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Space separation within the Proper Generalized Decomposition—PGD—rationale allows solving high dimensional problems as a sequence of lower dimensional ones. In our former works, different geometrical transformations were proposed for addressing complex shapes and spatially non-separable domains. Efficient implementation of separated representations needs expressing the domain as a product of characteristic functions involving the different space coordinates. In the case of complex shapes, more sophisticated geometrical transformations are needed to map the complex physical domain into a regular one where computations are performed. This paper aims at proposing a very efficient route for accomplishing such space separation. A NURBS-based geometry representation, usual in computer aided design—CAD—, is retained and combined with a fully separated representation for allying efficiency (ensured by the fully separated representations) and generality (by addressing complex geometries). Some numerical examples are considered to prove the potential of the proposed methodology.

International audience; Abstract Solutions of partial differential equations can exhibit multiple time scales. Standard discretization techniques are constrained to capture the finest scale to accurately predict the response of the system. In this paper, we provide an alternative route to circumvent prohibitive meshes arising from the necessity of capturing fine-scale behaviors. The proposed methodology is based on a time-separated representation within the standard Proper Generalized Decomposition, where the time coordinate is transformed into a multi-dimensional time through new separated coordinates, each representing one scale, while continuity is ensured in the scale coupling. For instance, when considering two different time scales, the governing Partial Differential Equation is commuted into a nonlinear system that iterates between the so-called microtime and macrotime, so that the time coordinate can be viewed as a 2D time. The macroscale effects are taken into account by means of a finite element-based macro-discretization, whereas the microscale effects are handled with unidimensional parent spaces that are replicated throughout the time domain. The resulting separated representation allows us a very fine time discretization without impacting the computational efficiency. The proposed formulation is explored and numerically verified on thermal and elastodynamic problems.; Solutions of partial differential equations can exhibit multiple time scales. Standard discretization techniques are constrained to capture the finest scale to accurately predict the response of the system. In this paper, we provide an alternative route to circumvent prohibitive meshes arising from the necessity of capturing fine-scale behaviors. The proposed methodology is based on a time-separated representation within the standard Proper Generalized Decomposition, where the time coordinate is transformed into a multi-dimensional time through new separated coordinates, each representing one scale, while continuity is ensured in the scale coupling. For instance, when considering two different time scales, the governing Partial Differential Equation is commuted into a nonlinear system that iterates between the so-called microtime and macrotime, so that the time coordinate can be viewed as a 2D time. The macroscale effects are taken into account by means of a finite element-based macro-discretization, whereas the microscale effects are handled with unidimensional parent spaces that are replicated throughout the time domain. The resulting separated representation allows us a very fine time discretization without impacting the computational efficiency. The proposed formulation is explored and numerically verified on thermal and elastodynamic problems.

International audience; The present study addresses the discrete simulation of the flow of concentrated suspensions encountered in the forming processes involving reinforced polymers, and more particularly the statistical characterization and description of the effects of the intense fiber interaction, occurring during the development of the flow induced orientation, on the fibers’ geometrical center trajectory. The number of interactions as well as the interaction intensity will depend on the fiber volume fraction and the applied shear, which should affect the stochastic trajectory. Topological data analysis (TDA) will be applied on the geometrical center trajectories of the simulated fiber to prove that a characteristic pattern can be extracted depending on the flow conditions (concentration and shear rate). This work proves that TDA allows capturing and extracting from the so-called persistence image, a pattern that characterizes the dependence of the fiber trajectory on the flow kinematics and the suspension concentration. Such a pattern could be used for classification and modeling purposes, in rheology or during processing monitoring.

Third millennium engineering is addressing new challenges in materials sciencesand engineering. In particular, the advances in materials engineering, combined with the advances in data acquisition, processing and mining as well as artificial intelligence, allow new ways of thinking in designing new materials and products. Additionally, this gives rise to new paradigms in bridging raw material data and processing to the induced properties and performance. On the one hand, the linkage can be done purely on a data-driven basis, i.e., models are created from scratch based on the obtained experimental data alone, forinstance with statistical methods or advanced methods of machine learning. Particularly obvious advantages of such kinds of models are that no simplification or assumptions need to be incorporated a priori, and that it allows real-time prediction, leading to a so-called digital twin of the specific material/process. However, such approaches typically face somegeneral challenges, such as the necessity of (maybe unnecessarily) large and comprehensive datasets, because they rely only on the data themselves and allow prediction only within the investigated/trained dataspace. Another way of addressing the challenge of predicting the complex processing–structure–property relationships in materials is the enhancement of already existing physics-based models via data and machine learning tools, i.e., combininga physics-based model (often called virtual twin) and a data-based model, leading to a so-called hybrid twin [1]. In this regard, possible deviations of the physics-based model, which rely on a number of simplifications and assumptions, can be healed by correcting the model based on a data-driven approach, i.e., combining the advantages of both models.

International audience; 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.

We present a method for the data-driven learning of physical phenomena whose evolution in time depends on history terms. It is well known that a Mori-Zwanzig-type projection produces a description of the physical phenomena that depends on history, and also incorporates noise. If the data stream is sampled from the projected Mori-Zwanzig manifold, the description of the phenomenon will always depend on one or more unresolved variables, a priori unknown, and will also incorporate noise. The present work introduces a novel technique able to unveil the presence of such internal variables—although without giving it a precise physical meaning—and to minimize the inherent noise. The method is based upon a refinement of the scale at which the phenomenon is described by means of kernel-PCA techniques. By learning the metriplectic form of the evolution of the physics, the resulting approximation satisfies basic thermodynamic principles such as energy conservation and positive entropy production. Examples are provided that show the potential of the method in both discrete and continuum mechanics. This project has been partially funded by the ESI Group through the ESI Chair at ENSAM ParisTech and through the project “Simulated Reality” at the University of Zaragoza. The support of the Spanish Ministry of Economy and Competitiveness through grant number CICYT-DPI2017-85139-C2-1-R and by the Regional Government of Aragon, through the project T24_20R, and the European Social Fund, are also gratefully acknowledged.

International audience; This work aims at analyzing the scaling behavior and develop correlations during surface growing for different germination lengths. The surface growing by random deposition is simulated using a kinetic Monte Carlo approach, by considering different germination lengths. Different surface descriptors are extracted, among them the roughness and the correlation. The former allows extracting the scaling behavior, while the latter proves the existence of correlations independent of the system size but dependent on the germination length. Moreover, as in the case of random deposition with a null germination length, the growing roughness never saturates.

Experimental data bases are typically very large and high dimensional. To learn from them requires to recognize important features (a pattern), often present at scales different to that of the recorded data. Following the experience collected in statistical mechanics and thermodynamics, the process of recognizing the pattern (the learning process) can be seen as a dissipative time evolution driven by entropy from a detailed level of description to less detailed. This is the way thermodynamics enters machine learning. On the other hand, reversible (typically Hamiltonian) evolution is propagation within the levels of description, that is also to be recognized. This is how Poisson geometry enters machine learning. Learning to handle free surface liquids and damped rigid body rotation serves as an illustration.

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. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.

A novel model order reduction (MOR) technique is presented to achieve fast and real-time predictions as well as high-dimensional parametric solutions for the electromagnetic force which will help the design, analysis of performance and implementation of electric machines concerning industrial applications such as the noise, vibration, and harshness in electric motors. The approach allows to avoid the long-time simulations needed to analyze the electric machine at different operation points. In addition, it facilitates the computation and coupling of the motor model in other physical subsystems. Specifically, we propose a novel formulation of the sparse proper generalized decomposition procedure, combining it with a reduced basis approach, which is used to fit correctly the reduced order model with the numerical simulations as well as to obtain a further data compression. This technique can be applied to construct a regression model from high-dimensional data. These data can come, for example, from finite element simulations. As will be shown, an excellent agreement between the results of the proposed approach and the finite element method models are observed. We thank Professor Jose Roger-Folch (Univer-sitat Politècnica de València) for useful discussion, comments and feedback about the present work.

International audience; For better designing manufacturing processes, surrogate models were widely considered in the past, where the effect of different material and process parameters was considered from the use of a parametric solution. The last contains the solution of the model describing the system under study, for any choice of the selected parameters. These surrogate models, also known as meta-models, virtual charts or computational vademecum, in the context of model order reduction, were successfully employed in a variety of industrial applications. However, they remain confronted to a major difficulty when the number of parameters grows exponentially. Thus, processes involving trajectories or sequencing entail a combinatorial exposition (curse of dimensionality) not only due to the number of possible combinations, but due to the number of parameters needed to describe the process. The present paper proposes a promising route for circumventing, or at least alleviating that difficulty. The proposed technique consists of a parametric transfer function that, as soon as it is learned, allows for, from a given state, inferring the new state after the application of a unitary operation, defined as a step in the sequenced process. Thus, any sequencing can be evaluated almost in real time by chaining that unitary transfer function, whose output becomes the input of the next operation. The benefits and potential of such a technique are illustrated on a problem of industrial relevance, the one concerning the induced deformation on a structural part when printing on it a series of stiffeners.

International audience; Solving mechanical problems in large structures with rich localized behaviors remains a challenging issue despite the enormous advances in numerical procedures and computational performance. In particular, these localized behaviors need for extremely fine descriptions, and this has an associated impact in the number of degrees of freedom from one side, and the decrease of the time step employed in usual explicit time integrations, whose stability scales with the size of the smallest element involved in the mesh. In the present work we propose a data-driven technique for learning the rich behavior of a local patch and integrate it into a standard coarser description at the structure level. Thus, localized behaviors impact the global structural response without needing an explicit description of that fine scale behaviors.

The present paper describes the use of the technique known as PGD-Vademecum in potential-based path planning for mobile robots. The basic idea of the method is to obtain a Vademecum with all the possible robot paths from any start to any goal derived from a harmonic potential field in a predefined map, including any possible dynamic obstacle positions. The PGD is a numerical technique that offers three important advantages over other methods. First, the ability to calculate all the possible Poisson equation solutions for all start, goal and dynamic obstacle combinations in a map, ensuring that the resulting potential field does not have local minima. Second, the PGD-Vademecum can be expressed as a sum of uncoupled multiplied terms: the geometric map and the start and goal configurations. Consequently, the harmonic potential field for any start and goal robot positions can be reconstructed very fast, in an almost negligible computational time, allowing real-time path planning. Third, just a few uncoupled parameters are required to reconstruct the potential field with a minimum discretization error. The abilities of this technique are demonstrated by means of simulation results.

We present an algorithm to learn the relevant latent variables of a large-scale discretized physical system and predict its time evolution using thermodynamically-consistent deep neural networks. Our method relies on sparse autoencoders, which reduce the dimensionality of the full order model to a set of sparse latent variables with no prior knowledge of the coded space dimensionality. Then, a second neural network is trained to learn the metriplectic structure of those reduced physical variables and predict its time evolution with a so-called structure-preserving neural network. This data-based integrator is guaranteed to conserve the total energy of the system and the entropy inequality, and can be applied to both conservative and dissipative systems. The integrated paths can then be decoded to the original full-dimensional manifold and be compared to the ground truth solution. This method is tested with two examples applied to fluid and solid mechanics., 17 pages, 7 figures

We address the problem of machine learning of constitutive laws when large experimental deviations are present. This is particularly important in soft living tissue modeling, for instance, where large patient-dependent data is found. We focus on two aspects that complicate the problem, namely, the presence of an important dispersion in the experimental results and the need for a rigorous compliance to thermodynamic settings. To address these difficulties, we propose to use, respectively, Topological Data Analysis techniques and a regression over the so-called General Equation for the Nonequilibrium Reversible-Irreversible Coupling (GENERIC) formalism (M. Grmela and H. Ch. Oettinger, Dynamics and thermodynamics of complex fluids. I. Development of a general formalism. Phys. Rev. E 56, 6620, 1997). This allows us, on one hand, to unveil the true &ldquo, shape&rdquo, of the data and, on the other, to guarantee the fulfillment of basic principles such as the conservation of energy and the production of entropy as a consequence of viscous dissipation. Examples are provided over pseudo-experimental and experimental data that demonstrate the feasibility of the proposed approach.

In this paper we present the basics of a novel methodology for the development of simulation-based and augmented learning tools in the context of applied science and engineering. It is based on the extensive use of model order reduction, and particularly, of the so-called Proper Generalized Decomposition (PGD) method. This method provides a sort of meta-modeling tool without the need for prior computer experiments that allows the user to obtain real-time response in the solution of complex engineering or physical problems. This real-time capability also allows for its implementation in deployed, touch-screen, handheld devices or even to be immersed into electronic textbooks. We explore here the basics of the proposed methodology and give examples on a few challenging applications never until now explored, up to our knowledge.

International audience; In the recent years, automotive car industry is evolving towards a new generation of autonomous vehicles, where decision making is not fully perform by the driver but it partially relies on the technology of the car itself. Indeed, a CPU inside the car will process all information coming from the sensors, distinguishing different scenarios appearing in the real life and ultimately allowing decision making. Since the CPU will be confronted with plenty of information, tools like machine learning or big-data analysis will be a useful ally to separate data from information. These existing machine learning techniques, such as kernel Principal Component Analysis (k-PCA), Locally Linear Embedding (LLE) among many other techniques, are useful to unveil the latent parameters defining a given scenario. Indeed, these algorithms have been already used to perform real-time classification of signals appearing throughout the road. Selecting the modeling of the electromagnetic response of the radar plays an important role to achieve real time constraints. Even though Helmholtz equation represents accurately the physics, the computational cost of such simulation is not affordable for real-time applications due to high radar operating frequencies, resulting into a very fine finite element mesh. On the other hand, far field approaches are not so accurate when the objects are very close due to plane wave assumption. In the first part of this work, the Geometrical Optics method is investigated in this work as a possible route to fulfill both real-time and accuracy constraints. The main hypothesis under such model is that waves are treated as straight lines constrained to optical reflection laws. Therefore, there is no need to mesh the interior of the domain. However, the accuracy of such approach is compromised when the size of the objects inside the domain are comparable to the wave lengths or in the vicinity of angular points. The second part is mainly focused on of the application of manifold learning and big data analysis into a data set of precomputed scenarios. Indeed, the identification of an unknown scenario from electromagnetic signals is purchased. Nevertheless, current research lines are devoted to give an answer to questions such as how many receptors do we need to identify unequivocally the scenario, where to locate the receptors, or which parts of the scenario have a negligible impact in the electromagnetic response.

International audience; Even if the diffusion equation has been widely used in physics and engineering, and its physical content is well understood, some variants of it escape fully physical understanding. In particular, anormal diffusion appears in the so-called fractional diffusion equation, whose main particularity is its non-local behavior, whose physical interpretation represents the main part of the present work.

International audience; This paper is concerned with the solution to structural dynamics equations. The technique here presented is closely related to Harmonic Analysis, and therefore it is only concerned with the long-term forced response. Proper Generalized Decomposition (PGD) is used to compute space-frequency separated representations by considering the frequency as an extra coordinate. This formulation constitutes an alternative to classical methods such as Modal Analysis and it is especially advantageous when parametrized structural dynamics equations are of interest. In such case, there is no need to solve the parametrized eigenvalue problem and the space-time solution can be recovered with a Fourier inverse transform. The PGD solution is valid for any forcing term that can be written as a combination of the considered frequencies. Finally, the solution is available for any value of the parameter. When the problem involves frequency-dependent parameters the proposed technique provides a specially suitable method that becomes computationally more efficient when it is combined with a modal representation.

International audience; The properties of ceramic materials are dependent on crystal size and their distribution. These parameters can be controlled using electrospinning of the two/phase mixed system. The pre/ ceramic solution consists of silicon nano/particles and polyacrylonitrile (PAN) polymer mixture. Particles distribution during the electrospinning technique was characterized using TEM microscopy and modeled using Finite Element Method (FEM). The experimental and numerical results were in agreement. Large silicon particles were located in the skin and the smaller ones were located at the core. This illustrated by the migration rate from the core which was the fastest for large particles and it diminished as the particles become smaller in size. The threshold for Stokes number was found to be around 2.2E-4 with a critical particle size of 1.0E7 m in diameter. The current results are very promising, as it demonstrated a novel way for the fabrication of PAN/Si ceramic nano/fibers with a gradient of particle size and properties from the skin to the core.

International audience; In the paradigm of data-intensive science, automated, unsupervised discovering of governing equations for a given physical phenomenon has attracted a lot of attention in several branches of applied sciences. In this work, we propose a method able to avoid the identification of the constitutive equations of complex systems and rather work in a purely numerical manner by employing experimental data. In sharp contrast to most existing techniques, this method does not rely on the assumption on any particular form for the model (other than some fundamental restrictions placed by classical physics such as the second law of thermodynamics, for instance) nor forces the algorithm to find among a predefined set of operators those whose predictions fit best to the available data. Instead, the method is able to identify both the Hamiltonian (conservative) and dissipative parts of the dynamics while satisfying fundamental laws such as energy conservation or positive production of entropy, for instance. The proposed method is tested against some examples of discrete as well as continuum mechanics, whose accurate results demonstrate the validity of the proposed approach.

"This is the peer reviewed version of the following article: Huerta, Antonio, Enrique Nadal, and Francisco Chinesta. 2018. Proper Generalized Decomposition Solutions within a Domain Decomposition Strategy. International Journal for Numerical Methods in Engineering 113 (13). Wiley: 1972 94. doi:10.1002/nme.5729, which has been published in final form at https://doi.org/10.1002/nme.5729. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving."

The properties of reinforced polymers strongly depend on the microstructural state, that is, the orientation state of the fibres suspended in the polymeric matrix, induced by the forming process. Understanding flow-induced anisotropy is thus a key element to optimize both materials and process. Despite the important progresses accomplished in the modelling and simulation of suspensions, few works addressed the fact that usual processing flows evolve in confined configurations, where particles characteristic lengths may be greater than the thickness of the narrow gaps in which the flow takes place. In those circumstances, orientation kinematics models proposed for unconfined flows must be extended to the confined case. In this short communication, we propose an alternative modelling framework based on the use of unilateral mechanics, consequently exhibiting a clear analogy with plasticity and contact mechanics. This framework allows us to revisit the motion of confined particles in Newtonian and non-Newtonian matrices. We also prove that the confined kinematics provided by this model are identical to those derived from microstructural approaches (Perez et al. (2016) [1] ).

Upscaling behaviors of heterogeneous microstructures to define macroscopic effective media is of major interest in many areas of computational mechanics, in particular those related to materials and processes engineering. In this paper, we explore the possibility of defining a macroscopic behavior manifold from microscopic calculations, and then use it directly for efficiently performing manifold-based simulations at the macroscopic scale. We consider in this work upscaling of non-Newtonian flows in porous media, and more particularly the ones involving short-fibre suspensions.

International audience; We discuss the use of hierarchical collocation to approximate the numerical solution of parametric models. With respect to traditional projection-based reduced order modeling, the use of a collocation enables non-intrusive approach based on sparse adaptive sampling of the parametric space. This allows to recover the low-dimensional structure of the parametric solution subspace while also learning the functional dependency from the parameters in explicit form. A sparse low-rank approximate tensor representation of the parametric solution can be built through an incremental strategy that only needs to have access to the output of a determin-istic solver. Non-intrusiveness makes this approach straightforwardly applicable to challenging problems characterized by nonlinearity or non affine weak forms. As we show in the various examples presented in the paper, the method can be interfaced with no particular effort to existing third party simulation software making the proposed approach particularly appealing and adapted to practical engineering problems of industrial interest.

The use of constitutive equations calibrated from data has been implemented into standard numerical solvers for successfully addressing a variety problems encountered in simulation-based engineering sciences (SBES). However, the complexity remains constantly increasing due to the need of increasingly detailed models as well as the use of engineered materials. Data-Driven simulation constitutes a potential change of paradigm in SBES. Standard simulation in computational mechanics is based on the use of two very different types of equations. The first one, of axiomatic character, is related to balance laws (momentum, mass, energy, $$\ldots $$ ), whereas the second one consists of models that scientists have extracted from collected, either natural or synthetic, data. Data-driven (or data-intensive) simulation consists of directly linking experimental data to computers in order to perform numerical simulations. These simulations will employ laws, universally recognized as epistemic, while minimizing the need of explicit, often phenomenological, models. The main drawback of such an approach is the large amount of required data, some of them inaccessible from the nowadays testing facilities. Such difficulty can be circumvented in many cases, and in any case alleviated, by considering complex tests, collecting as many data as possible and then using a data-driven inverse approach in order to generate the whole constitutive manifold from few complex experimental tests, as discussed in the present work.

PurposeThe purpose of this paper is to present a reduced order computational strategy for a multi-physics simulation involving a fluid flow, electromagnetism and heat transfer in a hot-wall chemical vapour deposition reactor. The main goal is to produce a multi-parametric solution for fast exploration of the design space to perform numerical prototyping and process optimisation.Design/methodology/approachDifferent reduced order techniques are applied. In particular, proper generalized decomposition is used to solve the parameterised heat transfer equation in a five-dimensional space.FindingsThe solution of the state problem is provided in a compact separated-variable format allowing a fast evaluation of the process-specific quantities of interest that are involved in the optimisation algorithm. This is completely decoupled from the solution of the underlying state problem. Therefore, once the whole parameterised solution is known, the evaluation of the objective function is done on-the-fly.Originality/valueReduced order modelling is applied to solve a multi-parametric multi-physics problem and generate a fast estimator needed for preliminary process optimisation. Different order reduction techniques are combined to treat the flow, heat transfer and electromagnetism problems in the framework of separated-variable representations.

Summary One of the main difficulties that a reduced-order method could face is the poor separability of the solution. This problem is common to both a posteriori model order reduction (proper orthogonal decomposition, reduced basis) and a priori [proper generalized decomposition (PGD)] model order reduction. Early approaches to solve it include the construction of local reduced-order models in the framework of POD. We present here an extension of local models in a PGD—and thus, a priori—context. Three different strategies are introduced to estimate the size of the different patches or regions in the solution manifold where PGD is applied. As will be noticed, no gluing or special technique is needed to deal with the resulting set of local reduced-order models, in contrast to most proper orthogonal decomposition local approximations. The resulting method can be seen as a sort of a priori manifold learning or nonlinear dimensionality reduction technique. Examples are shown that demonstrate pros and cons of each strategy for different problems.

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&mdash, the so-called computational vademecums&mdash, 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.

International audience; In the framework of civil aviation noise levels are becoming restricted every year, on one hand to provide comfort to the passengers and on the other hand to be compliant with regulations protecting airports surroundings. New technologies are required to reduce noise to cope with this restrictions as well as to guarantee a comfortable flight for passengers. For technological industries it is compulsory to stay competitive and keep improving the technology related to air intake acoustic liners. With an unceasingly growing market, for industries it is key to stay in the vanguard of air inlet technologies, ensuring innovation and establishing a proactive environment for future product generations. One of the main objectives in this framework is the reduction of the development time of these new technologies in all the stages of the process. In this work we focus on the design stage of a new prototype and we propose a hybrid technique enabling faster design and the reduction of development time. When designing new technologies or prototypes there are usually two constraints. On one hand, more innovative prototypes may present unconventional shapes are not accurately represented by conventional physical models. On the other hand, the available data is scarce, thus limiting the use of most innovative techniques based on the state-of-art of Artificial Intelligence. In this paper we propose a solution laying in the hybrid twin paradigm, combining both, data in the low limit and physics to provide a hybrid model able to represent unconventional and innovative acoustic solutions.

We present a real-time method for computing the mechanical interaction between real and virtual objects in an augmented reality environment. Using model order reduction methods we are able to estimate the physical behavior of deformable objects in real time, with the precision of a high-fidelity solver but working at the speed of a video sequence. We merge tools of machine learning, computer vision, and computer graphics in a single application to describe the behavior of deformable virtual objects allowing the user to interact with them in a natural way. Three examples are provided to test the performance of the method. Ministerio de Ciencia e Innovación, Grant/Award Number: CICYT-DPI2017-85139-C2-1-R

International audience; This paper is concerned with the computation of the inverse impulse response of a parametrized structural dynamics problem using reduced-order modeling and randomized excitations. A two-stages approach is proposed, involving the solution of both direct and inverse problems. In the first stage, the parametrized structural dynamics problem is formulated in the frequency domain, and solved using a reduced-order modeling approach. As a result, the parametric transfer function of the structure is obtained, and then readily transformed into a parametric direct impulse response (DIR). In the second stage, the parametric inverse impulse response (IIR) is computed. We use randomized excitations to generate synthetic samples inexpensively from the parametric DIR. Based on these, the parametric IIR is computed by minimizing the mean square error between the estimate and the samples. Most importantly, we show that the randomized excitations can be generated by sampling the frequency domain only. Hence, the parametric domain does not need to be sampled, which makes the computation of the parametric IIR very efficient.

International audience; In this paper, a novel self-learning digital twin strategy is developed for fluid sloshing phenomena. This class of problems is of utmost importance for robotic manipulation of fluids, for instance, or, in general, in simulation-assisted decision making. The proposed method infers the (linear or non-linear) constitutive behavior of the fluid from video sequences of the sloshing phenomena. Real-time prediction of the fluid response is obtained from a reduced order model (ROM) constructed by means of thermodynamics-informed data-driven learning. From these data, we aim to predict the future response of a twin fluid reacting to the movement of the real container. The constructed system is able to perform accurate forecasts of its future reactions to the movements of the containers. The system is completed with augmented reality techniques, so as to enable comparisons among the predicted result with the actual response of the same liquid and to provide the user with insightful information about the physics taking place.

Lithium-ion batteries are widely used in the automobile industry (electric vehicles and hybrid electric vehicles) due to their high energy and power density. However, this raises new safety and reliability challenges which require development of novel sophisticated Battery Management Systems (BMS). A BMS ensures the safe and reliable operation of a battery pack and to realize it a model must be solved. However, current BMSs are not adapted to the specifications of the automotive industry, as they are unable to give accurate results at real-time rates and during a wide operation range. For this reason, the main focus of this work is to develop a Hybrid Twin, as introduced in Chinesta et al. (Arch Comput Methods Eng (in press), 2018. https://doi.org/10.1007/s11831-018-9301-4 ), so as to meet the requirements of the new generation of BMS. To achieve this, three reduced order model techniques are applied to the most commonly used physics-based models, each one for a different range of application. First, a POD model is used to greatly reduce the simulation time and the computational effort for the pseudo-2D model, while maintaining its accuracy. In this way, cell design, optimization of parameters, and simulation of battery packs can be done while saving time and computational resources. In addition, its real-time performance has been studied. Next, a regression model is constructed from data by using the sparse-Proper Generalized Decomposition (s-PGD). It is shown that it achieves real-time performance for the whole electric vehicle (EV) system with a battery pack. In addition, this regression model can be used in a BMS without issues because of the simple algebraic expression obtained. A simulation of the EV with the proposed approach is demonstrated using the system simulation tool SimulationX (ESI ITI GmbH. Dresden, Germany). Furthermore, the Digital Twin created using the s-PGD does not only allow for real-time simulations, but it can also adapt its predictions taking into consideration the real driving conditions and the real driving cycle to change the planning in real-time. Finally, a data-driven model based on the employment of Dynamic Mode Decomposition techniques is developed to extract an on-line model that corrects the gap between prediction and measurement, thus constructing the first (to our knowledge) hybrid twin of a Li-ion battery able to self-correct from data. In addition, thanks to this model, the above gap is corrected during the driving process, taking into consideration real-time restrictions.

International audience; Rheological behavior of nanolayered films of polyethylene/polyamide 6 (PE/PA6) compatibilized in situ during the coextrusion process has been studied at a temperature between the melting temperatures of PE and PA6. Thanks to the high number of interfaces, a drastic increase in dynamic moduli has been measured when increasing the interphase volume fraction in the films, and a solid-like behavior for the interphase was identified. Different models are compared to capture the complex viscosity of nanolayered films as a function of angular frequency. A model considering interphase and bulk viscosities and a single fitting parameter, namely, the thickness over which the viscosity decreases linearly from the interphase to the bulk one, captures the complex viscosity of all samples. This thickness is comparable to the PE layer thickness up to values about 1 μm before a significant bulk region has to be added to capture the behavior for thicker layers. This suggests that the melt rheology is impacted by the presence of a nanometric interphase over very large (micronic) length scales.

International audience; Nonlinear behavior of soils during a seismic event has a predominant role in current site response analysis. Soil response analysis, and more concretely laboratory data, indicate that the stress-strain relationship of soils is nonlinear and exhibits hysteresis. An equivalent linearization method, in which non-linear characteristics of shear modulus and damping factor of soils are modeled as equivalent linear relations of the shear strain is usually applied, but this assumption, however, may lead to a conservative approach of the seismic design. In this paper, we propose an alternative analysis formulation, able to address forced response simulation of soils exhibiting their characteristic nonlinear behavior. The proposed approach combines ingredients of modal and harmonic analyses enabling efficient time-integration of nonlinear soil behaviors based on the offline construction of a dynamic response parametric solution by using Proper Generalized Decomposition (PGD)-based model order reduction technique.

International audience; Simulations of flows containing non-spherical particles (fibres or ellipsoids) rely on the knowledge of the equation governing the particle motion in the flow. Most models used nowadays are based on the pioneering work of Jeffery (1922), who obtained an equation for the motion of an ellipsoidal particle immersed in a Newtonian fluid, despite the fact that this model relies on strong assumptions: negligible inertia, unconfined flow, dilute regime, flow unperturbed by the presence of the suspended particle, etc. In this work, we propose a dumbbell-based model aimed to describe the motion of an inertial fibre or ellipsoid suspended in a Newtonian fluid. We then use this model to study the orientation kinematics of such particle in a linear shear flow and compare it to the inertialess case. In the case of fibres, we observe the appearance of periodic orbits (whereas inertialess fibres just align in the flow field). For spheroids, our model predicts an orbit drift towards the flow-gradient plane, either gradually (slight inertia) or by first rotating around a moving oblique axis (heavy particles). Multi-Particle Collision Dynamics (MPCD) simulations were carried out to assess the model predictions in the case of inertial fibres and revealed similar behaviours.

This is a post-peer-review, pre-copyedit version of an article published in Journal of scientific computing. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10915-019-00917-2 Tensor representations allow compact storage and efficient manipulation of multi-dimensional data. Based on these, tensor methods build low-rank subspaces for the solution of multi-dimensional and multi-parametric models. However, tensor methods cannot always be implemented efficiently, specially when dealing with non-linear models. In this paper, we discuss the importance of achieving a tensor representation of the model itself for the efficiency of tensor-based algorithms. We investigate the adequacy of interpolation rather than projection-based approaches as a means to enforce such tensor representation, and propose the use of cross approximations for models in moderate dimension. Finally, linearization of tensor problems is analyzed and several strategies for the tensor subspace construction are proposed.

International audience; Fine modeling of the structure and mechanics of materials from the nanometric to the micrometric scales uses descriptions ranging from quantum to statistical mechanics. Most of these models consist of a partial differential equation defined in a highly multidimensional domain (e.g. Schrodinger equation, Fokker-Planck equations among many others). The main challenge related to these models is their associated curse of dimensionality. We proposed in some of our former works a new strategy able to circumvent the curse of dimensionality based on the use of separated representations (also known as finite sums decomposition). This technique proceeds by computing at each iteration a new sum that consists of a product of functions each one defined in one of the model coordinates. The issue related to error estimation has never been addressed. This paper presents a first attempt on the accuracy evaluation of such a kind of discretization techniques.

International audience; Unveiling physical laws from data is seen as the ultimate sign of human intelligence. While there is a growing interest in this sense around the machine learning community, some recent works have attempted to simply substitute physical laws by data. We believe that getting rid of centuries of scientific knowledge is simply nonsense. There are models whose validity and usefulness is out of any doubt, so try to substitute them by data seems to be a waste of knowledge. While it is true that fitting well-known physical laws to experimental data is sometimes a painful process, a good theory continues to be practical and provide useful insights to interpret the phenomena taking place. That is why we present here a method to construct, based on data, automatic corrections to existing models. Emphasis is put in the correct thermodynamic character of these corrections, so as to avoid violations of first principles such as the laws of thermodynamics. These corrections are sought under the umbrella of the GENERIC framework (Grmela and Oettinger, 1997), a generalization of Hamiltonian mechanics to non-equilibrium thermodynamics. This framework ensures the satisfaction of the first and second laws of thermodynamics, while providing a very appealing context for the proposed automated correction of existing laws. In this work we focus on solid mechanics, particularly large strain (visco-)hyperelasticity.

Este artículo se encuentra disponible en la siguiente URL: https://www.mdpi.com/2076-3417/11/14/6554 Modal analysis is widely used for addressing NVH—Noise, Vibration, and Hardness—in automotive engineering. The so-called principal modes constitute an orthogonal basis, obtained from the eigenvectors related to the dynamical problem. When this basis is used for expressing the displacement field of a dynamical problem, the model equations become uncoupled. Moreover, a reduced basis can be defined according to the eigenvalues magnitude, leading to an uncoupled reduced model, especially appealing when solving large dynamical systems. However, engineering looks for optimal designs and therefore it focuses on parametric designs needing the efficient solution of parametric dynamical models. Solving parametrized eigenproblems remains a tricky issue, and, therefore, nonintrusive approaches are privileged. In that framework, a reduced basis consisting of the most significant eigenmodes is retained for each choice of the model parameters under consideration. Then, one is tempted to create a parametric reduced basis, by simply expressing the reduced basis parametrically by using an appropriate regression technique. However, an issue remains that limits the direct application of the just referred approach, the one related to the basis ordering. In order to order the modes before interpolating them, different techniques were proposed in the past, being the Modal Assurance Criterion—MAC—one of the most widely used. In the present paper, we proposed an alternative technique that, instead of operating at the eigenmodes level, classify the modes with respect to the deformed structure shapes that the eigenmodes induce, by invoking the so-called Topological Data Analysis—TDA—that ensures the invariance properties that topology ensure.

International audience; Transient wave propagation problems may involve rich discretizations, both in space and in time, leading to computationally expensive simulations, even for simple spatial domains. The Proper Generalized Decomposition (PGD) is an attractive model order reduction technique to address this issue, especially when the spatial domain is separable. In this work, we propose a space separation with a time adaptive number of modes to efficiently capture transient wave propagation in separable domains. We combine standard time integration schemes with this original space separated representation for empowering standard procedures. The numerical behavior of the proposed method is explored through several 2D wave propagation problems involving radial waves, propagation on long time analyses, and wave conversions. We show that the PGD solution approximates its standard finite element solution counterpart with acceptable accuracy, while reducing the storage needs and the computation time (CPU time). Numerical results show that the CPU time per time step linearly increases when refining the mesh, even with implicit time integration schemes, which is not the case with standard procedures.

We develop a method to learn physical systems from data that employs feedforward neural networks and whose predictions comply with the first and second principles of thermodynamics. The method employs a minimum amount of data by enforcing the metriplectic structure of dissipative Hamiltonian systems in the form of the so-called General Equation for the Non-Equilibrium Reversible-Irreversible Coupling, GENERIC [M. Grmela and H.C Oettinger (1997). Dynamics and thermodynamics of complex fluids. I. Development of a general formalism. Phys. Rev. E. 56 (6): 6620-6632]. The method does not need to enforce any kind of balance equation, and thus no previous knowledge on the nature of the system is needed. Conservation of energy and dissipation of entropy in the prediction of previously unseen situations arise as a natural by-product of the structure of the method. Examples of the performance of the method are shown that include conservative as well as dissipative systems, discrete as well as continuous ones., Comment: 19 pages, 11 figures

The classical Jeffery model allows for the prediction of the flow-induced orientation in dilute fibre suspensions. In most industrial applications, however, fibre suspensions are concentrated and fibre-fibre interactions cannot be ignored any longer. These interactions have been traditionally modelled at the mesoscopic and macroscopic scales by introducing a phenomenological diffusion term inducing a randomizing effect. In the so-called Folgar & Tucker (F&T) model, widely used in applications, the diffusion coefficient is assumed to scale linearly with the flow intensity, the latter being described by the second invariant of the rate of strain tensor. Modifications and alternatives to the F&T model have been proposed in view of the difficulty for the F&T model to explain an apparent orientation delay observed experimentally in injection-moulded parts. The noticed deviations were attributed to the intense fibre-fibre interactions, thus pointing to the limitations of a phenomenological diffusion term for describing them. In the present work, we revisit the F&T model and compare its predictions with those obtained bysimplified yet state-of-the-art direct numerical simulation (DNS) in unconfined and confined simple shear flows for a range of shear rates and concentrations, the latter ensuring intense fibre-fibre interactions. In unconfined flows, we find that the F&T model agrees quantitatively with the DNS results once an adequate closure relation is considered for approximating the fourth-order orientation tensor involved in the F&T model. Thus, the results seem to confirm, at least in simple shear flows, the F&T assumption for the form of the isotropic rotary diffusion function scaling linearly with the magnitude of the scalar rate of deformation. Also, a linear scalingof the diffusivity with the fibre concentration is observed. This conclusion remains unexpectedly valid under moderately-confined flow conditions as soon as an advanced fitted closure, like the IBOF, is considered within the F&T model. Other simpler closures (e.g. quadratic or hybrid), however, definitively fail to address confinement issues as also reported in our former work for the dilute regime. Obviously, these conclusions rest on the validity of the considered state-of-the-art DNS, which remains at present an open question.

We address the extension of Jeffery’s model, governing the orientation of rods immersed in a Newtonian fluid, to confined regimes occurring when the thickness of the flow domain is narrower than the rod length. The main modelling ingredients concern: (i) the consideration of the rod interactions with one or both gap walls and their effects on the rod orientation kinematics; and (ii) the consideration of non-uniform strain rates at the scale of the rod, requiring higher-order descriptions. Such scenarios are very close to those encountered in real composites forming processes and have never been appropriately addressed from a microstructural point of view. We also show that confinement conditions affect the rheology of the suspension.

Standard simulation in classical mechanics is based on the use of two very different types of equations. The first one, of axiomatic character, is related to balance laws (momentum, mass, energy, ...), whereas the second one consists of models that scientists have extracted from collected, natural or synthetic data. Even if one can be confident on the first type of equations, the second one contains modeling errors. Moreover, this second type of equations remains too particular and often fails in describing new experimental results. The vast majority of existing models lack of generality, and therefore must be constantly adapted or enriched to describe new experimental findings. In this work we propose a new method, able to directly link data to computers in order to perform numerical simulations. These simulations will employ axiomatic, universal laws while minimizing the need of explicit, often phenomenological, models. This technique is based on the use of manifold learning methodologies, that allow to extract the relevant information from large experimental datasets.

Thermoplastic composites are attractive because they can be recycled and exhibit superior mechanical properties. As part of a more general research effort, in this paper attention is paid to squeeze flow of continuous fiber laminates. In the case of unidirectional prepregs, the ply constitutive equation, when elastic effects are neglected, can be modeled as a transversally isotropic fluid, that must satisfy the fiber inextensibility as well as the fluid incompressibility. When laminate is squeezed, depending on the plies orientation and the lubrication conditions at their interfaces, the flow kinematics exhibits a complex dependency along the laminate thickness requiring one to describe the detailed velocity field through the thickness. Simulations at this scale are computationally intensive or almost impossible with standard FE techniques. In this work the squeeze flow of laminates is revisited from the perspective of the Proper Generalized Decomposition that makes possible extremely detailed 3D calculations with a computational cost characteristic of 2D (sometimes 1D) simulations.

Dynamic simulations of pantograph catenary interaction are nowadays essential for improving the performance of railway locomotives, by achieving better current collection at higher speeds and lower wear of thecollecting parts.The first step in performing these simulations is to compute the static equilibrium of the overhead line.The initial dropper lengths play an important role in hanging the contact wire at an appropriate height. From a classical point of view, if one wants to obtain the static equilibrium configuration of the system for different combinations of dropper lengths, one static pro- blem must be solved for each combination of lengths, which involves a prohibitive computational cost. In this paper we propose a parametric model of the catenary, including the undeformed dropper lengths as extra-coordinates of the problem. This multidimensional problem is efficiently solved by means of the Proper Generalized Decomposition (PGD) technique, avoiding the curse of dimensionality issue. The capabilities and performance of the proposed method are shown by numerical examples., The authors would like to acknowledge the financial support of the FPU program offered by the Ministerio de Educacion, Cultura y Deporte under Grant number FPU13/04191. The funding from Universitat Politecnica de Valencia and Generalitat Valenciana (PROMETEO/2012/023) are also acknowledged.

Thermoplastic automated tape placement process allows the manufacture of large composite parts. This method is based on the continuous welding by fusion bonding of a thermoplastic matrix composite ply on a substrate. It has received an increasing interest in recent years due to its ability to produce parts out of autoclave. In order to control and optimize the quality of the part, accurate predictions of the thermo-mechanical history applied during the manufacturing of the laminate are needed, usually through the numerical solution of the involved thermo-mechanical models. In a former work a parametric thermal modeling was successfully accomplished. The present work focusses on the thermo-mechanical modeling able to predict the residual stresses installed in the part during the forming process. An efficient (fast and accurate) thermo-mechanical solver for predicting residual stresses is compulsory for optimizing the process.

A new efficient updated Lagrangian strategy for numerical simulations of material forming processes is presented. The basic ingredient is the tensorial decomposition of the velocity field into a finite sum of in-plane and an out-of-plane components, giving rise to an equivalent computational complexity of some two-dimensional problems and some one-dimensional ones (therefore, much less than the true three-dimensional complexity of the original problem). This is efficiently achieved by using Proper Generalized Decomposition (PGD) techniques, which are here employed in an updated Lagrangian framework for the very first time. This updated Lagrangian nature of the method needs the use of a robust numerical integration technique (in this case, the Stabilized Conforming Nodal Integration has been chosen) for addressing the highly distorted projected meshes. The resulting strategy is of general purpose, although it is especially well suited for addressing models defined in plate or shell (in general, parallelepipedic) domains. The basics of the just-developed method are shown, together with some numerical examples to show the potential of the technique.