Neural Stochastic Flows: Solver-Free Modelling and Inference for SDE Solutions

TL;DR

Neural Stochastic Flows (NSFs) provide a fast, direct method for sampling from SDEs without numerical solvers, maintaining accuracy while significantly reducing computation time.

Contribution

Introduction of Neural Stochastic Flows that learn SDE transition laws with normalising flows, enabling one-shot sampling and speed-ups over traditional numerical methods.

Findings

NSFs achieve up to 100x faster sampling for large time gaps.

NSFs maintain distributional accuracy comparable to numerical solvers.

Effective on synthetic and real-world data, including video tracking.

Abstract

Stochastic differential equations (SDEs) are well suited to modelling noisy and irregularly sampled time series found in finance, physics, and machine learning. Traditional approaches require costly numerical solvers to sample between arbitrary time points. We introduce Neural Stochastic Flows (NSFs) and their latent variants, which directly learn (latent) SDE transition laws using conditional normalising flows with architectural constraints that preserve properties inherited from stochastic flows. This enables one-shot sampling between arbitrary states and yields up to two orders of magnitude speed-ups at large time gaps. Experiments on synthetic SDE simulations and on real-world tracking and video data show that NSFs maintain distributional accuracy comparable to numerical approaches while dramatically reducing computation for arbitrary time-point sampling.