2020 journal article

Physics-enhanced neural networks learn order and chaos

Physical Review E.

By: A. Choudhary  n, J. Lindner  n, E. Holliday n, S. Miller  n, S. Sinha  n & W. Ditto n 

TL;DR: This work uses neural networks that incorporate Hamiltonian dynamics to efficiently learn phase space orbits even as nonlinear systems transition from order to chaos. (via Semantic Scholar)
Source: ORCID
Added: June 19, 2020

Artificial neural networks are universal function approximators. They can forecast dynamics, but they may need impractically many neurons to do so, especially if the dynamics is chaotic. We use neural networks that incorporate Hamiltonian dynamics to efficiently learn phase space orbits even as nonlinear systems transition from order to chaos. We demonstrate Hamiltonian neural networks on a widely used dynamics benchmark, the Hénon-Heiles potential, and on nonperturbative dynamical billiards. We introspect to elucidate the Hamiltonian neural network forecasting.