Physical knowledge improves historic data forecasting of groundwater levels
Physical knowledge on historical data matters more than enforcing physical constraints on the forecast
Artificial Intelligence
Summary
Forecasting things that depend on physical processes, like groundwater levels, is hard because some important parts can't be measured directly. The authors created a new method that predicts these hidden physical variables alongside the usual forecast, using knowledge about how the physical process works. This makes their predictions more reliable and easier to understand. They tested their approach on real groundwater data and found it often works better than other models, and experts confirmed the predictions make physical sense.
What this means in practice
- •For environmental modelers: Predict groundwater levels more accurately by integrating historic data with physical knowledge of subsurface water flows.
- •For water resource managers: Use forecasts with interpretable physical variables to improve decision-making about water supply and conservation.
Authors
Etienne Lehembre, Pascal Audigane, Vincent Nguyen, Christel Vrain, Thi-Bich-Hanh Dao
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.