Hyperverlet: A Symplectic Hypersolver for Hamiltonian Systems

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