Sensitivity analysis on chaotic dynamical system by Non-Intrusive Least Square Shadowing (NILSS)

TL;DR

This paper introduces a non-intrusive Least-squares Shadowing (NILSS) method for efficiently computing sensitivities in chaotic dynamical systems, reducing computational costs by focusing on unstable subspaces and requiring minimal modifications to existing solvers.

Contribution

The paper presents a novel non-intrusive formulation of LSS that simplifies implementation and reduces computational effort in sensitivity analysis of chaotic systems.

Findings

NILSS effectively computes sensitivities in chaotic flow simulations.

The method significantly reduces computational cost compared to traditional LSS.

Demonstrated on a chaotic flow over a backward-facing step with promising results.

Abstract

This paper develops the non-intrusive formulation of the Least-squares shadowing (LSS) method, for computing the sensitivity of long-time averaged objectives in chaotic dynamical systems. This non-intrusive formulation constrains the computation to only the unstable subspace, greatly reducing the cost of LSS for many problems; moreover, it reparametrizes the LSS problem, requiring only minor modifications to existing tangent solvers. NILSS is demonstrated on a chaotic flow over a backward-facing step simulated with a mesh of 12e3 cells.