Adjoint sensitivity analysis on chaotic dynamical systems by Non-Intrusive Least Squares Adjoint Shadowing (NILSAS)

We develop the NILSAS algorithm, which performs adjoint sensitivity analysis of chaotic systems via computing the adjoint shadowing direction. NILSAS constrains its minimization to the adjoint unstable subspace, and can be implemented with little modification to existing adjoint solvers. The computational cost of NILSAS is independent of the number of parameters. We demonstrate NILSAS on the Lorenz 63 system and a weakly turbulent three-dimensional flow over a cylinder.
Comment: 34 pages, 11 figures. The adjoint shadowing direction which we compute is defined at arXiv:1807.05568