Probability density adjoint for sensitivity analysis of the Mean of Chaos
| Autor: | Patrick J. Blonigan, Qiqi Wang |
|---|---|
| Přispěvatelé: | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics, Blonigan, Patrick Joseph, Wang, Qiqi |
| Jazyk: | angličtina |
| Rok vydání: | 2013 |
| Předmět: |
Numerical Analysis
Physics and Astronomy (miscellaneous) Applied Mathematics Mathematical analysis Chaotic MathematicsofComputing_NUMERICALANALYSIS Probability density function Dynamical Systems (math.DS) Numerical Analysis (math.NA) Lorenz system Computer Science Applications Computational Mathematics Adjoint equation Modeling and Simulation Attractor FOS: Mathematics Ergodic theory Invariant measure Sensitivity (control systems) Mathematics - Numerical Analysis Mathematics - Dynamical Systems Mathematics |
| Zdroj: | arXiv |
| Popis: | 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. The following paper presents a new method for sensitivity analysis of {\em 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. 29 pages, 27 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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