Stochastic Process Learning via Operator Flow Matching

TL;DR

This paper introduces Operator Flow Matching (OFM), a new framework for learning stochastic process priors on function spaces, enabling accurate density estimation and functional regression across arbitrary domains.

Contribution

The paper presents OFM, a novel operator flow matching approach that advances stochastic process learning by providing tractable density estimation and functional regression capabilities.

Findings

OFM outperforms existing models in stochastic process learning.

OFM enables functional regression with mean and density estimation.

The method is applicable across arbitrary domains.

Abstract

Expanding on neural operators, we propose a novel framework for stochastic process learning across arbitrary domains. In particular, we develop operator flow matching (OFM) for learning stochastic process priors on function spaces. OFM provides the probability density of the values of any collection of points and enables mathematically tractable functional regression at new points with mean and density estimation. Our method outperforms state-of-the-art models in stochastic process learning, functional regression, and prior learning.