Physical knowledge on historical data matters more than enforcing physical constraints on the forecast

2026-09-17

AI Summary

本文针对物理过程时间序列预测难题，提出了一种物理信息循环神经网络(PIRNN)，该方法结合历史数据和物理约束来预测目标及不可观测的中间变量。

Abstract

Time series forecasting has seen signicant advancements with the emergence of new deep learning models. However, forecasting time series in applications involving physical processes remains a major challenge. Despite the apparition of Physics Informed Neural Networks (PINN), recent models do not estimate unobservable intermediate physical variables, which are important for domain experts to understand the target behavior. To this end, we propose a Physics Informed Recurrent Neural Network (PIRNN) which predicts, along the target, unobservable variables on both historic data and forecast target. This approach enhances the model robustness and results interpretation using domain knowledge. Our method is easily adaptable to any physical model using several equations, each having its own set of unobservable variables, to describe it-self. As a case study, we incorporate physical equations used for groundwater levels predictions by the physical model called Gardenia. This model uses transfers equations between reservoirs, optimized with data assimilation, to simulate the evolution of groundwater levels. Evaluation includes several well known neural network models and the Gardenia model compared on twelve real world datasets. In addition, we study the impact of each component through an ablation study. Our model outperforms other models on ve out of the twelve datasets and our ablation study underlines the importance of having a physical background in our time series forecasting task. Finally, the coherence of the physical variables predicted by our neural network is assessed by a domain expert.

Problem

• time series forecasting
• physical processes
• unobservable variables
• Physics Informed Neural Networks
• domain experts

Innovation

• Physics Informed Recurrent Neural Network
• unobservable variables
• domain knowledge
• robustness
• time series forecasting