A non-intrusive parallel-in-time approach for simultaneous optimization with unsteady PDEs

Günther, S.; Gauger, N. R.; Schroder, J. B.

doi:10.1080/10556788.2018.1504050

A non-intrusive parallel-in-time approach for simultaneous optimization with unsteady PDEs

Journal Article · Mon Aug 06 00:00:00 EDT 2018 · Optimization Methods and Software

DOI:https://doi.org/10.1080/10556788.2018.1504050· OSTI ID:1773244

Günther, S. ^[1]; Gauger, N. R. ^[1]; Schroder, J. B. ^[2]

Technische Universität Kaiserslautern (Germany)
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

This paper presents a non-intrusive framework for integrating existing unsteady partial differential equation (PDE) solvers into a parallel-in-time simultaneous optimization algorithm. The time-parallelization is provided by the non-intrusive software library XBraid [Parallel multigrid in time, software available at http://llnl.gov/casc/xbraid], which applies an iterative multigrid reduction technique to the time domain of existing time-marching schemes for solving unsteady PDEs. Its general user-interface has been extended in [S. Günther, N.R. Gauger, and J.B. Schroder, A non-intrusive parallel-in-time adjoint solver with the XBraid library, Comput. Vis. Sci. 19 (2018), pp. 85–95. Available at arXiv, math.OC/1705.00663] for computing adjoint sensitivities such that gradients of output quantities with respect to design changes can be computed parallel-in-time alongside with the primal PDE solution. In this paper, the primal and adjoint XBraid iterations are embedded into a simultaneous optimization framework, namely the One-shot method. In this method, design updates towards optimality are employed after each state and adjoint update such that optimality and feasibility of the design and the PDE solution are reached simultaneously. Finally, the time-parallel optimization method is validated on an advection-dominated flow control problem which shows significant speedup over a classical time-serial optimization algorithm.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 1773244

Report Number(s):: LLNL-JRNL--744565; 899850

Journal Information:: Optimization Methods and Software, Journal Name: Optimization Methods and Software Journal Issue: 6 Vol. 34; ISSN 1055-6788

Publisher:: Taylor & FrancisCopyright Statement

Country of Publication:: United States

Language:: English

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Layer-Parallel Training of Deep Residual Neural Networks Günther, S.; Ruthotto, L.; Schroder, J. B. arXiv https://doi.org/10.48550/arxiv.1812.04352	preprint	January 2018

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97 MATHEMATICS AND COMPUTING
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