Flow Matching for Posterior Inference with Simulator Feedback

TL;DR

This paper introduces a flow-based method refined with simulator feedback for efficient and accurate inverse problem solving, significantly outperforming classical methods in speed and accuracy.

Contribution

It presents a novel flow matching approach that incorporates simulator feedback during fine-tuning, reducing computational costs while improving inference accuracy.

Findings

Improves inference accuracy by 53%.

Achieves up to 67 times faster inference.

Competitive with traditional MCMC methods.

Abstract

Flow-based generative modeling is a powerful tool for solving inverse problems in physical sciences that can be used for sampling and likelihood evaluation with much lower inference times than traditional methods. We propose to refine flows with additional control signals based on a simulator. Control signals can include gradients and a problem-specific cost function if the simulator is differentiable, or they can be fully learned from the simulator output. In our proposed method, we pretrain the flow network and include feedback from the simulator exclusively for finetuning, therefore requiring only a small amount of additional parameters and compute. We motivate our design choices on several benchmark problems for simulation-based inference and evaluate flow matching with simulator feedback against classical MCMC methods for modeling strong gravitational lens systems, a challenging inverse problem in astronomy. We demonstrate that including feedback from the simulator improves the accuracy by $53\%$, making it competitive with traditional techniques while being up to $67$x faster for inference.