Simplified Least Squares Shadowing sensitivity analysis for chaotic ODEs and PDEs

TL;DR

This paper introduces a simplified Least Squares Shadowing method using windowing to compute sensitivities in chaotic ODEs and PDEs, making the approach easier to implement especially for PDEs.

Contribution

It proposes a novel variant of the LSS method that replaces explicit time dilation with windowing, simplifying the sensitivity analysis process.

Findings

Effective in chaotic ODEs and PDEs

Easier implementation for PDEs

Maintains accuracy of sensitivity computations

Abstract

This paper develops a variant of the Least Squares Shadowing (LSS) method, which has successfully computed the derivative for several chaotic ODEs and PDEs. The development in this paper aims to simplify Least Squares Shadowing method by improving how time dilation is treated. Instead of adding an explicit time dilation term as in the original method, the new variant uses windowing, which can be simpler to implement, especially for PDEs.