Physics-Informed Echo State Networks for Chaotic Systems Forecasting
This work addresses the problem of accurate time prediction for chaotic dynamical systems, which is crucial for fields like meteorology and engineering, but it is incremental as it builds on existing Echo State Networks by adding physics constraints.
The authors tackled chaotic systems forecasting by proposing a physics-informed Echo State Network that incorporates physical laws into training, resulting in an improvement of the predictability horizon by about two Lyapunov times compared to conventional methods.
We propose a physics-informed Echo State Network (ESN) to predict the evolution of chaotic systems. Compared to conventional ESNs, the physics-informed ESNs are trained to solve supervised learning tasks while ensuring that their predictions do not violate physical laws. This is achieved by introducing an additional loss function during the training of the ESNs, which penalizes non-physical predictions without the need of any additional training data. This approach is demonstrated on a chaotic Lorenz system, where the physics-informed ESNs improve the predictability horizon by about two Lyapunov times as compared to conventional ESNs. The proposed framework shows the potential of using machine learning combined with prior physical knowledge to improve the time-accurate prediction of chaotic dynamical systems.