Title: An Efficient Parallel-in-Time Method for Optimization with Parabolic PDEs

Journal Article · · SIAM Journal on Scientific Computing
DOI: https://doi.org/10.1137/19m1239313 · OSTI ID:1580377
ORCiD logo [1]; ORCiD logo [2]
  1. Zuse Inst. Berlin, Berlin (Germany)
  2. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
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To solve optimization problems with parabolic PDE constraints, often methods working on the reduced objective functional are used. They are computationally expensive due to the necessity of solving both the state equation and a backward-in-time adjoint equation to evaluate the reduced gradient in each iteration of the optimization method. In this study, we investigate the use of the parallel-in-time method PFASST in the setting of PDE-constrained optimization. In order to develop an efficient fully time-parallel algorithm, we discuss different options for applying PFASST to adjoint gradient computation, including the possibility of doing PFASST iterations on both the state and the adjoint equations simultaneously. Here, we also explore the additional gains in efficiency from reusing information from previous optimization iterations when solving each equation. Numerical results for both a linear and a nonlinear reaction-diffusion optimal control problem demonstrate the parallel speedup and efficiency of different approaches.

Research Organization:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Organization:
Alexander von Humboldt Foundation; German Research Foundation (DFG); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
Grant/Contract Number:
AC02-05CH11231
OSTI ID:
1580377
Journal Information:
SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing Journal Issue: 6 Vol. 41; ISSN 1064-8275
Publisher:
SIAMCopyright Statement
Country of Publication:
United States
Language:
English

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Cited By (2)

Fast Iterative Solver for the Optimal Control of Time-Dependent PDEs with Crank-Nicolson Discretization in Time preprint January 2020
A Practical Layer-Parallel Training Algorithm for Residual Networks preprint January 2020

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Related Subjects

97 MATHEMATICS AND COMPUTING
PDE-constrained optimization
PFASST
parallel-in-time methods