Learning SDE Solutions with Neural Stochastic Flows

Naoki Kiyohara, Edward Johns, Yingzhen Li

Keywords: Neural Stochastic Differential Equations, Neural Ordinary Differential Equations, Stochastic Flows, Irregular Time Series Data

TL;DR: A novel model for learning solutions of stochastic differential equations, allowing one-step sampling and conditional probability density estimation.

Abstract:

We introduce neural stochastic flows, a novel framework for learning solutions of stochastic differential equations (SDEs). It addresses the challenge of simulating neural SDEs by directly learning the weak solution of the underlying SDE governing the data generation process.
Key to our approach is the introduction of a flow-based, time-dependent neural network to directly compute the conditional probability densities of its associated SDE at any time interval. Unlike neural SDEs, neural stochastic flows avoid time-consuming simulations of SDE solvers and enable single-step sampling from the learnt stochastic process. Our work contributes to stochastic process modelling, offering a flexible method that has the potential to improve computational efficiency in various applications.

Submission Number: 2