ISALT: Inference-based schemes adaptive to large time-stepping for locally Lipschitz ergodic systems

<p style='text-indent:20px;'>Efficient simulation of SDEs is essential in many applications, particularly for ergodic systems that demand efficient both short-time dynamics and large-time statistics. However, locally Lipschitz often require special treatments such as implicit schemes with small time-steps to accurately simulate the measures. We introduce a framework construct inference-based adaptive large (ISALT) from data, achieving reduction time by several orders magnitudes. The key statistical learning an approximation infinite-dimensional discrete-time flow map. explore use numerical (such Euler-Maruyama, hybrid RK4, scheme) derive informed basis functions, leading parameter inference problem. scalable algorithm estimate parameters least squares, we prove convergence estimators data size increases.</p><p style='text-indent:20px;'>We test ISALT on three non-globally SDEs: 1D double-well potential, 2D multiscale gradient system, 3D stochastic Lorenz equation degenerate noise. Numerical results show can tolerate time-step magnitudes larger than plain schemes. It reaches optimal accuracy reproducing invariant measure when medium-large.</p>