Abstract
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.
Original language | English |
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Title of host publication | Proceedings of the AAAI Conference on Artificial Intelligence |
Publisher | AAAI Publications |
Publication date | 2022 |
Pages | 4575-4582 |
DOIs | |
Publication status | Published - 2022 |
Event | Thirty-Sixth AAAI Conference on Artificial Intelligence - Virtually Duration: 22 Feb 2022 → 1 Mar 2022 |
Conference
Conference | Thirty-Sixth AAAI Conference on Artificial Intelligence |
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Location | Virtually |
Period | 22/02/2022 → 01/03/2022 |