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

Naoki Kiyohara, Edward Johns, Yingzhen Li

Keywords: Neural stochastic flows, stochastic differential equations, normalising flows, continuous-time models, latent dynamics, time series modelling

TL;DR: A solver-free approach for modelling stochastic differential equations using conditional normalising flows that enables direct sampling between arbitrary time points within trained horizon.

Abstract: Stochastic differential equations (SDEs) are well suited to modelling noisy and/or irregularly-sampled time series, which are omnipresent in finance, physics, and machine learning applications. Traditional approaches require costly simulation of numerical solvers when sampling between arbitrary time points. We introduce Neural Stochastic Flows (NSFs) and their latent dynamic versions, which learns (latent) SDE transition laws directly using conditional normalising flows, with architectural constraints that preserve properties inherited from stochastic flow. This enables sampling between arbitrary states in a single step, providing up to two orders of magnitude speedup for distant time points. Experiments on synthetic SDE simulations and real-world tracking and video data demonstrate that NSF maintains distributional accuracy comparable to numerical approaches while dramatically reducing computation for arbitrary time-point sampling, enabling applications where numerical solvers remain prohibitively expensive.

Primary Area: Probabilistic methods (e.g., variational inference, causal inference, Gaussian processes)

Submission Number: 3660