Enhancing epidemic forecasting with a physics-informed spatial identity neural network.

Forecasting the future number of confirmed cases in each region is a critical challenge in controlling the spread of infectious diseases. Accurate predictions enable the proactive development of optimal containment strategies. Recently, deep learning-based models have increasingly leveraged graph structures to capture the spatial dynamics of epidemic spread. While intuitive, this approach often increases model complexity, and the resulting performance gains may not justify the added burden. In some cases, it may even lead to overfitting. Moreover, infectious disease data is typically noisy, making it difficult to extract infectious disease-specific dynamics from data without guidance based on epidemiological domain knowledge. To address these issues, we propose a simple yet effective hybrid model for multi-region epidemic forecasting, termed Physics-Informed Spatial IDentity neural network (PISID). This model integrates a spatio-temporal identity (STID)-based neural network module, which encodes spatio-temporal information without relying on graph structures, with an SIR module grounded in classical epidemiological dynamics. Regional characteristics are incorporated via a spatial embedding matrix, and epidemiological parameters are inferred through a fully connected neural network. These parameters are then used to govern the dynamics of the SIR model for forecasting purposes. Experiments on real-world datasets demonstrate that the proposed PISID model achieves stable and superior predictive performance compared to baseline models, with approximately 27K parameters and an average training time of 0.45 seconds per epoch. Additionally, ablation studies validate the effectiveness of the neural network's encoding architecture, and analysis of the decoded epidemiological parameters highlights the model's interpretability. Overall, PISID contributes to reliable epidemic forecasting by integrating data-driven learning with epidemiological domain knowledge.