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Open AccessArticle

Nonlinear Regression Operating on Microstructures Described from Topological Data Analysis for the Real-Time Prediction of Effective Properties

1
PIMM Laboratory & ESI Group Chair, Arts et Métiers Institute of Technology, CNRS, Cnam, HESAM Université, 151 boulevard de l’Hôpital, 75013 Paris, France
2
Aragon Institute of Engineering Research, Universidad de Zaragoza, 50009 Zaragoza, Spain
3
ESI Group, Bâtiment Seville, 3bis rue Saarinen, 50468 Rungis, France
*
Author to whom correspondence should be addressed.
Materials 2020, 13(10), 2335; https://doi.org/10.3390/ma13102335
Received: 25 April 2020 / Revised: 11 May 2020 / Accepted: 13 May 2020 / Published: 19 May 2020
(This article belongs to the Special Issue Empowering Materials Processing and Performance from Data and AI)
Real-time decision making needs evaluating quantities of interest (QoI) in almost real time. When these QoI are related to models based on physics, the use of Model Order Reduction techniques allows speeding-up calculations, enabling fast and accurate evaluations. To accommodate real-time constraints, a valuable route consists of computing parametric solutions—the so-called computational vademecums—that constructed off-line, can be inspected on-line. However, when dealing with shapes and topologies (complex or rich microstructures) their parametric description constitutes a major difficulty. In this paper, we propose using Topological Data Analysis for describing those rich topologies and morphologies in a concise way, and then using the associated topological descriptions for generating accurate supervised classification and nonlinear regression, enabling an almost real-time evaluation of QoI and the associated decision making.
Keywords: machine learning; data-driven mechanics; TDA; Code2Vect; nonlinear regression; effective properties; microstructures machine learning; data-driven mechanics; TDA; Code2Vect; nonlinear regression; effective properties; microstructures
MDPI and ACS Style

Yun, M.; Argerich, C.; Cueto, E.; Duval, J.L.; Chinesta, F. Nonlinear Regression Operating on Microstructures Described from Topological Data Analysis for the Real-Time Prediction of Effective Properties. Materials 2020, 13, 2335.

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