# Multiple Shooting Shadowing for Sensitivity Analysis of Chaotic Dynamical Systems

## TL;DR

This paper introduces multiple shooting shadowing (MSS), a more efficient method for sensitivity analysis in chaotic systems, reducing computational costs compared to the least squares shadowing (LSS) approach.

## Contribution

The paper proposes MSS, an improved shadowing method that enhances computational efficiency and reduces memory usage for sensitivity analysis in chaotic dynamical systems.

## Key findings

- MSS converges faster than LSS.
- MSS requires less memory and computational time.
- Applicable to chaotic vortex shedding and turbulence simulations.

## Abstract

Sensitivity analysis methods are important tools for research and design with simulations. Many important simulations exhibit chaotic dynamics, including scale-resolving turbulent fluid flow simulations. Unfortunately, conventional sensitivity analysis methods are unable to compute useful gradient information for long-time-averaged quantities in chaotic dynamical systems. Sensitivity analysis with least squares shadowing (LSS) can compute useful gradient information for a number of chaotic systems, including simulations of chaotic vortex shedding and homogeneous isotropic turbulence. However, this gradient information comes at a very high computational cost. This paper presents multiple shooting shadowing (MSS), a more computationally efficient shadowing approach than the original LSS approach. Through an analysis of the convergence rate of MSS, it is shown that MSS can have lower memory usage and run time than LSS.