Fast Adjoint Algorithm for Linear Responses of Hyperbolic Chaos.

We develop an algorithm for the equivariant divergence formula of the unstable perturbation of unstable transfer operators, by progressively computing 2u many bounded vectors or covectors on one orbit, where u is the unstable dimension. Combining this with the nonintrusive adjoint shadowing algorithm, we obtain the fast adjoint response algorithm for the linear responses on physical measures of discrete-time uniformly hyperbolic systems. The cost is independent of the number of parameters. We demonstrate our algorithm on a 21-dimensional chaotic system, a system with stochastic noise, and systems with discontinuities. Unlike previous methods, our algorithms are not cursed by dimensionality or the sensitive dependence on initial conditions. [ABSTRACT FROM AUTHOR]