[2603.14135] Conditional flow matching for physics-constrained inverse problems with finite training data

Statistics > Machine Learning arXiv:2603.14135 (stat) [Submitted on 14 Mar 2026 (v1), last revised 8 Apr 2026 (this version, v3)] Title:Conditional flow matching for physics-constrained inverse problems with finite training data Authors:Agnimitra Dasgupta, Ali Fardisi, Mehrnegar Aminy, Brianna Binder, Bryan Shaddy, Saeed Moazami, Assad Oberai View a PDF of the paper titled Conditional flow matching for physics-constrained inverse problems with finite training data, by Agnimitra Dasgupta and Ali Fardisi and Mehrnegar Aminy and Brianna Binder and Bryan Shaddy and Saeed Moazami and Assad Oberai View PDF HTML (experimental) Abstract:This study presents a conditional flow matching framework for solving physics-constrained Bayesian inverse problems. In this setting, samples from the joint distribution of inferred variables and measurements are assumed available, while explicit evaluation of the prior and likelihood densities is not required. We derive a simple and self-contained formulation of both the unconditional and conditional flow matching algorithms, tailored specifically to inverse problems. In the conditional setting, a neural network is trained to learn the velocity field of a probability flow ordinary differential equation that transports samples from a chosen source distribution directly to the posterior distribution conditioned on observed measurements. This black-box formulation accommodates nonlinear, high-dimensional, and potentially non-differentiable forward mo...