BIMSA > Seminar on Control Theory and Nonlinear Filtering Backprogation and adjoint differentiation of chaos
Backprogation and adjoint differentiation of chaos
Organizer
Shing Toung Yau
Speaker
Xiuang Ni
Time
Friday, December 29, 2023 9:00 PM - 10:00 PM
Venue
Online
Abstract
Computing the linear response, or the derivative of long-time-averaged observables with respect to system parameters, is a central problem for statistics and engineering. Conventionally, there are three straight-forward formulas for the linear response: the pathwise perturbation (including the backpropagation method), the divergence, and the kernel differentiation formula. We shall explain why none works for the general case, which is typically chaotic, high-dimensional, and small-noise. We present the fast response formula, which is an 'ergodic-theorem' for the linear response of hyperbolic chaos. It is the average of some function of u-many vectors over an orbit, where u is the unstable dimension, and those vectors can be computed recursively. Then we discuss how to further incorporate the kernel differentiation trick to overcome non-hyperbolicity. 主讲人简介： 倪昂修现任丘成桐数学中心助理教授。他2021年毕业于加州大学伯克利分校（导师John Strain），2023年博士后出站于北京大学（导师张平文）。他的主要研究方向为计算动力系统和工程应用，尤其是混沌系统的参数导数计算。