Forward and Adjoint Sensitivity Computation of Chaotic Dynamical Systems

TL;DR

This paper introduces forward and adjoint algorithms for efficiently computing sensitivity derivatives of long-term statistical quantities in chaotic systems, demonstrated on the Lorenz attractor with accurate results from short trajectories.

Contribution

It presents novel algorithms for sensitivity analysis in chaotic systems, enabling accurate derivative estimation from short trajectories, which was challenging before.

Findings

Sensitivity derivatives can be accurately estimated using short trajectories.

Algorithms are demonstrated on the Lorenz attractor.

The methods are applicable to long-term statistical quantities.

Abstract

This paper describes a forward algorithm and an adjoint algorithm for computing sensitivity derivatives in chaotic dynamical systems, such as the Lorenz attractor. The algorithms compute the derivative of long time averaged "statistical" quantities to infinitesimal perturbations of the system parameters. The algorithms are demonstrated on the Lorenz attractor. We show that sensitivity derivatives of statistical quantities can be accurately estimated using a single, short trajectory (over a time interval of 20) on the Lorenz attractor.