Simplified Least Squares Shadowing sensitivity analysis for chaotic ODEs and PDEs

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 more efficient and simpler to implement, especially for PDEs. Keywords: Sensitivity analysis, Linear response, Adjoint equation, Unsteady adjoint, Chaos, Least squares shadowing