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- W4385890331 abstract "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 $times$ 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." @default.
- W4385890331 created "2023-08-17" @default.
- W4385890331 creator A5043322188 @default.
- W4385890331 date "2023-08-15" @default.
- W4385890331 modified "2023-10-16" @default.
- W4385890331 title "No-propagate algorithm for linear responses of random chaotic systems" @default.
- W4385890331 doi "https://doi.org/10.48550/arxiv.2308.07841" @default.
- W4385890331 hasPublicationYear "2023" @default.
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