Incorporating Coupling Knowledge into Echo State Networks for Learning Spatiotemporally Chaotic Dynamics
This addresses the challenge of high data and model size requirements for chaotic dynamics prediction, offering a physics-informed approach that is incremental but potentially applicable to other ML methods.
The paper tackles the inefficiency of purely data-driven machine learning methods in learning large-scale, spatiotemporally chaotic systems by incorporating spatial coupling structure as an inductive bias into echo state networks, resulting in improved performance and robustness over existing models.
Machine learning methods have shown promise in learning chaotic dynamical systems, enabling model-free short-term prediction and attractor reconstruction. However, when applied to large-scale, spatiotemporally chaotic systems, purely data-driven machine learning methods often suffer from inefficiencies, as they require a large learning model size and a massive amount of training data to achieve acceptable performance. To address this challenge, we incorporate the spatial coupling structure of the target system as an inductive bias in the network design. Specifically, we introduce physics-guided clustered echo state networks, leveraging the efficiency of the echo state networks as a base model. Experimental results on benchmark chaotic systems demonstrate that our physics-informed method outperforms existing echo state network models in learning the target chaotic systems. Additionally, we numerically demonstrate that leveraging coupling knowledge into ESN models can enhance their robustness to variations of training and target system conditions. We further show that our proposed model remains effective even when the coupling knowledge is imperfect or extracted directly from time series data. We believe this approach has the potential to enhance other machine-learning methods.