姜立建 教授（同济大学）

于海军(AMSS 研究员), 翟佳羽(上海科技大学), 廖奇峰(上海科技大学)

Transfer Operators and Transport Maps for Bayesian Filtering

10月26日 (周一) 15:10-16:10，腾讯会议：602-613-835

Bayesian filtering is essential for state estimation and uncertainty quantification in stochastic dynamical systems. In this talk, I will present several approaches to nonlinear Bayesian filtering based on transfer operators and probability transport. First, we introduce a Perron–Frobenius operator filter for characterizing probability distribution evolution and Bayesian updates. Next, we develop an ensemble transport filter based on maximum mean discrepancy (MMD) optimization. Finally, we present a coupling-informed transport filtering framework that exploits the dependence between state and observation variables. These methods provide complementary perspectives and computational tools for nonlinear and non-Gaussian Bayesian filtering.

报告人简介：姜立建，同济大学教授，主要研究方向包括多尺度计算方法、数据驱动建模和数据同化。Texas A&M 大学数学博士，曾在明尼苏达大学 IMA、LANL 国家实验室从事博士后研究，并在油服公司担任首席科学家，国家青年人才计划入选者，主持多项国家自然科学基金项目；担任 JCAM、JCMDS 等多个期刊编委。

注：本报告由数学科学全国重点实验室开放课题SLMS-2025-KFKT-TD-11组织。