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Inversion of Convection-Diffusion Equation with Discrete Sources

Meenarli Sharma(meenarli***at***iitb.ac.in)
Mirko Hahn(mirhahn***at***ovgu.de)
Sven Leyffer(leyffer***at***anl.gov)
Lars Ruthotto(lruthotto***at***emory.edu)
Bart van Bloemen Waanders(bartv***at***sandia.gov)

Abstract: We present a convection-diffusion inverse problem that aims to identify an unknown number of sources and their locations. We model the sources using a binary function, and we show that the inverse problem can be formulated as a large-scale mixed-integer nonlinear optimization problem. We show empirically that current state-of-the-art mixed-integer solvers cannot solve this problem and that applying simple rounding heuristics to solutions of the relaxed problem can fail to identify the correct number and location of the sources. We develop two new rounding heuristics that exploit the value and a physical interpretation of the continuous relaxation solution, and we apply a steepest-descent improvement heuristic to obtain satisfactory solutions to both two- and three-dimensional inverse problems. We also provide the code used in our numerical experiments in open-source format.

Keywords: Mixed-Integer Optimization ̈ PDE-Constrained Optimization

Category 1: Integer Programming ((Mixed) Integer Nonlinear Programming )

Category 2: Nonlinear Optimization (Systems governed by Differential Equations Optimization )

Citation: Preprint ANL/MCS-P9270-1219

Download: [PDF]

Entry Submitted: 12/19/2019
Entry Accepted: 12/20/2019
Entry Last Modified: 12/19/2019

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