Sensitivity analysis on chaotic dynamical system by Non-Intrusive Least Square Shadowing (NILSS)
arXiv:1611.00880 · doi:10.1016/j.jcp.2017.06.033
Abstract
This paper develops the non-intrusive formulation of the Least-squares shadowing (LSS) method, for computing the sensitivity of long-time averaged objectives in chaotic dynamical systems. This non-intrusive formulation constrains the computation to only the unstable subspace, greatly reducing the cost of LSS for many problems; moreover, it reparametrizes the LSS problem, requiring only minor modifications to existing tangent solvers. NILSS is demonstrated on a chaotic flow over a backward-facing step simulated with a mesh of 12e3 cells.
26 pages, 10 figures
References in corpus (5)
- Hyperbolicity, shadowing directions and sensitivity analysis of a turbulent three-dimensional flow
- Adjoint sensitivity analysis on chaotic dynamical systems by Non-Intrusive Least Squares Adjoint Shadowing (NILSAS)
- Least Squares Shadowing for Sensitivity Analysis of Turbulent Fluid Flows
- Adjoint shadowing directions in hyperbolic systems for sensitivity analysis
- Linear Range in Gradient Descent
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