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6.14.17 Ni

Title: 87th NIA CFD Seminar: Sensitivity analysis on chaotic dynamical systems by Non-Intrusive Least Squares Shadowing (NILSS)

Speaker: Angxiu Ni, MS Candidate, UC Berkeley

Date: Wednesday, June 14, 2017

Time: 11:00am-noon (EST)

Room: NIA, Rm141

Link to view:

Abstract: This talk presents the Non-Intrusive Least Squares Shadowing (NILSS) method, which computes the sensitivity for long-time averaged objectives in chaotic dynamical systems.We will show that perturbing the parameters of a simulation has a transient effect and a long-time effect. The transient effect causes similar simulations to diverge, whereas the long-time effect that shifts the chaotic attractor, and thereby perturbs the long-time averages of the simulation. Although both effects are contained in the solution of a conventional tangent equation, the transient effect is usually orders of magnitude larger than the long-time effect. Computing the sensitivity for long-time averages requires finding a tangent solution that contains the long-term effect but tiny transient effect. NILSS achieves this by determining a linear combination of homogeneous tangent solutions and subtracting it from the conventional inhomogeneous tangent. The resulting inhomogeneous tangent solution, now with a non-zero condition, can be used to compute the sensitivity of interest. NILSS has two advantages. The first is that it is relatively easy to implement with existing solvers. The second is that, for chaotic systems with many degrees of freedom but a few unstable modes, NILSS has a low computational cost, sometimes even comparable to that of the primal simulation. At the end of the talk, we show the application of NILSS onto several chaotic PDE systems: 1) the Lorenz 63 system, 2) a two-dimensional CFD simulation of flow over a backward-facing step, and 3) a three-dimensional CFD simulation of flow over a cylinder. With reasonable cost, NILSS gives sensitivities that reflect the trends in the long-time averaged objectives of these dynamical systems.

Bio: Angxiu Ni is a new graduate student in the Department of Math at UC Berkeley. He received his master of science in aerospace engineering from MIT, under the advising of Qiqi Wang. His research interest is in computational methods for ODE/PDE. He developed the Non-Intrusive Least Squares Shadowing (NILSS) method with Qiqi Wang, a fast method for sensitivity analysis of chaotic dynamical systems.

Additional information, including the webcast link, can be found at the NIA CFD Seminar website:



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