Stochastic Process Learning via Operator Flow Matching
This addresses the challenge of stochastic process learning for applications in functional data analysis, though it appears incremental as an extension of neural operators.
The paper tackles the problem of learning stochastic process priors on function spaces by proposing operator flow matching (OFM), which provides probability densities for point collections and enables functional regression with mean and density estimation, outperforming state-of-the-art models in these tasks.
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.