Year: 2025
Type: article
Abstract: We derive the ‘fast response’ formula for the linear response, the parameter derivatives of long-time-averaged statistics, of hyperbolic deterministic and chaotic systems. The expression is pointwisely defined, so we can compute the linear response in high-dimensions via Monte-Carlo-type algorithms. This has two parts, where the shadowing contribution is computed by the nonintrusive shadowing algorithm. The unstable contribution is expressed by renormalized second-order tangent equations; importantly, it does not contain any distributional derivatives. The algorithm’s cost is solving u , the unstable dimension, and many first-order and second-order tangent equations along a long orbit; the main error is the sampling error of the orbit. We numerically demonstrate the algorithm on a 21-dimensional example, which is difficult for previous methods.
Author: Angxiu Ni
Institution: University of California, Irvine
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
Awards: G2663722928, G5955288434
OpenAlex ID: W4417423977