Flow Matching for Posterior Inference with Simulator Feedback
This work addresses simulation-based inference problems, such as modeling gravitational lens systems in astronomy, by providing a more efficient and accurate method, though it is incremental as it builds on existing flow-based techniques.
The paper tackled the challenge of solving inverse problems in physical sciences by refining flow-based generative models with simulator feedback, achieving a 53% improvement in accuracy and being up to 67 times faster than traditional methods like MCMC.
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.