2023/08/15 by Angxiu Ni, Ni, Angxiu
Computer Science · #Computational Physics (physics.comp-ph) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Neural Networks and Applications #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2308.07841
openalex publication_date 2023/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We develop the no-propagate algorithm for sampling the linear response of random dynamical systems, which are non-uniform hyperbolic deterministic systems perturbed by noise with smooth density. We first derive a Monte-Carlo type formula and then the algorithm, which is different from the ensemble (stochastic gradient) algorithms, finite-element algorithms, and fast-response algorithms; it does not involve the propagation of vectors or covectors, and only the density of the noise is differentiated, so the formula is not cursed by gradient explosion, dimensionality, or non-hyperbolicity. We demonstrate our algorithm on a tent map perturbed by noise and a chaotic neural network with 51 layers × 9 neurons. By itself, this algorithm approximates the linear response of non-hyperbolic deterministic systems, with an additional error proportional to the noise. We also discuss the potential of using this algorithm as a part of a bigger algorithm with smaller error.