Manifold learning for coherent design interpolation based on geometrical and topological descriptors

Munoz D.; Rodenas J.J.; Nadal E.Allix O.Chinesta F.

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Manifold learning for coherent design interpolation based on geometrical and topological descriptors

机译：Manifold learning for coherent design interpolation based on geometrical and topological descriptors

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? 2022 The Author(s)In the context of intellectual property in the manufacturing industry, know-how is referred to practical knowledge on how to accomplish a specific task. This know-how is often difficult to be synthesised in a set of rules or steps as it remains in the intuition and expertise of engineers, designers, and other professionals. Today, a new research line in this concern spot-up thanks to the explosion of Artificial Intelligence and Machine Learning algorithms and its alliance with Computational Mechanics and Optimisation tools. However, a key aspect with industrial design is the scarcity of available data, making it problematic to rely on deep-learning approaches. Assuming that the existing designs live in a manifold, in this paper, we propose a synergistic use of existing Machine Learning tools to infer a reduced manifold from the existing limited set of designs and, then, to use it to interpolate between the individuals, working as a generator basis, to create new and coherent designs. For this, a key aspect is to be able to properly interpolate in the reduced manifold, which requires a proper clustering of the individuals. From our experience, due to the scarcity of data, adding topological descriptors to geometrical ones considerably improves the quality of the clustering. Thus, a distance, mixing topology and geometry is proposed. This distance is used both, for the clustering and for the interpolation. For the interpolation, relying on optimal transport appear to be mandatory. Examples of growing complexity are proposed to illustrate the goodness of the method.

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《Computer Methods in Applied Mechanics and Engineering》 |2023年第15期|1-19|共19页
作者
Munoz D.; Rodenas J.J.; Nadal E.Allix O.Chinesta F.;
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作者单位

Institute of Mechanical and Biomechanical Engineering (I2MB) Universitat Politècnica de ValènciaInstitute of Mechanical and Biomechanical Engineering (I2MB) Universitat Politècnica de València||ESI Chair PIMM Arts et Métiers Institute of Technology;

||Institute of Mechanical and Biomechanical Engineering (I2MB) Universitat Politècnica de València;

ESI Chair PIMM Arts et Métiers Institute of TechnologyUniversité Paris-Saclay ENS Paris-Saclay CentraleSupélec CNRS LMPS - Laboratoire de Mécanique Paris-Saclay;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种英语
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Dimensionality reduction; Locally linear embedding; Machine learning; Optimal transport; Structural optimisation; Topological data analysis;

Manifold learning for coherent design interpolation based on geometrical and topological descriptors

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