Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systems

The process of transforming observed data into predictive mathematical models the physical world has always been paramount in science and engineering. data is currently being collected at an ever-increasing pace, devising models out of such observations in an automated fashion still an open problem. In this work, we put forth a machine learning approach identifying nonlinear dynamical systems from data. Specifically, we blend tools from numerical analysis, namely the multi-step time-stepping, with powerful nonlinear function approximators, namely deep neural, to distill the mechanisms that govern the evolution of a given-set. We test the effectiveness of our approach for several benchmark involving the identification of complex, nonlinear and chaotic, and we demonstrate how this allows us to accurately learn the, forecast future states, and identify basins of attraction. In, we study the Lorenz system, the fluid flow behind a cylinder, the bifurcation, and the Glycoltic oscillator model as an example of nonlinear dynamics typical of biological systems.