Physics-enhanced neural networks learn order and chaos
Anshul Choudhary, John F. Lindner, Elliott G. Holliday, Scott T. Miller, Sudeshna Sinha, William L. Ditto
Abstract
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.
Topics & Concepts
Artificial neural networkPhase spaceChaoticHamiltonian (control theory)Nonlinear systemStatistical physicsBenchmark (surveying)Hamiltonian systemHamiltonian mechanicsComputer scienceArtificial intelligencePhysicsMathematicsClassical mechanicsMathematical optimizationQuantum mechanicsGeographyGeodesyModel Reduction and Neural NetworksNeural Networks and ApplicationsComputational Physics and Python Applications