Stochastic Process Learning via Operator Flow Matching

• URL: http://arxiv.org/abs/2501.04126v2
• Date: Thu, 09 Jan 2025 02:20:28 GMT
• Title: Stochastic Process Learning via Operator Flow Matching
• Authors: Yaozhong Shi, Zachary E. Ross, Domniki Asimaki, Kamyar Azizzadenesheli,
• Abstract summary: We develop operator flow matching (OFM) for learning process priors on function spaces. OFM provides the probability density of the values of any collection of points. Our method outperforms state-of-the-art models in process learning, functional regression, and prior learning.
• Score: 12.275587079383603
• License:
• 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.

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