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.

翻译：基于流的生成建模是解决物理科学中逆问题的强大工具，可用于采样和似然评估，其推断时间远低于传统方法。我们提出利用基于模拟器的附加控制信号来优化流模型。若模拟器可微分，控制信号可包含梯度及问题特定的代价函数；若不可微分，则可完全从模拟器输出中学习控制信号。在所提方法中，我们预训练流网络，并仅在微调阶段引入模拟器反馈，因此仅需少量额外参数与计算量。我们通过多个基于模拟推断的基准问题论证设计选择的合理性，并在强引力透镜系统建模（天文学中的挑战性逆问题）中，将带模拟器反馈的流匹配方法与经典MCMC方法进行对比评估。实验表明，引入模拟器反馈可将精度提升53%，使其在达到与传统技术相当性能的同时，推断速度最高提升67倍。