https://sam.ensam.eu:443 The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material. Fri, 15 May 2026 22:36:32 GMT 2026-05-15T22:36:32Z http://hdl.handle.net/10985/14642 On the Proper Generalized Decomposition applied to microwave processes involving multilayered components TERTRAIS, Hermine; IBANEZ PINILLO, Ruben; BARASINSKI, Anais; GHNATIOS, Chady; CHINESTA SORIA, Francisco Many electrical and structural components are constituted of a stacking of multiple thin layers with different electromagnetic, mechanical and thermal properties. When 3D descriptions become compulsory the approximation of the fields along the thickness direction could involve thousands of nodes. To circumvent the numerical difficulties that such a rich description imply, we recently propose an in-plane–out-of-plane separated representation with the aim of computing fully 3D solutions as a sequence of 2D problems defined in the plane and others (1D) in the thickness. The main contribution of the present work is the proposal of an efficient in-plane–out-of-plane separated representation of the double-curl formulation of Maxwell equations able to address thin-layer laminates while ensuring the continuity and discontinuity of the tangential and normal electric field components respectively at the plies interface Tue, 01 Jan 2019 00:00:00 GMT http://hdl.handle.net/10985/14642 2019-01-01T00:00:00Z TERTRAIS, Hermine IBANEZ PINILLO, Ruben BARASINSKI, Anais GHNATIOS, Chady CHINESTA SORIA, Francisco Many electrical and structural components are constituted of a stacking of multiple thin layers with different electromagnetic, mechanical and thermal properties. When 3D descriptions become compulsory the approximation of the fields along the thickness direction could involve thousands of nodes. To circumvent the numerical difficulties that such a rich description imply, we recently propose an in-plane–out-of-plane separated representation with the aim of computing fully 3D solutions as a sequence of 2D problems defined in the plane and others (1D) in the thickness. The main contribution of the present work is the proposal of an efficient in-plane–out-of-plane separated representation of the double-curl formulation of Maxwell equations able to address thin-layer laminates while ensuring the continuity and discontinuity of the tangential and normal electric field components respectively at the plies interface http://hdl.handle.net/10985/15417 Sensitivity thermal analysis in the laser-assisted tape placement process PEREZ, Marta; BARASINSKI, Anaïs; COURTEMANCHE, Benoît; GHNATIOS, Chady; CHINESTA SORIA, Francisco Nowadays, the production of large pieces made of thermoplastic composites is an industrial challenging issue as there are yet several difficulties associated to their processing. The laserassisted tape placement (LATP) process is an automated manufacturing technique to produce long-fiber reinforced thermoplastic matrix composites. In this process, a tape is placed and progressively welded on the substrate. The main aim of the present work is to solve an almost state of the art thermal model by using an efficient numerical technique, the so-called Proper Generalized Decomposition (PGD) that considers parameters (geometrical and material) as model extra-coordinates. Within the PGD rationale the parametric temperature field is expressed in a separated form, as a finite sum of functional products, where each term depends on a single coordinate (space, time or each one of the parameters considered as extra-coordinates). Such a separated representation allows the explicit expression of the sensitivity fields, from the temperature derivative with respect to each parameter. These sensitivity fields represent a very valuable methodology to analyze and establish the influence of the critical input parameters on the thermal response, and therefore, for performing process optimization and control, as well as for evaluating the effect of parameters variability on the thermal response. Mon, 01 Jan 2018 00:00:00 GMT http://hdl.handle.net/10985/15417 2018-01-01T00:00:00Z PEREZ, Marta BARASINSKI, Anaïs COURTEMANCHE, Benoît GHNATIOS, Chady CHINESTA SORIA, Francisco Nowadays, the production of large pieces made of thermoplastic composites is an industrial challenging issue as there are yet several difficulties associated to their processing. The laserassisted tape placement (LATP) process is an automated manufacturing technique to produce long-fiber reinforced thermoplastic matrix composites. In this process, a tape is placed and progressively welded on the substrate. The main aim of the present work is to solve an almost state of the art thermal model by using an efficient numerical technique, the so-called Proper Generalized Decomposition (PGD) that considers parameters (geometrical and material) as model extra-coordinates. Within the PGD rationale the parametric temperature field is expressed in a separated form, as a finite sum of functional products, where each term depends on a single coordinate (space, time or each one of the parameters considered as extra-coordinates). Such a separated representation allows the explicit expression of the sensitivity fields, from the temperature derivative with respect to each parameter. These sensitivity fields represent a very valuable methodology to analyze and establish the influence of the critical input parameters on the thermal response, and therefore, for performing process optimization and control, as well as for evaluating the effect of parameters variability on the thermal response. http://hdl.handle.net/10985/15677 Advanced separated spatial representations for hardly separable domains GHNATIOS, Chady; ABISSET-CHAVANNE, Emmanuelle; AMMAR, Amine; CUETO, Elias; DUVAL, Jean-Louis; CHINESTA SORIA, Francisco This work aims at proposing a new procedure for parametric problems whose separated representation has been considered difficult, or whose SVD compression impacted the results in terms of performance and accuracy. The proposed technique achieves a fully separated representation for layered domains with interfaces exhibiting waviness or – more generally – deviating from planar surfaces, parallel to the coordinate plane. This will make possible a simple separated representation, equivalent to others, already analyzed in some of our former works. To prove the potentialities of the proposed approach, two benchmarks will be addressed, one of them involving an efficient space–time separated representation achieved by considering the same rationale. Tue, 01 Jan 2019 00:00:00 GMT http://hdl.handle.net/10985/15677 2019-01-01T00:00:00Z GHNATIOS, Chady ABISSET-CHAVANNE, Emmanuelle AMMAR, Amine CUETO, Elias DUVAL, Jean-Louis CHINESTA SORIA, Francisco This work aims at proposing a new procedure for parametric problems whose separated representation has been considered difficult, or whose SVD compression impacted the results in terms of performance and accuracy. The proposed technique achieves a fully separated representation for layered domains with interfaces exhibiting waviness or – more generally – deviating from planar surfaces, parallel to the coordinate plane. This will make possible a simple separated representation, equivalent to others, already analyzed in some of our former works. To prove the potentialities of the proposed approach, two benchmarks will be addressed, one of them involving an efficient space–time separated representation achieved by considering the same rationale. http://hdl.handle.net/10985/18539 Incremental dynamic mode decomposition: A reduced-model learner operating at the low-data limit REILLE, Agathe; HASCOET, Nicolas; CUETO, Elias; DUVAL, Jean-Louis; KEUNINGS, Roland; GHNATIOS, Chady; AMMAR, Amine; CHINESTA SORIA, Francisco The present work aims at proposing a new methodology for learning reduced models from a small amount of data. It is based on the fact that discrete models, or their transfer function counterparts, have a low rank and then they can be expressed very efficiently using few terms of a tensor decomposition. An efficient procedure is proposed as well as a way for extending it to nonlinear settings while keeping limited the impact of data noise. The proposed methodology is then validated by considering a nonlinear elastic problem and constructing the model relating tractions and displacements at the observation points. Tue, 01 Jan 2019 00:00:00 GMT http://hdl.handle.net/10985/18539 2019-01-01T00:00:00Z REILLE, Agathe HASCOET, Nicolas CUETO, Elias DUVAL, Jean-Louis KEUNINGS, Roland GHNATIOS, Chady AMMAR, Amine CHINESTA SORIA, Francisco The present work aims at proposing a new methodology for learning reduced models from a small amount of data. It is based on the fact that discrete models, or their transfer function counterparts, have a low rank and then they can be expressed very efficiently using few terms of a tensor decomposition. An efficient procedure is proposed as well as a way for extending it to nonlinear settings while keeping limited the impact of data noise. The proposed methodology is then validated by considering a nonlinear elastic problem and constructing the model relating tractions and displacements at the observation points. http://hdl.handle.net/10985/19415 A non-local void dynamics modeling and simulation using the Proper Generalized Decomposition SIMACEK, Pavel; ADVANI, Suresh G.; GHNATIOS, Chady; CHINESTA SORIA, Francisco In this work we develop a void filling and void motion dynamics model using volatile pressure and squeeze flow during tape placement process. The void motion and filling are simulated using a non-local model where their presence is reflected in the global macroscale behavior. Local pressure gradients during compression do play a critical role in void dynamics, and hence the need for a non-local model. Deriving a non-local model accounting for all the void motion and dynamics entails a prohibitive number of degrees of freedom, leading to unrealistic computation times with classical solution techniques. Hence, Proper Generalized Decomposition – PGD – is used to solve the aforementioned model. In fact, PGD circumvents the curse of dimensionality by using separated representation of the space coordinates. For example, a 2D problem can be solved as a sequence of 1D problems to find the 2D solution. The non-local model solution sheds light on the fundamental of the void dynamics including their pressure variation, motion and closure mechanisms. Finally, a post treatment of the transient compression of the voids is used to derive conclusions regarding the physics of the void dynamics. Wed, 01 Jan 2020 00:00:00 GMT http://hdl.handle.net/10985/19415 2020-01-01T00:00:00Z SIMACEK, Pavel ADVANI, Suresh G. GHNATIOS, Chady CHINESTA SORIA, Francisco In this work we develop a void filling and void motion dynamics model using volatile pressure and squeeze flow during tape placement process. The void motion and filling are simulated using a non-local model where their presence is reflected in the global macroscale behavior. Local pressure gradients during compression do play a critical role in void dynamics, and hence the need for a non-local model. Deriving a non-local model accounting for all the void motion and dynamics entails a prohibitive number of degrees of freedom, leading to unrealistic computation times with classical solution techniques. Hence, Proper Generalized Decomposition – PGD – is used to solve the aforementioned model. In fact, PGD circumvents the curse of dimensionality by using separated representation of the space coordinates. For example, a 2D problem can be solved as a sequence of 1D problems to find the 2D solution. The non-local model solution sheds light on the fundamental of the void dynamics including their pressure variation, motion and closure mechanisms. Finally, a post treatment of the transient compression of the voids is used to derive conclusions regarding the physics of the void dynamics. http://hdl.handle.net/10985/18480 Data-driven GENERIC modeling of poroviscoelastic materials GONZÁLEZ, David; CUETO, Elias; ALFARO, Icíar; GHNATIOS, Chady; CHINESTA SORIA, Francisco Biphasic soft materials are challenging to model by nature. Ongoing efforts are targeting their effective modeling and simulation. This work uses experimental atomic force nanoindentation of thick hydrogels to identify the indentation forces are a function of the indentation depth. Later on, the atomic force microscopy results are used in a GENERIC general equation for non-equilibrium reversible-irreversible coupling (GENERIC) formalism to identify the best model conserving basic thermodynamic laws. The data-driven GENERIC analysis identifies the material behavior with high fidelity for both data fitting and prediction. Tue, 01 Jan 2019 00:00:00 GMT http://hdl.handle.net/10985/18480 2019-01-01T00:00:00Z GONZÁLEZ, David CUETO, Elias ALFARO, Icíar GHNATIOS, Chady CHINESTA SORIA, Francisco Biphasic soft materials are challenging to model by nature. Ongoing efforts are targeting their effective modeling and simulation. This work uses experimental atomic force nanoindentation of thick hydrogels to identify the indentation forces are a function of the indentation depth. Later on, the atomic force microscopy results are used in a GENERIC general equation for non-equilibrium reversible-irreversible coupling (GENERIC) formalism to identify the best model conserving basic thermodynamic laws. The data-driven GENERIC analysis identifies the material behavior with high fidelity for both data fitting and prediction. http://hdl.handle.net/10985/25753 A Parsimonious Separated Representation Empowering PINN–PGD-Based Solutions for Parametrized Partial Differential Equations GHNATIOS, Chady; CHINESTA SORIA, Francisco The efficient solution (fast and accurate) of parametric partial differential equations (pPDE) is of major interest in many domains of science and engineering, enabling evaluations of the quantities of interest, optimization, control, and uncertainty propagation—all them under stringent real-time constraints. Different methodologies have been proposed in the past within the model order reduction (MOR) community, based on the use of reduced bases (RB) or the separated representation at the heart of the so-called proper generalized decompositions (PGD). In PGD, an alternate-direction strategy is employed to circumvent the integration issues of operating in multi-dimensional domains. Recently, physics informed neural networks (PINNs), a particular collocation schema where the unknown field is approximated by a neural network (NN), have emerged in the domain of scientific machine learning. PNNs combine the versatility of NN-based approximation with the ease of collocating pPDE. The present paper proposes a combination of both procedures to find an efficient solution for pPDE, that can either be viewed as an efficient collocation procedure for PINN, or as a monolithic PGD that bypasses the use of the fixed-point alternated directions. Mon, 01 Jul 2024 00:00:00 GMT http://hdl.handle.net/10985/25753 2024-07-01T00:00:00Z GHNATIOS, Chady CHINESTA SORIA, Francisco The efficient solution (fast and accurate) of parametric partial differential equations (pPDE) is of major interest in many domains of science and engineering, enabling evaluations of the quantities of interest, optimization, control, and uncertainty propagation—all them under stringent real-time constraints. Different methodologies have been proposed in the past within the model order reduction (MOR) community, based on the use of reduced bases (RB) or the separated representation at the heart of the so-called proper generalized decompositions (PGD). In PGD, an alternate-direction strategy is employed to circumvent the integration issues of operating in multi-dimensional domains. Recently, physics informed neural networks (PINNs), a particular collocation schema where the unknown field is approximated by a neural network (NN), have emerged in the domain of scientific machine learning. PNNs combine the versatility of NN-based approximation with the ease of collocating pPDE. The present paper proposes a combination of both procedures to find an efficient solution for pPDE, that can either be viewed as an efficient collocation procedure for PINN, or as a monolithic PGD that bypasses the use of the fixed-point alternated directions. http://hdl.handle.net/10985/25773 Optimal velocity planning based on the solution of the Euler-Lagrange equations with a neural network based velocity regression GHNATIOS, Chady; DI LORENZO, Daniele; CHAMPANEY, Victor; CUETO, Elias; CHINESTA SORIA, Francisco Trajectory optimization is a complex process that includes an infinite number of possibilities and combinations. This work focuses on a particular aspect of the trajectory optimization, related to the optimization of a velocity along a predefined path, with the aim of minimizing power consumption. To tackle the problem, a functional formulation and minimization strategy is developed, by means of the Euler-Lagrange equation. The minimization is later performed using a neural network approach. The strategy is deemed Lagrange-Net, as it is based on the minimization of the energy functional, by the means of Lagrange's equation and neural network approximations. Mon, 01 Jul 2024 00:00:00 GMT http://hdl.handle.net/10985/25773 2024-07-01T00:00:00Z GHNATIOS, Chady DI LORENZO, Daniele CHAMPANEY, Victor CUETO, Elias CHINESTA SORIA, Francisco Trajectory optimization is a complex process that includes an infinite number of possibilities and combinations. This work focuses on a particular aspect of the trajectory optimization, related to the optimization of a velocity along a predefined path, with the aim of minimizing power consumption. To tackle the problem, a functional formulation and minimization strategy is developed, by means of the Euler-Lagrange equation. The minimization is later performed using a neural network approach. The strategy is deemed Lagrange-Net, as it is based on the minimization of the energy functional, by the means of Lagrange's equation and neural network approximations. http://hdl.handle.net/10985/25772 A new methodology for anisotropic yield surface description using model order reduction techniques and invariant neural network GHNATIOS, Chady; CAZACU, Oana; REVIL-BAUDARD, Benoit; CHINESTA SORIA, Francisco In this paper, we present a general methodology that we call spectral neural network (SNN) which enables to generate automatically knowing a few datapoints (eight at most), a sound and plausible yield surface for any variations of a given anisotropic material, e.g. batches of the same material or same type of material produced by a different supplier. It relies on the use of a reliable parametrization of a performant analytic orthotropic yield function for the generation of a large database of yield surface shapes and the singular value decomposition method to create a reduced basis. For a specific material, a surrogate model for the reduced basis coordinates is further constructed using few additional datapoints. The dense neural network is built such as to ensure that the invariance requirements dictated by the material symmetry as well as the convexity of the yield surface are automatically enforced. The capabilities of this new methodology are demonstrated for hexagonal closed packed materials titanium materials, which are known to be particularly challenging to model due to their anisotropy and tension–compression asymmetry. Furthermore, we show that the SNN methodology can be extended such as to include variations of multiple materials of vastly different plastic behavior and yield surface shapes. The in-depth analysis presented reveals the benefits and limits of the hybrid data-driven models for description of anisotropic plasticity. Mon, 01 Jan 2024 00:00:00 GMT http://hdl.handle.net/10985/25772 2024-01-01T00:00:00Z GHNATIOS, Chady CAZACU, Oana REVIL-BAUDARD, Benoit CHINESTA SORIA, Francisco In this paper, we present a general methodology that we call spectral neural network (SNN) which enables to generate automatically knowing a few datapoints (eight at most), a sound and plausible yield surface for any variations of a given anisotropic material, e.g. batches of the same material or same type of material produced by a different supplier. It relies on the use of a reliable parametrization of a performant analytic orthotropic yield function for the generation of a large database of yield surface shapes and the singular value decomposition method to create a reduced basis. For a specific material, a surrogate model for the reduced basis coordinates is further constructed using few additional datapoints. The dense neural network is built such as to ensure that the invariance requirements dictated by the material symmetry as well as the convexity of the yield surface are automatically enforced. The capabilities of this new methodology are demonstrated for hexagonal closed packed materials titanium materials, which are known to be particularly challenging to model due to their anisotropy and tension–compression asymmetry. Furthermore, we show that the SNN methodology can be extended such as to include variations of multiple materials of vastly different plastic behavior and yield surface shapes. The in-depth analysis presented reveals the benefits and limits of the hybrid data-driven models for description of anisotropic plasticity. http://hdl.handle.net/10985/20417 Fast Computation of Multi-Parametric Electromagnetic Fields in Synchronous Machines by Using PGD-Based Fully Separated Representations SANCARLOS, Abel; GHNATIOS, Chady; DUVAL, Jean-Louis; ZERBIB, Nicolas; CUETO, Elias; CHINESTA SORIA, Francisco A novel Model Order Reduction (MOR) technique is developed to compute high-dimensional parametric solutions for electromagnetic fields in synchronous machines. Specifically, the intrusive version of the Proper Generalized Decomposition (PGD) is employed to simulate a Permanent-Magnet Synchronous Motor (PMSM). The result is a virtual chart allowing real-time evaluation of the magnetic vector potential as a function of the operation point of the motor, or even as a function of constructive parameters, such as the remanent flux in permanent magnets. Currently, these solutions are highly demanded by the industry, especially with the recent developments in the Electric Vehicle (EV). In this framework, standard discretization techniques require highly time-consuming simulations when analyzing, for instance, the noise and vibration in electric motors. The proposed approach is able to construct a virtual chart within a few minutes of off-line simulation, thanks to the use of a fully separated representation in which the solution is written from a series of functions of the space and parameters coordinates, with full space separation made possible by the use of an adapted geometrical mapping. Finally, excellent performances are reported when comparing the reduced-order model with the more standard and computationally costly Finite Element solutions. Fri, 01 Jan 2021 00:00:00 GMT http://hdl.handle.net/10985/20417 2021-01-01T00:00:00Z SANCARLOS, Abel GHNATIOS, Chady DUVAL, Jean-Louis ZERBIB, Nicolas CUETO, Elias CHINESTA SORIA, Francisco A novel Model Order Reduction (MOR) technique is developed to compute high-dimensional parametric solutions for electromagnetic fields in synchronous machines. Specifically, the intrusive version of the Proper Generalized Decomposition (PGD) is employed to simulate a Permanent-Magnet Synchronous Motor (PMSM). The result is a virtual chart allowing real-time evaluation of the magnetic vector potential as a function of the operation point of the motor, or even as a function of constructive parameters, such as the remanent flux in permanent magnets. Currently, these solutions are highly demanded by the industry, especially with the recent developments in the Electric Vehicle (EV). In this framework, standard discretization techniques require highly time-consuming simulations when analyzing, for instance, the noise and vibration in electric motors. The proposed approach is able to construct a virtual chart within a few minutes of off-line simulation, thanks to the use of a fully separated representation in which the solution is written from a series of functions of the space and parameters coordinates, with full space separation made possible by the use of an adapted geometrical mapping. Finally, excellent performances are reported when comparing the reduced-order model with the more standard and computationally costly Finite Element solutions.