Stochastic Process Learning via Operator Flow Matching

ICLR 2025 Conference Submission12485 Authors

Keywords: Neural Operator, Flow Matching, Stochastic Process, Uncertainty Quantification

Abstract: Using neural operators, we propose a novel framework for stochastic process learning across arbitrary domains. In particular, we develop operator flow matching for learning stochastic process priors on function spaces. Operator flow matching provides the probability density of any finite 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 at stochastic process learning, functional regression, and prior learning.

Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)

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Submission Number: 12485