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

Xingjie Li, Fei Lu, Molei Tao, Felix X.-F. Ye

Abstract: Highlights•Introduce a framework using data to innovate classical numerical integrators.•NySALT are adaptive to large time-stepping and are tailored to each specific system.•NySALT works for both deterministic and stochastic Hamiltonian systems.•NySALT enlarges the maximal admissible step size while maintaining accuracy.•The estimator converges when the number of data trajectories increases.