Automatic-differentiated Physics-Informed Echo State Network (API-ESN)
This work addresses the problem of inaccurate time-derivative computation in existing physics-informed echo state networks, which is a significant issue for researchers working with chaotic dynamical systems.
The paper introduces the Automatic-differentiated Physics-Informed Echo State Network (API-ESN) which uses automatic differentiation to compute the exact time-derivative of the reservoir, thereby increasing the accuracy of the time-derivative by up to seven orders of magnitude compared to the original Physics-Informed Echo State Network. This enhanced accuracy is crucial for reconstructing unmeasured states in chaotic dynamical systems.
We propose the Automatic-differentiated Physics-Informed Echo State Network (API-ESN). The network is constrained by the physical equations through the reservoir's exact time-derivative, which is computed by automatic differentiation. As compared to the original Physics-Informed Echo State Network, the accuracy of the time-derivative is increased by up to seven orders of magnitude. This increased accuracy is key in chaotic dynamical systems, where errors grows exponentially in time. The network is showcased in the reconstruction of unmeasured (hidden) states of a chaotic system. The API-ESN eliminates a source of error, which is present in existing physics-informed echo state networks, in the computation of the time-derivative. This opens up new possibilities for an accurate reconstruction of chaotic dynamical states.