Variational optimization and data assimilation in chaotic time-delayed systems with automatic-differentiated shadowing sensitivity

TL;DR

This paper introduces an automatic differentiation-enhanced shadowing algorithm for sensitivity analysis, parameter optimization, and data assimilation in chaotic time-delayed systems, demonstrated on a thermoacoustic model.

Contribution

It presents a novel approach combining automatic differentiation with shadowing methods for efficient sensitivity analysis and data assimilation in chaotic systems.

Findings

Effective sensitivity analysis of long-time averages in chaotic systems.

Successful application to a thermoacoustic model.

Potential for broad use in chaotic system analysis.

Abstract

In this computational paper, we perform sensitivity analysis of long-time (or ensemble) averages in the chaotic regime using the shadowing algorithm. We introduce automatic differentiation to eliminate the tangent/adjoint equation solvers used in the shadowing algorithm. In a gradient-based optimization, we use the computed shadowing sensitivity to minimize different long-time averaged functionals of a chaotic time-delayed system by optimal parameter selection. In combined state and parameter estimation for data assimilation, we use the computed sensitivity to predict the optimal trajectory given information from a model and data from measurements beyond the predictability time. The algorithms are applied to a thermoacoustic model. Because the computational framework is rather general, the techniques presented in this paper may be used for sensitivity analysis of ensemble averages, parameter optimization and data assimilation of other chaotic problems, where shadowing methods are applicable.