Fast adjoint differentiation of chaos via computing unstable perturbations of transfer operators

Understand

We devise the fast adjoint response algorithm for the gradient of physical measures (long-time-average statistics) of discrete-time hyperbolic chaos with respect to many system parameters.

• Its cost is independent of the number of parameters.
• The algorithm transforms our new theoretical tools, the adjoint shadowing lemma and the equivariant divergence formula, into the form of progressively computing $u$ many bounded vectors on one orbit.
• Here $u$ is the unstable dimension.