Hyperverlet: A Symplectic Hypersolver for Hamiltonian Systems

Frederik Mathiesen, Bin Yang, Jilin Hu

Publikation: Bidrag til bog/antologi/rapport/konference proceedingKonferenceartikel i proceedingForskningpeer review

Abstrakt

Hamiltonian systems represent an important class of dynamical systems such as pendulums, molecular dynamics, and cosmic systems. The choice of solvers is significant to the accuracy when simulating Hamiltonian systems, where symplectic solvers show great significance. Recent advances in neural network-based hypersolvers, though achieve competitive results, still lack the symplecity necessary for reliable simulations, especially over long time horizons. To alleviate this, we introduce Hyperverlet, a new hypersolver composing the traditional, symplectic velocity Verlet and symplectic neural network-based solvers. More specifically, we propose a parameterization of symplectic neural networks and prove that hyperbolic tangent is r-finite expanding the set of allowable activation functions for symplectic neural networks, improving the accuracy. Extensive experiments on a spring-mass and a pendulum system justify the design choices and suggest that Hyperverlet outperforms both traditional solvers and hypersolvers.
OriginalsprogEngelsk
TitelAAAI
Publikationsdato2022
DOI
StatusUdgivet - 2022
BegivenhedThirty-Sixth AAAI Conference on Artificial Intelligence - Virtually
Varighed: 22 feb. 20221 mar. 2022

Konference

KonferenceThirty-Sixth AAAI Conference on Artificial Intelligence
LokationVirtually
Periode22/02/202201/03/2022

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