Probability density adjoint for sensitivity analysis of the Mean of Chaos

Journal Article · Fri Aug 01 00:00:00 EDT 2014 · Journal of Computational Physics

DOI:https://doi.org/10.1016/J.JCP.2014.04.027· OSTI ID:22314887

Wang, Qiqi

Sensitivity analysis, especially adjoint based sensitivity analysis, is a powerful tool for engineering design which allows for the efficient computation of sensitivities with respect to many parameters. However, these methods break down when used to compute sensitivities of long-time averaged quantities in chaotic dynamical systems. This paper presents a new method for sensitivity analysis of ergodic chaotic dynamical systems, the density adjoint method. The method involves solving the governing equations for the system's invariant measure and its adjoint on the system's attractor manifold rather than in phase-space. This new approach is derived for and demonstrated on one-dimensional chaotic maps and the three-dimensional Lorenz system. It is found that the density adjoint computes very finely detailed adjoint distributions and accurate sensitivities, but suffers from large computational costs.

• OSTI ID: 22314887
• Journal Information: Journal of Computational Physics, Vol. 270; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ATTRACTORS
CALCULATION METHODS
CHAOS THEORY
ONE-DIMENSIONAL CALCULATIONS
PHASE SPACE
PROBABILITY
SENSITIVITY ANALYSIS
THREE-DIMENSIONAL CALCULATIONS