用Transformer加速贝叶斯反问题推断，精度高且快2000倍。
Bayesian Inverse Problems Meet Flow Matching: Efficient and Flexible Inference via Transformers
- 结合流匹配与Transformer，直接学习条件概率轨迹。
- 参数恢复相对误差低至1.5%，推理速度提升2000倍。
- 适合需要快速高精度推断的科学建模场景。
贝叶斯反问题的高效求解仍受传统采样方法计算成本高的制约。本文提出一种新框架，将条件流匹配（Conditional Flow Matching, CFM）与基于Transformer的架构结合，实现从复杂后验分布中快速灵活采样。该方法直接从数据中学习条件概率轨迹，利用CFM避免迭代模拟、Transformer处理任意数量观测的能力。在三个任务上验证：简单非线性模型、疾病动力学框架、二维达西流偏微分方程。结果表明，参数恢复的相对误差最低达1.5%，且在CPU上推理时间相比蒙特卡洛马尔可夫链（MCMC）最多减少2000倍。该框架通过学习后的条件分布采样，实现了贝叶斯问题的高效求解。
原文摘要 · Abstract (English)
The efficient resolution of Bayesian inverse problems remains challenging due to the high computational cost of traditional sampling methods. In this paper, we propose a novel framework that integrates Conditional Flow Matching (CFM) with a transformer-based architecture to enable fast and flexible sampling from complex posterior distributions. The proposed methodology involves the direct learning of conditional probability trajectories from the data, leveraging CFM's ability to bypass iterative simulation and transformers' capacity to process arbitrary numbers of observations. The efficacy of the proposed framework is demonstrated through its application to three problems: a simple nonlinear model, a disease dynamics framework, and a two-dimensional Darcy flow Partial Differential Equation. The primary outcomes demonstrate that the relative errors in parameters recovery are as low as 1.5%, and that the inference time is reduced by up to 2000 times on CPU in comparison with the Monte Carlo Markov Chain. This framework facilitates the expeditious resolution of Bayesian problems through the utilisation of sampling from the learned conditional distribution.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。