AI 中文总结
本文提出用条件流匹配替代MCMC进行贝叶斯逆问题后验采样，实现摊销快速推断，并给出可计算的精度估计及渐近精确的混合采样器，在数值示例中验证了效果。
AI 中文摘要
从后验分布中采样是计算贝叶斯逆问题的核心任务。贝叶斯推断的标准工具——马尔可夫链蒙特卡洛（MCMC）——是顺序执行的，产生相关样本，并且必须针对每次观测重新运行。条件流匹配提供了一种摊销替代方案：一个传输映射，在参数和数据的联合样本上训练一次，即可为任何观测产生独立的近似后验样本，在线成本可忽略不计，无需新的似然评估。我们对基于PDE的、参数为函数值的逆问题中的流匹配进行了细致的、精通MCMC的评估。利用流的可处理密度，我们推导了底层近似后验在总变差距离和Kullback-Leibler散度方面的可计算精度估计，此外，还提出了一种通过Metropolization实现渐近精确的混合采样器。我们在几个数值示例中验证了精度估计并展示了摊销效果，包括电阻抗断层扫描和免似然的Lotka-Volterra模型。
英文摘要
Sampling from the posterior is the central task of computational Bayesian inverse problems. The standard workhorse in Bayesian inference - Markov chain Monte Carlo (MCMC) - is sequential, yields correlated samples, and must be rerun for each observation. Conditional flow matching offers an amortized alternative: a transport map, trained once on joint samples of parameter and data, that yields independent approximate posterior samples for any observation at negligible online cost, without new likelihood evaluations. We give a careful, MCMC-literate assessment of flow matching for PDE-based inverse problems with function-valued parameters. Exploiting the flow's tractable density, we derive computable accuracy estimates of the underlying approximate posterior in total-variation distance and Kullback-Leibler divergence and, moreover, propose a hybrid sampler that is asymptotically exact by Metropolization. We validate the accuracy estimates and demonstrate the amortization in several numerical examples, including electrical impedance tomography and a likelihood-free Lotka-Volterra model.
Comments38 pages, 18 figures
