Sensitivity analysis on chaotic dynamical systems by Non-Intrusive Least Squares Adjoint Shadowing (NILSAS).
This paper develops the Non-Intrusive Least Squares Adjoint Shadowing (NILSAS) algorithm, which computes the gradient for long-time averaged objectives in chaotic dynamical systems. The computational cost of NILSAS scales with the number of unstable adjoint directions and the number of objectives, but is independent of the number of parameters. For developing the algorithm, we first prove several properties of the adjoint flow. Based on properties of the adjoint flow, we derive the adjoint shadowing direction. Finally, we approximate the adjoint shadowing direction by a `non-intrusive' formulation of a least squares problem: this formulation not only allows NILSAS be implemented with little modification to existing adjoint solvers, but also allows NILSAS to constrain the minimization to over only the unstable adjoint directions. Finally, we demonstrate NILSAS on the Lorenz 63 system.
Publisher URL: http://arxiv.org/abs/1801.08674