Toward the Fully Physics-Informed Echo State Network -- an ODE Approximator Based on Recurrent Artificial Neurons

Abstract: Inspired by recent theoretical arguments, physics-informed echo state network (ESN) is discussed on the attempt to train a reservoir model absolutely in physics-informed manner. As the plainest work on such a purpose, an ODE (ordinary differential equation) approximator is designed to replicate the solution in sequence with respect to the recurrent evaluations. On the principal invariance of differential equations, the constraint in recurrence just takes shape to secure a proper regression method for the ESN-based ODE approximator. After then, the actual training process is established on the idea of two-pass strategy for regression. Aiming at the fully physics-informed reservoir model, a couple of nonlinear dynamical problems are demonstrated as the computations obtained from the proposed method in this study.