3755363
doi
10.5281/zenodo.3755363
oai:zenodo.org:3755363
user-romsoc
user-eu
Ijzerman, Wilbert L.
Signify Research Hightech Campus
Rukhaia, Giorgi
INRIA-Paris, MOKAPLAN
An Entropic Optimal Transport Numerical Approach to the Reflector Problem
Benamou, Jean-David
INRIA-Paris, MOKAPLAN
info:eu-repo/semantics/openAccess
Creative Commons Attribution 4.0 International
https://creativecommons.org/licenses/by/4.0/legalcode
<p>The point source far field reflector design problem is one of the main classic optimal transport problems with a non-euclidean displacement cost [Wang, 2004] [Glimm and Oliker, 2003].This work describes the use of Entropic Optimal Transport and the associated Sinkhorn algorithm [Cuturi, 2013] to solve it numerically. As the reflector modelling is based on the Kantorovich potentials, several questions arise. First, on the convergence of the discrete entropic approximation and here we follow the recent work of [Berman, 2017] and in particular the imposed discretization requirements therein. Secondly, the correction of the Entropic bias induced by the Entropic OT, as discussed inparticular in [Ramdas et al., 2017] [Genevay et al., 2018] [Feydy et al., 2018], is another important tool to achieve reasonable results. The paper reviews the necessary mathematical and numerical tools needed to produce and discuss the obtained numerical results. We find that Sinkhorn algorithm may be adapted, at least in simple academic cases, to the resolution of the far field reflector problem. Sinkhorn canonical extension to continuous potentials is needed to generate continuous reflector approximations.The use of Sinkhorn divergences [Feydy et al., 2018] is useful to mitigate the entropic bias.</p>
working paper or preprint
Zenodo
2020-04-17
info:eu-repo/semantics/preprint
3755362
user-romsoc
user-eu
1.0
award_title=Reduced Order Modelling, Simulation and Optimization of Coupled systems; award_number=765374; award_identifiers_scheme=url; award_identifiers_identifier=https://cordis.europa.eu/projects/765374; funder_id=00k4n6c32; funder_name=European Commission;
1587154815.837908
2223167
md5:fb78c9d7f7c7d26949542f60865f053a
https://zenodo.org/records/3755363/files/EntropicReflectorSubmitted.pdf
public
10.5281/zenodo.3755362
isVersionOf
doi