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

TL;DR

This paper introduces NILSAS, a novel algorithm for adjoint sensitivity analysis of chaotic systems that is efficient, easy to implement, and applicable to complex turbulent flows.

Contribution

The paper presents NILSAS, a new non-intrusive method that computes sensitivities in chaotic systems by focusing on the unstable subspace, with cost independent of parameter count.

Findings

Successfully applied to Lorenz 63 system

Effective on turbulent flow over a cylinder

Computational cost remains constant with parameter number

Abstract

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.