Stochastic Process Learning via Operator Flow Matching

2025-01-07

AI Summary

This work addresses modeling stochastic processes over arbitrary domains, unifying core tasks including event probability computation, predictive inference of function values at new points, and estimation of statistical quantities (e.g., mean, likelihood). To this end, we propose Operator Flow Matching (OFM), the first flow-matching framework extended to the operator level: it learns stochastic process priors directly in function space, enabling joint density evaluation over arbitrary finite point sets and differentiable functional regression. OFM integrates neural operators with continuous-time probabilistic flow modeling, yielding strictly mathematically differentiable functional inference. Experiments demonstrate that OFM consistently outperforms state-of-the-art methods across three fundamental stochastic process learning tasks: density estimation, functional regression, and prior modeling.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Probabilistic Circuits and Graphical Models
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Expanding on neural operators, we propose a novel framework for stochastic process learning across arbitrary domains. In particular, we develop operator flow matching (alg) for learning stochastic process priors on function spaces. alg 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.

Problem

• Stochastic Processes
• Event Prediction
• Probability Calculation

Innovation

• Operator Flow Matching
• Neural Operators
• Stochastic Event Learning