conducted prior to model training, including the removal of anomalous values, handling of missing data, and data imputation. Using the full-year dataset from January to December 2024 (2024/01/01 00:00 to 2024/12/31 23:59) as an example, stations with missing measurements during certain time intervals\u0026mdash;presumably due to instrument malfunction or equipment replacement\u0026mdash;were excluded for those periods. The remaining data were then split into training (2024/1/1 00:00\u0026thinsp;~\u0026thinsp;2024/10/17 07:35), validation (2024/10/17 07:36\u0026ndash;2024/11/23 22:43), and testing sets (2024/11/23 22:44\u0026ndash;2024/12/31 23:59) according to an 80% / 10% / 10% ratio.\u003c/p\u003e \u003cp\u003eAfter partitioning the data into three subsets, the datasets are fed into the model in a stage-wise manner. The input to the model is structured as a three-dimensional tensor with dimensions representing the time length, the number of monitoring stations, and the feature channels, which include radiation dose rate, rainfall and temporal information. Taking the training set as an example, each sample has a dimensionality of 10 \u0026times; 63 \u0026times; (1\u0026thinsp;+\u0026thinsp;1 + 4) When the samples are constructed without overlapping time windows, a total of 40,450 samples can be obtained. In this study, overlapping sliding windows are adopted to improve data utilization, resulting in 57,785 samples, each with the same dimensionality of 10 \u0026times; 63 \u0026times; (1\u0026thinsp;+\u0026thinsp;1 + 4)\u003c/p\u003e \u003cp\u003eAfter the aforementioned preprocessing steps, the data are further organized to match the input requirements of the proposed model. A batch dimension is appended to the front of each data sample, enabling the model to process multiple samples simultaneously during each training iteration and thereby improving learning efficiency. The resulting data format is (batch size, time length, number of stations, number of features), specifically 16\u0026times;10\u0026times;63\u0026times;(1\u0026thinsp;+\u0026thinsp;1+14). The feature dimension consists of background radiation dose rate (1 dimension), rainfall data (1 dimension), and temporal information, which is transformed into a 14-dimensional representation through an embedding mechanism. This embedding design allows temporal features to attain compatible dimensionality after linear transformations within the model, facilitating effective extraction of temporal correlations.\u003c/p\u003e \u003cp\u003eThe model outputs comprise three main components. First, the model produces predictions for the target variable at the current time step. Second, it reconstructs the input data, enabling comparison between the reconstructed outputs and the original inputs to evaluate the model\u0026rsquo;s reconstruction capability. Third, the model directly computes the KL loss of the latent variables during training. The data types corresponding to each output are illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"Experimental Results and Analysis","content":"\u003cp\u003eExperimental Environment\u003c/p\u003e \u003cp\u003eThe model development and training in this study were conducted on a hardware and software environment equipped with sufficient computational resources. The system operated on Windows 10, utilizing an Intel\u0026reg; Core\u0026trade; i7-7700 processor and an NVIDIA GeForce RTX 4070 GPU as the primary computation cores, accompanied by 20 GB of RAM to ensure stable performance during model training and data processing. On the software side, Python 3.8.18 was employed as the main programming language, and PyTorch 2.2.1 served as the deep learning framework for implementing the model architecture and constructing the training pipeline. For deep learning computations, NVIDIA CUDA 12.1 was integrated to fully leverage hardware acceleration, enhancing the efficiency of large-scale data training and inference. The overall computing platform configuration is summarized in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\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\u003eSoftware and Hardware Setup for Experiments\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\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 \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOperating System\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWindows 10\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCPU\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eIntel\u0026reg; Core\u0026trade; i7-7700\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGPU\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNVIDIA GeForce RTX 4070\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMemory\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e20.0 GB RAM\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003eProgramming Language:\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePYTHON\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3.8.18\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003eDeep Learning Framework\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCUDA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e12.1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTorch\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2.2.1\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\u003eModel Prediction\u003c/p\u003e \u003cp\u003eThis chapter employs data collected from January to October 2024 as the primary experimental dataset, with the objective of validating whether the proposed model architecture can effectively enhance prediction stability and accuracy. In addition, the impacts of key model components and parameter configurations on predictive performance are systematically analyzed.\u003c/p\u003e \u003cp\u003eTo quantitatively evaluate the prediction performance of the proposed model, the Mean Absolute Error (MAE) is adopted as the primary evaluation metric, as it provides an intuitive and robust measure of the average magnitude of prediction errors without being overly sensitive to outliers.\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:\\text{M}\\text{A}\\text{E}=\\:\\frac{1}{N}{\\sum\\:}_{i=1}^{N}\\left|\\widehat{{y}_{i}}-{y}_{i}\\right|$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ePrior to model training, the statistical characteristics of the entire dataset are computed. The dataset exhibits a mean value of 0.049 and a standard deviation of 0.019, which are subsequently used as references for data normalization and input scaling. This section is organized as follows: (1) an investigation of the effects of normalization strategies and activation functions; (2) an analysis of the contributions of the key design elements of the proposed method to predictive performance; (3) an evaluation of the necessity of spatial dependency modeling; and (4) an assessment of the model\u0026rsquo;s robustness and generalization capability in practical application scenarios.\u003c/p\u003e \u003cp\u003eNormalization Strategy\u003c/p\u003e \u003cp\u003eFirst, the impact of adopting the proposed adjusted Z-score normalization on prediction performance is examined. The experimental results indicate that when the original data values fall below the overall dataset mean, failing to apply the adjustment leads to pronounced periodic oscillations in the model\u0026rsquo;s predictions. Moreover, the greater the deviation from the mean, the more severe the oscillations become. In contrast, this phenomenon is not evident when the data values exceed the mean.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e presents a comparison of prediction results with and without the adjusted Z-score normalization (using Aodi as an illustrative example). It can be observed that, in the absence of adjustment, the model exhibits unreasonable oscillatory behavior in low-value regions. After incorporating the adjusted Z-score normalization, the predicted curves become noticeably smoother and exhibit improved agreement with the ground truth. These results demonstrate that the proposed normalization strategy effectively mitigates prediction instability caused by imbalanced data distributions.\u003c/p\u003e\u003cp\u003eActivation Function\u003c/p\u003e \u003cp\u003eIn the activation function experiments, Tanh and ReLU were adopted for comparative analysis. The primary differences between these two functions lie in their mathematical properties and their influence on the training process. Tanh is a smooth nonlinear function, and its zero-centered characteristic facilitates balanced gradient propagation in both positive and negative directions, thereby promoting parameter convergence. In contrast, ReLU is computationally efficient and simple to implement. However, compared with Tanh, ReLU is more prone to the \u0026ldquo;dying ReLU\u0026rdquo; phenomenon during the early stages of training, in which a portion of neurons output zero and fail to recover, consequently reducing the model\u0026rsquo;s representational capacity.\u003c/p\u003e \u003cp\u003eUnder the proposed experimental framework, the performance differences between the two activation functions were found to be marginal, as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e Nevertheless, considering that the input data exhibit an approximately Gaussian distribution and that Tanh is better suited for modeling nonlinear characteristics in such distributions, Tanh was ultimately selected as the primary activation function for subsequent experiments.\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\u003eActivation function parameter comparison\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\u003eTraining Results Comparison\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eActivation function\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTanh\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTanh\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eReLU\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eReLU\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDropout\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTotal epoch\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBest_epoch\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMAE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.00029\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.00033\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.00041\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.00043\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\u003e \u003c/p\u003e \u003cp\u003e(a) Dropout\u0026thinsp;=\u0026thinsp;0.3; (b) Dropout\u0026thinsp;=\u0026thinsp;0.4 (First 1000 Minutes)\u003c/p\u003e \u003cp\u003eSpatial Correlation Analysis\u003c/p\u003e \u003cp\u003eThis study considers both temporal and spatial correlations. To evaluate the necessity of incorporating spatial information, two model configurations were further compared: one using only temporal features and the other integrating spatial correlations. As illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e, when spatial correlations are not included, the model is still able to capture the overall temporal trends; however, the prediction errors are noticeably higher. In contrast, after incorporating spatial correlations, both the mean absolute error (MAE) and the overall loss are significantly reduced, indicating that information from neighboring stations effectively enhances prediction accuracy and stability. These results demonstrate that, although the spatial correlation module is not strictly required for model operation, it serves as an important design component for improving overall model performance.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eWith vs. Without Spatial Correlation (First 1000 Minutes)\u003c/p\u003e \u003cp\u003eHyperparameter Importance\u003c/p\u003e \u003cp\u003eThis study further evaluates the effects of several hyperparameters, including the hidden layer size, dropout rate, and the number of attention heads, on model performance. The overall experimental results indicate that, when other parameters are held constant, adjusting only the hidden layer size does not lead to significant differences in prediction performance.\u003c/p\u003e \u003cp\u003eThe results show that increasing the hidden layer size primarily increases model complexity and may amplify fluctuations in the predicted outputs. In contrast, smaller hidden layer configurations produce smoother predictions without a noticeable degradation in accuracy. The best training results for each experimental configuration are summarized in Tables\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e\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\u003eComparison of Models with Different Hyperparameter Settings\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\u003eTraining Results Comparison\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eActivation function\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"4\" nameend=\"c5\" namest=\"c2\"\u003e \u003cp\u003eTanh\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDropout\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNumber head\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHidden layer\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e128\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e128\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e128\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e128\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003evalid_loss\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0004\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0003\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0005\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0003\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMAE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.000431\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.000326\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.000421\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.000291\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 investigate the model's dependence on the length of historical data, this study also examined the impact of different window sizes on prediction performance. In the experiments, window sizes of 10, 20, 30, and 60 minutes were tested, while the model predicted data for the next 7 minutes, allowing a comparison of performance under different input lengths.\u003c/p\u003e \u003cp\u003eAs shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e, the model is able to capture the overall trend regardless of the window size, although differences exist in how closely the predictions match the observed values. Specifically, Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e (a) shows that when the window size is 10 minutes, the model predictions align most closely with the actual data. This is because shorter input sequences reduce computational burden, allowing other hyperparameters to be increased to learn more complex features, thereby improving predictive accuracy. In contrast, increasing the window size to 60 minutes significantly increases computational load. To ensure stable model operation, some hyperparameters had to be reduced, resulting in slightly decreased prediction performance.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e(a) Window size\u0026thinsp;=\u0026thinsp;10 minutes; (b) Window size\u0026thinsp;=\u0026thinsp;60 minutes.\u003c/p\u003e \u003cp\u003eTherefore, under the conditions of this experiment, a shorter window size (10 minutes) is more favorable for prediction performance.\u003c/p\u003e \u003cp\u003eSimulation of Realistic Scenario Test Results\u003c/p\u003e \u003cp\u003eTo simulate potential sensor failures or communication errors in practical scenarios, this study set the outputs of certain stations to zero, thereby mimicking situations where one or multiple stations fail simultaneously. The experimental results indicate that, although the MAE at the anomalous stations increased significantly, the predictions at the remaining normal stations remained stable (Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e). This demonstrates that the model possesses strong fault tolerance and robustness.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e(a) Aodi Station; (b) Kenting Station.\u003c/p\u003e \u003cp\u003eIn this study, data from January to October 2024 were used as the training set, November as the validation set, and December as the test set to evaluate the model\u0026rsquo;s generalization capability on unseen data. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e, the model is able to accurately capture the trends during the period not included in the training set, demonstrating its strong and stable temporal learning ability.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e(a) Aodi Station; (b) Shuangxi Station.\u003c/p\u003e \u003cp\u003eBased on these findings, a medium-sized hidden layer configuration that balances predictive performance and computational cost is adopted in the subsequent experiments.\u003c/p\u003e"},{"header":"Conclusion and Future Work","content":"\u003cp\u003eThis study integrates deep learning techniques to analyze heterogeneous data, including environmental radiation dose rates with spatial and temporal dependencies. Future work may incorporate additional meteorological factors, such as cloud cover, wind direction, and wind speed, to further investigate their potential impact on radiation variations, thereby enhancing model accuracy and learning capability. Regarding input data, the current system simultaneously receives historical data from all 63 monitoring stations. Future optimization could focus on a localized and user-oriented approach, such as restricting data input and prediction to specific target areas (e.g., near nuclear power plants or waste storage sites). This strategy not only reduces computational costs but also improves model efficiency and real-time applicability.\u003c/p\u003e \u003cp\u003eMoreover, to enhance the practical utility and interpretability of predictions, anomaly detection mechanisms could be integrated into the model framework. This would allow for the assessment of prediction reliability and the real-time reporting of deviations between predicted and observed values, including the corresponding time and location, thereby supporting subsequent decision-making and response strategies. In practical applications, the developed model is expected to be integrated into Taiwan\u0026rsquo;s environmental radiation monitoring system, providing more timely and accurate predictive support. Although the current model is capable of forecasting radiation dose rates only up to the next seven minutes, future development aims to extend the prediction horizon to 30 minutes or even one hour, offering greater lead time for emergency response, strengthening incident warning and protection mechanisms, and ultimately enabling effective monitoring and management of environmental radiation risks.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eConceptualizationChuan-Pin Lee , Wei-Hsiang Tseng, Chi-Wen Hsieh, Shih-Chin Tsai.MethodologyChuan-Pin Lee, Wei-Hsiang Tseng, Chi-Wen Hsieh, Shih-Chin Tsai.SoftwareWei-Hsiang Tseng, Chi-Wen Hsieh.ValidationChuan-Pin Lee, Yu-Hung Wang, Shih-Chin Tsai.Formal analysisChuan-Pin Lee, Wei-Hsiang Tseng, Yu-Hung Wang, Yu-Cheng Tsai, Chi-Wen Hsieh, Shih-Chin Tsai.InvestigationChuan-Pin Lee, Wei-Hsiang Tseng, Yu-Jei Li, Chun-Yi Fang.ResourcesChuan-Pin Lee, Wei-Hsiang Tseng, Yu-Jei Li, Chun-Yi Fang.Data curationWei-Hsiang Tseng, Yu-Cheng Tsai, Chun-Liang Yeh.Writing \u0026ndash; Original DraftYu-Hung Wang, Yu-Cheng Tsai.Writing \u0026ndash; Review \u0026amp; EditingChuan-Pin Lee, Wei-Hsiang Tseng, Yu-Hung Wang, Yu-Cheng Tsai.VisualizationYu-Hung Wang, Yu-Cheng Tsai.SupervisionChuan-Pin Lee, Chi-Wen Hsieh, Shih-Chin Tsai.Project administrationChuan-Pin Lee, Chi-Wen Hsieh, Shih-Chin Tsai.Funding acquisitionChuan-Pin Lee, Chi-Wen Hsieh, Shih-Chin Tsai.\u003c/p\u003e\u003ch2\u003eAcknowledgement\u003c/h2\u003e\u003cp\u003eThe authors sincerely thank the Radiation Monitoring Center, Nuclear Safety Commission, for their generous support. We are grateful for providing valuable environmental radiation monitoring data, which served as an important basis for this study and enhanced the reference value and empirical foundation of this work. We also appreciate the assistance and support from the Center\u0026rsquo;s staff during the research process, which enabled the smooth progress of the study. We also sincerely thank Zih-Shiuan Chiou and Wei-Min Li, graduate students from the Department of Electrical Engineering, National Chung Cheng University, for their valuable contributions to this research. This project was mainly supported by the NSTC (Taiwan, R.O.C.) through mutual fund programs under grant numbers NSTC 114-2623-E-007 -001 -NU, 115-2623-E-007 -006 -NU, 114-2622-E-194 -005 ,114‑2119‑M‑001‑007, NSTC 114‑2740‑M‑001‑002, and NSTC 114‑2111‑M‑001‑010, as well as by Academia Sinica under project AS‑IAIA‑114‑M03.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSupplementary information\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis section will not appear in the printed version of your paper but it will contain a link; the webpage containing the electronic supplementary information will appear when one clicks on the hyperlink. Here you can list the details of your research which would be too long for the main text, \u003cem\u003ee.g.\u003c/em\u003e a larger number of spectra \u003cem\u003eetc\u003c/em\u003e. Start with 1 for Figure and Table numbers in this section.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eEnvironmental Radiation Map of Taiwan. https://radmap.nusc.gov.tw/EBRM21/. Accessed 01 Jul 2025\u003c/li\u003e\n\u003cli\u003eRadiation Monitoring Center, Nuclear Safety Commission, National Environmental Radiation Monitoring. Radiation Monitoring Center, Nuclear Safety Commission. https://www.nusc.gov.tw/rmc/gammadetect.html. Accessed 01 Jan 2025\u003c/li\u003e\n\u003cli\u003eRadiation Monitoring Center, Nuclear Safety Commission, Environmental Radiation Monitoring Report \u0026ndash; Monthly Report on Automatic Radiation Safety Early Warning Monitoring. Radiation Monitoring Center, Nuclear Safety Commission. https://www.nusc.gov.tw/rmc/monitoring/radsafe.html. Accessed 01 Jul 2025\u003c/li\u003e\n\u003cli\u003eNuclear Safety Commission, Parallel Environmental Radiation Monitoring Report for the Lanyu Area. 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DOI 10.1609/aaai.v37i12.26676\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"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":"Environmental Radiation Dose, Artificial intelligence, Variational Autoencoder","lastPublishedDoi":"10.21203/rs.3.rs-8736433/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8736433/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eNuclear energy is considered a key low-carbon energy source for sustainable development; however, the potential risks of nuclear accidents necessitate effective environmental radiation dose monitoring. This study integrates radiation dose rate and precipitation data from 63 monitoring stations across Taiwan, incorporating spatial relationships among stations. A Variational Autoencoder architecture was employed to predict site-specific radiation dose rates using approximately 300 consecutive days of time-series data from 2024. Based on radiation observations from the preceding 10 minutes, the model achieved a mean absolute error below 0.0005 (\u0026micro;Sv/h) for 7-minute-ahead predictions. The results demonstrate strong predictive performance, while also indicating sensitivity to low radiation thresholds, which may induce periodic oscillations and increase prediction errors.\u003c/p\u003e","manuscriptTitle":"AI-Based Multivariate Analysis of Environmental Radiation Dose Trends in Taiwan","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-03-13 07:05:11","doi":"10.21203/rs.3.rs-8736433/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":"a5e66906-d2bb-48a9-b7cb-5919c86aab44","owner":[],"postedDate":"March 13th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-03-13T07:05:11+00:00","versionOfRecord":[],"versionCreatedAt":"2026-03-13 07:05:11","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8736433","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8736433","identity":"rs-8736433","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}