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

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.

Automated summary

A physics-informed hierarchical echo state network (Pi-HESN) is proposed for predicting the dynamics of chaotic systems. It captures latent evolutionary patterns hidden in the data layer by layer and integrates data and physical laws to ensure physical consistency. Experimental results demonstrate that Pi-HESN outperforms the original ESN and existing hierarchical ESN-based models in accuracy and predictability horizon on four classical chaotic systems.