- 控制理论和非线性滤波讨论班

Backprogation and adjoint differentiation of chaos

组织者

丘成栋

演讲者

倪昂修

时间

2023年12月29日 21:00 至 22:00

地点

Online

摘要

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。