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

01/04/2018
by   Maziar Raissi, et al.
0

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

READ FULL TEXT

page 1

page 2

page 3

page 4

research
01/20/2018

Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations

A long-standing problem at the interface of artificial intelligence and ...
research
08/22/2017

Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systems

The Koopman operator has recently garnered much attention for its value ...
research
12/14/2021

Learn bifurcations of nonlinear parametric systems via equation-driven neural networks

Nonlinear parametric systems have been widely used in modeling nonlinear...
research
05/31/2018

Long-time predictive modeling of nonlinear dynamical systems using neural networks

We study the use of feedforward neural networks (FNN) to develop models ...
research
02/09/2021

On the Universal Transformation of Data-Driven Models to Control Systems

As in almost every other branch of science, the major advances in data s...
research
05/25/2022

Learning dynamics from partial observations with structured neural ODEs

Identifying dynamical systems from experimental data is a notably diffic...
research
09/25/2018

Automated, predictive, and interpretable inference of C. elegans escape dynamics

The roundworm C. elegans exhibits robust escape behavior in response to ...

Please sign up or login with your details

Forgot password? Click here to reset