https://sam.ensam.eu:443 The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material. Wed, 11 Mar 2026 22:40:17 GMT 2026-03-11T22:40:17Z http://hdl.handle.net/10985/20218 Book of abstracts - 14th WCCM & ECCOMAS Congress 2020 CHINESTA SORIA, Francisco; ABGRALL, Rémi; ALLIX, Olivier; NÉRON, David; KALISKE, Michael No abstract Fri, 01 Jan 2021 00:00:00 GMT http://hdl.handle.net/10985/20218 2021-01-01T00:00:00Z CHINESTA SORIA, Francisco ABGRALL, Rémi ALLIX, Olivier NÉRON, David KALISKE, Michael No abstract http://hdl.handle.net/10985/24632 Manifold learning for coherent design interpolation based on geometrical and topological descriptors MUNOZ, David; ALLIX, Olivier; CHINESTA SORIA, Francisco; RÓDENAS, Juan José 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. Sun, 01 Jan 2023 00:00:00 GMT http://hdl.handle.net/10985/24632 2023-01-01T00:00:00Z MUNOZ, David ALLIX, Olivier CHINESTA SORIA, Francisco RÓDENAS, Juan José 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. http://hdl.handle.net/10985/25869 Empowering PGD-based parametric analysis with Optimal Transport MUNOZ, David; TORREGROSA JORDAN, Sergio; ALLIX, Olivier; CHINESTA SORIA, Francisco The Proper Generalized Decomposition (PGD) is a Model Order Reduction framework that has been proposed to be able to do parametric analysis of physical problems. These parameters may include material properties, boundary conditions, etc. With this framework most of the computation may done in an off-line stage allowing to perform real time simulation in a variety of situations. Nevertheless, this scheme may lose its efficiency where the domain itself is also considered as “a parameter”. Optimal transport techniques, on the other hand, have demonstrated exceptional performance in interpolating different types of fields described over geometrical domains with varying shapes. Hence trying allying both techniques is quite natural. The core idea is that PGD handles the parametric solution, while the optimal transport-based methodology transports the solution for a family of domains defined by geometrical parameters such as lengths, radii, thicknesses, etc. In this first attempt the associated methodology is proposed and apply in simple 1D and 2D cases showing interesting performances. Mon, 01 Jan 2024 00:00:00 GMT http://hdl.handle.net/10985/25869 2024-01-01T00:00:00Z MUNOZ, David TORREGROSA JORDAN, Sergio ALLIX, Olivier CHINESTA SORIA, Francisco The Proper Generalized Decomposition (PGD) is a Model Order Reduction framework that has been proposed to be able to do parametric analysis of physical problems. These parameters may include material properties, boundary conditions, etc. With this framework most of the computation may done in an off-line stage allowing to perform real time simulation in a variety of situations. Nevertheless, this scheme may lose its efficiency where the domain itself is also considered as “a parameter”. Optimal transport techniques, on the other hand, have demonstrated exceptional performance in interpolating different types of fields described over geometrical domains with varying shapes. Hence trying allying both techniques is quite natural. The core idea is that PGD handles the parametric solution, while the optimal transport-based methodology transports the solution for a family of domains defined by geometrical parameters such as lengths, radii, thicknesses, etc. In this first attempt the associated methodology is proposed and apply in simple 1D and 2D cases showing interesting performances.