PIMRL: Physics-Informed Multi-Scale Recurrent Learning for Spatiotemporal Prediction
This addresses the computational cost and robustness issues in spatiotemporal simulation for fields like biology and meteorology, but it is incremental as it builds on existing physics-informed and multi-scale learning approaches.
The paper tackled the problem of long-term spatiotemporal prediction in systems governed by partial differential equations, where error accumulation and insufficient data compromise stability and accuracy, and achieved state-of-the-art performance with average improvements of over 9% in RMSE and MAE across five benchmark datasets.
Simulation of spatiotemporal systems governed by partial differential equations is widely applied in fields such as biology, chemistry, aerospace dynamics, and meteorology. Traditional numerical methods incur high computational costs due to the requirement of small time steps for accurate predictions. While machine learning has reduced these costs, long-term predictions remain challenged by error accumulation, particularly in scenarios with insufficient data or varying time scales, where stability and accuracy are compromised. Existing methods often neglect the effective utilization of multi-scale data, leading to suboptimal robustness in predictions. To address these issues, we propose a novel multi-scale learning framework, namely, the Physics-Informed Multi-Scale Recurrent Learning (PIMRL), to effectively leverage multi-scale data for spatiotemporal dynamics prediction. The PIMRL framework comprises two modules: the micro-scale module embeds physical knowledge into neural networks via pretraining, and the macro-scale module adopts a data-driven approach to learn the temporal evolution of physics in the latent space. Experimental results demonstrate that the PIMRL framework consistently achieves state-of-the-art performance across five benchmark datasets ranging from one to three dimensions, showing average improvements of over 9\% in both RMSE and MAE evaluation metrics, with maximum enhancements reaching up to 80%.