Stochastic Process Learning via Operator Flow Matching

Yaozhong Shi, Zachary E. Ross, Domniki Asimaki, Kamyar Azizzadenesheli
1/7/2025
cs.LG

No official code found. Best implementation: yzshi5/SPL_OFM (23 stars, MIT, last commit 2026-04-26).

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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Code Implementations(1)

yzshi5/SPL_OFMCommunity100%
MIT

[NeurIPS 2025 Spotlight] "Stochastic Process Learning via Operator Flow Matching"

231Python, Jupyter NotebookDec 20, 20245 months agoMIT

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Cite this paper

@article{shi2025stochastic,
  title  = {Stochastic Process Learning via Operator Flow Matching},
  author = {Yaozhong Shi and Zachary E. Ross and Domniki Asimaki and Kamyar Azizzadenesheli},
  year   = {2025},
  eprint = {2501.04126},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2501.04126v3}
}

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