Physics-Informed Echo State Networks
This work addresses the challenge of accurate time prediction for chaotic dynamical systems, such as the Lorenz and Charney-DeVore systems, by integrating prior physical knowledge into machine learning, though it is incremental as it builds on existing ESN methods.
The authors tackled the problem of predicting chaotic systems by proposing a physics-informed Echo State Network (ESN) that incorporates physical laws into training, resulting in an improvement of the predictability horizon by about two Lyapunov times compared to conventional ESNs.
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, which is based on the system's governing equations. The additional loss function penalizes non-physical predictions without the need of any additional training data. This approach is demonstrated on a chaotic Lorenz system and a truncation of the Charney-DeVore system. Compared to the conventional ESNs, the physics-informed ESNs improve the predictability horizon by about two Lyapunov times. This approach is also shown to be robust with regard to noise. 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.