NySALT: Nyström-type inference-based schemes adaptive to large time-stepping

Large time-stepping is important for efficient long-time simulations of deterministic and stochastic Hamiltonian dynamical systems. Conventional structure-preserving integrators, while being successful generic systems, have limited tolerance to time step size due stability accuracy constraints. We propose use data innovate classical integrators so that they can be adaptive large are tailored each specific system. In particular, we introduce NySALT, Nystr\"{o}m-type inference-based schemes time-stepping. The NySALT has optimal parameters learnt from by minimizing the one-step prediction error. Thus, it system achieve performance tolerate in an fashion. prove numerically verify convergence estimators as increases. Furthermore, analysis numerical tests on Fermi-Pasta-Ulam (FPU) models show enlarges maximal admissible linear stability, quadruples St\"{o}rmer--Verlet BAOAB when maintaining similar levels accuracy.