Sparse Weak-Form Discovery of Stochastic Generators

arXiv:2603.20904v4 Announce Type: replace-cross Abstract: We propose a novel data-driven algorithm for the sparsimonious symbolic discovery of stochastic differential equations (SDEs). The central novelty of our approach lies in extending the Weak-formulation framework to stochastic SINDy, which explicitly avoids computing noisy finite-difference derivative estimates that arise in Kramers-Moyal-based formulations, thus improving robustness in the presence of stochasticity and measurement noise. We further show that the introduction of spatial Gaussian test functions in place of conventional temporal test functions for the Weak-formulation problem preserves unbiasedness in expectation and mitigates the structural regression bias that commonly emerges in temporal test-function approaches. We validate the algorithm on three standard stochastic systems, for which we recover all active non-linear terms with coefficient errors below 4%, stationary-density total-variation distances below 0.01, and autocorrelation functions that reproduce true relaxation timescales across all three benchmarks faithfully.