Least Squares Shadowing Sensitivity Analysis of a Modified Kuramoto-Sivashinsky Equation

TL;DR

This paper applies a novel least squares shadowing sensitivity analysis method to a modified Kuramoto-Sivashinsky equation, successfully computing accurate gradients in a chaotic system where traditional methods often fail.

Contribution

The paper introduces the application of least squares shadowing sensitivity analysis to a modified K-S equation, demonstrating its effectiveness in chaotic systems.

Findings

Accurate gradient computation for a range of parameters.

Method overcomes limitations of traditional sensitivity analysis in chaos.

Applicable to other chaotic physical systems.

Abstract

Computational methods for sensitivity analysis are invaluable tools for scientists and engineers investigating a wide range of physical phenomena. However, many of these methods fail when applied to chaotic systems, such as the Kuramoto-Sivashinsky (K-S) equation, which models a number of different chaotic systems found in nature. The following paper discusses the application of a new sensitivity analysis method developed by the authors to a modified K-S equation. We find that least squares shadowing sensitivity analysis computes accurate gradients for solutions corresponding to a wide range of system parameters.