Hyperverlet: A Symplectic Hypersolver for Hamiltonian Systems
Frederik Baymler Mathiesen, Bin Yang, Jilin Hu
[AAAI-22] Main Track
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.
Introduction Video
Sessions where this paper appears
-
Poster Session 1
Thu, February 24 4:45 PM - 6:30 PM (+00:00)
Red 2
-
Poster Session 10
Sun, February 27 4:45 PM - 6:30 PM (+00:00)
Red 2
-
Oral Session 1
Thu, February 24 6:30 PM - 7:45 PM (+00:00)
Red 2