报告题目 Title：Statistical inference for infinite-dimensional non-linear dynamical systems

报告人 Speaker：Richard Nickl

报告人所在单位 Affiliation：University of Cambridge

时间 Time：2026-12-24 10:00-12:00

地点 Venue：Room 2201, Guanghua Eastern Main Tower, Fudan University (Handan Campus)

报告摘要 Abstract：We study optimal statistical inference procedures for the states of time evolution phenomena modelled by partial differential equations in applications to the physical sciences. It is a common algorithmic practice to assign a Gaussian process prior on the initial condition of a dynamical system and to update it to a Bayesian posterior measure in the space of possible trajectories given a discrete sample of the process. In key applications the dynamics are non-linear, such as with 2D Navier-Stokes equations in geophysical sciences or reaction-diffusion equations in biochemistry and population dynamics. While Bayesian posterior distributions are widely computed by filtering or MCMC methods, little is known about the statistical behaviour of these posterior measures in non-linear settings. In this talk we will introduce a theoretical framework for such models and then present recent results, known as `Bernstein-von Mises theorems’, that show that the posterior measures are approximated in function space by the Gaussian laws of solutions to certain SPDEs that involve the inverse Fisher information of the underlying statistical model. We also discuss results about inference when the system has asymptotically equilibrated to its global attractor. The lecture will be targeted at a general mathematical audience.

个人简介 Bio：Richard Nickl is Professor of Mathematical Statistics at the University of Cambridge and a Fellow of Gonville & Caius College. He received his PhD from the University of Vienna in 2005. His research lies at the interface of mathematical statistics, probability and analysis, encompassing nonparametric and Bayesian inference, statistical inverse problems, and the theory of high- and infinite-dimensional statistical models. His recent work develops rigorous foundations for statistical inference and uncertainty quantification in nonlinear dynamical systems governed by partial differential equations. He was an invited speaker at the International Congress of Mathematicians in 2022 and is a recipient of the Bernoulli Society’s Ethel Newbold Prize and European Research Council Consolidator and Advanced Grants. His monograph Mathematical Foundations of Infinite-Dimensional Statistical Models, co-authored with Evarist Giné, received the 2017 PROSE Award in Mathematics.

海报 Poster: Richard Nickl  Distinguished Lecture.jpg