Quadrature rule based discovery of dynamics by data-driven denoising.

In this paper, we study the discovery of unknown dynamical systems with observed noisy data of the dynamics by neural networks. It is well-known that the performance of the neural network approach is degraded when observed data is noisy, even if the noise level is small. The main contribution of this paper is to propose a new network-based formulation for the dynamics discovery using numerical quadrature rules and to employ a self-supervision network to denoise observed data from the underlying dynamics. Our experimental results show that the performance of the proposed approach is better than that of existing dynamical discovery methods. • Design a neural network method for the discovery of unknown and noisy dynamical systems. • Propose a new quadrature rule. • Consider self-supervised denoising scheme in the network. [ABSTRACT FROM AUTHOR]