arXiv：cs.LG· Jan Blechschmidt, Oliver G. Ernst, Moritz Poguntke, Bj\"orn Sprungk·· 3 小时前AI 评分36
Flow Matching 如何实现贝叶斯逆问题的快速后验采样
Flow Matching for Fast Posterior Sampling in Bayesian Inverse Problems
AI 导读
针对 PDE 逆问题中函数值参数的后验采样，研究提出用条件 Flow Matching 训练一次传输映射，即可对任意观测以可忽略的在线成本生成独立近似后验样本，无需重新评估似然。
正文
Abstract: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.
| Comments: | 38 pages, 18 figures |
| Subjects: | Numerical Analysis (math.NA); Machine Learning (cs.LG); Computation (stat.CO) |
| MSC classes: | 65C05, 62F15, 65C20, 35R30 |
| Cite as: | arXiv:2610.02377 [math.NA] |
| (or arXiv:2610.02377v1 [math.NA] for this version) | |
| https://doi.org/10.48550/arXiv.2610.02377 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Bjoern Sprungk [view email]
[v1]
Thu, 1 Oct 2026 18:58:36 UTC (7,444 KB)
来源：arXiv：cs.LG · arxiv.org