发表机构
Université d’Orléans; INSA CVL; BRGM（奥尔良大学; INSA中央-卢瓦尔河谷; 法国地质调查局）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出物理信息循环神经网络（PIRNN），在预测目标时同时估计不可观测物理变量，利用物理知识增强鲁棒性和可解释性，在12个真实数据集上5个优于其他模型，表明历史物理知识比强制约束更重要。
AI 中文摘要
随着新型深度学习模型的出现，时间序列预测取得了显著进展。然而，在涉及物理过程的应用中对时间序列进行预测仍然是一个重大挑战。尽管物理信息神经网络（PINN）已经出现，但最近的模型并不估计不可观测的中间物理变量，而这些变量对于领域专家理解目标行为非常重要。为此，我们提出了一种物理信息循环神经网络（PIRNN），该网络在预测目标的同时，在历史数据和预测目标上预测不可观测变量。这种方法利用领域知识增强了模型的鲁棒性和结果的可解释性。我们的方法易于适应任何使用多个方程（每个方程具有自己的一组不可观测变量）来描述自身的物理模型。作为案例研究，我们整合了物理模型Gardenia用于地下水位预测的物理方程。该模型使用水库之间的传递方程，并通过数据同化进行优化，以模拟地下水位的演变。评估包括几个著名的神经网络模型和Gardenia模型在十二个真实世界数据集上的比较。此外，我们通过消融研究来研究每个组件的影响。我们的模型在十二个数据集中的五个上优于其他模型，我们的消融研究强调了在我们的时间序列预测任务中具有物理背景的重要性。最后，领域专家评估了我们的神经网络预测的物理变量的一致性。
英文摘要
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.
