Stochastic Process Learning via Operator Flow Matching

Yaozhong Shi, Zachary E Ross, Domniki Asimaki, Kamyar Azizzadenesheli

Keywords: Operator Learning, Fourier Neural Operator, Bayesian Methods, Gaussian Process, AI for Science

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.

Primary Area: Machine learning for sciences (e.g. climate, health, life sciences, physics, social sciences)

Submission Number: 7415