Physics-informed hierarchical echo state network for predicting the dynamics of chaotic systems

Abstract

Echo state network (ESN), a type of special recurrent neural network, has gained attention for its simplicity and low computational cost, making it commonly used for data-driven prediction of complex dynamical systems. However, in cases of insufficient or poor-quality data, data-driven approaches can suffer from low prediction accuracy caused by overfitting. To address this problem, a physics-informed hierarchical echo state network (Pi-HESN) is proposed for predicting the dynamics of chaotic systems. Firstly, the Pi-HESN can capture the latent evolutionary patterns hidden in the dynamical systems by processing data layer by layer in stacked reservoirs. Secondly, the Pi-HESN integrates data and physical laws in a unified way, incorporating prior physical knowledge into the objective function to ensure basic physical principles are respected. The combination of data-based and knowledge-based approaches in Pi-HESN improves model generalization, alleviates the shortage of training data, and ensures physical consistency of results. Experiments on four classical chaotic systems illustrate that the proposed Pi-HESN outperforms the original ESN and existing hierarchical ESN-based models in accuracy and predictability horizon.