报告题目：Preconditioned one-step generative modelling for Bayesian inverse problems

摘要：We propose a machine-learning algorithm for Bayesian inverse problems in the function-space regime based on one-step generative transport. Building on the Mean Flows, we learn a fully conditional amortized sampler with a neural-operator backbone that maps a reference Gaussian noise to approximate posterior samples. We show that while white-noise references may be admissible at fixed discretization, they become incompatible with the function-space limit, leading to instability in inference for Bayesian problems arising from PDEs. To address this issue, we adopt a prior-aligned anisotropic Gaussian reference distribution and establish the Lipschitz regularity of the resulting transport. Our method is not distilled from MCMC: training relies only on prior samples and simulated partial and noisy observations. Once trained, it generates a 64x64 posterior sample in ∼1e-3s, avoiding the repeated PDE solves of MCMC while matching key posterior summaries.

报告人简介：王中剑，新加坡南洋理工大学助理教授。2016年本科毕业于清华大学，2020年博士毕业于香港大学，2020-2023年在美国芝加哥大学担任William H. Kruskal Instructor，现阶段主要研究方向为生成模型、降阶方法以及偏微分方程计算中的粒子方法。在SINUM、SISC、JCP、IP、IEEE TAC、ICLR、ICML等国际高水平刊物上发表论文多篇。

报告时间及地点：2026年7月14日 15：00；理学楼609