Stochastic Process Learning via Operator Flow Matching

Kamyar Azizzadenesheli (Purdue University) · Yaozhong Shi (California Institute of Technology) · Zachary Ross (California Institute of Technology) · Domniki Asimaki (California Institute of Technology)
arbitrary domainscollection of pointsdensity estimationfunction spacesfunctional regressionmathematical tractabilitymean estimationneural operatorsnovel frameworkoperator flow matchingprior learningprobability densitystate-of-the-art modelsstochastic process learningstochastic process priors

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.