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Numerical simulations have long been used in many engineering process industries for the virtual evaluation of responses from an accurate solution of the physics/mathematical models describing it. However, in most industrial cases, these simulations tend to be time-consuming, especially in studies involving parameter optimization studies/inverse analysis where a multitude of direct computations are necessary. Non-intrusive Model Order Reduction techniques (SSL-PGD, s-PGD) enable the construction of parametric solution spaces to ensure almost instantaneous responses to changes in input parameters. These parametrized solutions are built from snapshots generated from simulations using commercially available software, but the process parameters and re-meshing rules add a condition that the different snapshots be suitably parametrized for being able to compute and represent the parametric solutions using the MOR techniques. The snapshots generated in the case of sheet-metal forming simulations are 3D surfaces. Even though surface parametrization is a fairly easy process in the case of planar surfaces, the problem ceases to be trivial in the case of 3D surfaces. In this work, we present a conformal mapping procedure based on the Riemannian surface parametrization using the Yamabe-flow for the parametrization of 3D surfaces into planar 2D surfaces. These parametrized surfaces can then be interpolated to create parametric solution configurations for the full range of input parameters and hence allows the application of non-intrusive model order reduction techniques to simulations which include adaptive mesh refinement.

Several defects might affect a casting part and degrade its quality and the process efficiency. Porosity formation is one of the major defects that can appear in the resulting product. Thus, several research studies aimed at investigating methods that minimize this anomaly. In the present work, a porosity prediction procedure is proposed to assist users at optimizing porosity distribution according to their application. This method is based on a supervised learning approach to predict shrinkage porosity from thermal history. Learning data are generated by a casting simulation software operating for different process parameters. Machine learning was coupled with a modal representation to interpolate thermal history time series for new parameters combinations. By comparing the predicted values of local porosity to the simulated results, it was demonstrated that the proposed model is efficient and can open perspectives in the casting process optimization.

Learning and reasoning about physical phenomena is still a challenge in robotics development, and computational sciences play a capital role in the search for accurate methods able to provide explanations for past events and rigorous forecasts of future situations. We propose a thermodynamics-informed active learning strategy for fluid perception and reasoning from observations. As a model problem, we take the sloshing phenomena of different fluids contained in a glass. Starting from full-field and high-resolution synthetic data for a particular fluid, we develop a method for the tracking (perception) and analysis (reasoning) of any previously unseen liquid whose free surface is observed with a commodity camera. This approach demonstrates the importance of physics and knowledge not only in data-driven (grey box) modeling but also in the correction for real physics adaptation in low data regimes and partial observations of the dynamics. The method presented is extensible to other domains such as the development of cognitive digital twins, able to learn from observation of phenomena for which they have not been trained explicitly., 15 pages, 8 figures

International audience; Fused deposition modeling (FDM) is a promising additive manufacturing technique for fabrication of continuous fiber-reinforced thermoplastic composites. For composite applications, the balance of material properties, including rigidity and toughness, needs to be considered. To overcome the drawbacks induced by single continuous fiber reinforcement, this study focused on the design and characterization of hybrid continuous fiber (continuous carbon and Kevlar fibers)-reinforced polyamide (PA)-based composites, prepared by 3D printing, to achieve comprehensive performance improvements and designable mechanical properties. The deformation and failure behaviors with the effects of hybrid conception, stacking sequences, and raster orientations of composites were investigated. A hybrid effect model was introduced to evaluate the hybrid effect of 3D printed continuous fiber-filled composites. Besides, compared to composites fabricated via conventional methods, a major difference in 3D printed hybrid composites is the performance of interfacial bonding. A roller peeling test was therefore conducted to investigate the interfacial strength of different materials. An analytical approach was developed to predict the tensile modulus of the printed hybrid composites by introducing an interfacial strengthening coefficient into the volume average stiffness model. The combined experimental and predicted results showed that hybrid composite specimens with separated distribution sequence showed a higher tensile modulus compared to hybrid composites with concentrated distribution. The higher tensile properties of the printed hybrid composites with separated continuous fiber-reinforced layers were attributed to the strong interfacial bonding, which delayed crack initiation and propagation.

Many composite manufacturing processes employ the consolidation of pre-impregnated preforms. However, in order to obtain adequate performance of the formed part, intimate contact and molecular diffusion across the different composites’ preform layers must be ensured. The latter takes place as soon as the intimate contact occurs and the temperature remains high enough during the molecular reptation characteristic time. The former, in turn, depends on the applied compression force, the temperature and the composite rheology, which, during the processing, induce the flow of asperities, promoting the intimate contact. Thus, the initial roughness and its evolution during the process, become critical factors in the composite consolidation. Processing optimization and control are needed for an adequate model, enabling it to infer the consolidation degree from the material and process features. The parameters associated with the process are easily identifiable and measurable (e.g., temperature, compression force, process time, . . . ). The ones concerning the materials are also accessible; however, describing the surface roughness remains an issue. Usual statistical descriptors are too poor and, moreover, they are too far from the involved physics. The present paper focuses on the use of advanced descriptors out-performing usual statistical descriptors, in particular those based on the use of homology persistence (at the heart of the so-called topological data analysis—TDA), and their connection with fractional Brownian surfaces. The latter constitutes a performance surface generator able to represent the surface evolution all along the consolidation process, as the present paper emphasizes.

The imminent impact of immersive technologies in society urges for active research in real-time and interactive physics simulation for virtual worlds to be realistic. In this context, realistic means to be compliant to the laws of physics. In this paper we present a method for computing the dynamic response of (possibly non-linear and dissipative) deformable objects induced by real-time user interactions in mixed reality using deep learning. The graph-based architecture of the method ensures the thermodynamic consistency of the predictions, whereas the visualization pipeline allows a natural and realistic user experience. Two examples of virtual solids interacting with virtual or physical solids in mixed reality scenarios are provided to prove the performance of the method., Comment: 11 pages, 7 figures

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.

El objetivo de este trabajo es utilizar inteligencia artificial para aprender las leyes físicas que gobiernan un sistema arbitrario y predecir así su evolución en el tiempo. Para ello se utilizan varios sesgos inductivos, que aseguran la correcta estructura matemática del problema y mejoran su capacidad de generalización.

Two main problems are studied in this article. The first one is the use of the extrusion process for controlled thermo-mechanical degradation of polyethylene for recycling applications. The second is the data-based modelling of such reactive extrusion processes. Polyethylenes (high density polyethylene (HDPE) and ultra-high molecular weight polyethylene (UHMWPE)) were extruded in a corotating twin-screw extruder under high temperatures (350 °C < T < 420 °C) for various process conditions (flow rate and screw rotation speed). These process conditions involved a decrease in the molecular weight due to degradation reactions. A numerical method based on the Carreau-Yasuda model was developed to predict the rheological behaviour (variation of the viscosity versus shear rate) from the in-line measurement of the die pressure. The results were successfully compared to the viscosity measured from offline measurement assuming the Cox-Merz law. Weight average molecular weights were estimated from the resulting zero-shear rate viscosity. Furthermore, the linear viscoelastic behaviours (Frequency dependence of the complex shear modulus) were also used to predict the molecular weight distributions of final products by an inverse rheological method. Size exclusion chromatography (SEC) was performed on five samples, and the resulting molecular weight distributions were compared to the values obtained with the two aforementioned techniques. The values of weight average molecular weights were similar for the three techniques. The complete molecular weight distributions obtained by inverse rheology were similar to the SEC ones for extruded HDPE samples, but some inaccuracies were observed for extruded UHMWPE samples. The Ludovic® (SC-Consultants, Saint-Etienne, France) corotating twin-screw extrusion simulation software was used as a classical process simulation. However, as the rheo-kinetic laws of this process were unknown, the software could not predict all the flow characteristics successfully. Finally, machine learning techniques, able to operate in the low-data limit, were tested to build predicting models of the process outputs and material characteristics. Support Vector Machine Regression (SVR) and sparsed Proper Generalized Decomposition (sPGD) techniques were chosen to predict the process outputs successfully. These methods were also applied to material characteristics data, and both were found to be effective in predicting molecular weights. More precisely, the sPGD gave better results than the SVR for the zero-shear viscosity prediction. Stochastic methods were also tested on some of the data and showed promising results.

The use of mesh-based numerical methods for a 3D elasticity solution of thick plates involves high computational costs. This particularly limits parametric studies and material distribution design problems because they need a large number of independent simulations to evaluate the effects of material distribution and optimization. In this context, in the current work, the Proper Generalized Decomposition (PGD) technique is adopted to overcome this difficulty and solve the 3D elasticity problems in a high-dimensional parametric space. PGD is an a priori model order reduction technique that reduces the solution of 3D partial differential equations into a set of 1D ordinary differential equations, which can be solved easily. Moreover, PGD makes it possible to perform parametric solutions in a unified and efficient manner. In the present work, some examples of a parametric elasticity solution and material distribution design of multi-directional FGM composite thick plates are presented after some validation case studies to show the applicability of PGD in such problems.

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.

We present here a review on some of our latest works concerning the development of thermodynamics-aware machine learning strategies for the data-driven construction of constitutive models. We suggest a methodology constructed upon three main ingredients. (i) the employ of manifold learning strategies to unveil the true dimensionality of data, thus pointing out the need for the definition of “internal” variables, different of the experimental ones. (ii) the process will be described by the so-called General Equation for the Non-Equilibrium Reversible-Irreversible Coupling (GENERIC). (iii) the precise form of the GENERIC terms will be unveiled by regression of data.

International audience; The present work aims at performing a molecular dynamics modeling of suspensions composed of flexible linear molecules. Molecules are represented by a series of connected beads, whose dynamics is governed by three potentials: the extension potential affecting the elongation of segments connecting consecutive beads, the one governing the molecule bending and finally the Lennard-Jones describing the interaction of non-consecutive beads. A population of non-interacting molecules is simulated in elongation and shear flows for different flow and molecule parameters. The flow-induced conformation is analyzed in the different considered situations. Finally a model for predicting the evolution of the population conformation will be obtained by using deep-learning.

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.

International audience; 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.

Nowadays, the use of simulation in industrial applications is a routine practice. However, the need of considering high fidelity models and their associated solutions is demanding for more efficient solvers. Despite the remarkable progress accomplished in hardware and software in the last decades, the ability to simulate high fidelity 3D models, taking into consideration all their richness is still challenging. For example, if we wish to simulate a 3D problem including 10 parameters, each of them taking 10 different values we should solve 1010 3D problems. This issue is known as the curse of dimensionality, and compromises the solution of models defined in high dimensional spaces.

Este artículo se encuentra disponible en la siguiente URL: https://www.mdpi.com/1424-8220/21/12/3943 Este artículo de investigación pertenece al número especial "Autonomous Navigation in Robotics: A New Challenge towards Social Robots". This paper presents a real-time global path planning method for mobile robots using harmonic functions, such as the Poisson equation, based on the Proper Generalized Decomposition (PGD) of these functions. The main property of the proposed technique is that the computational cost is negligible in real-time, even if the robot is disturbed or the goal is changed. The main idea of the method is the off-line generation, for a given environment, of the whole set of paths from any start and goal configurations of a mobile robot, namely the computational vademecum, derived from a harmonic potential field in order to use it on-line for decision-making purposes. Up until now, the resolution of the Laplace or Poisson equations has been based on traditional numerical techniques unfeasible for real-time calculation. This drawback has prevented the extensive use of harmonic functions in autonomous navigation, despite their powerful properties. The numerical technique that reverses this situation is the Proper Generalized Decomposition. To demonstrate and validate the properties of the PGD-vademecum in a potential-guided path planning framework, both real and simulated implementations have been developed. Simulated scenarios, such as an L-Shaped corridor and a benchmark bug trap, are used, and a real navigation of a LEGO®MINDSTORMS robot running in static environments with variable start and goal configurations is shown. This device has been selected due to its computational and memory-restricted capabilities, and it is a good example of how its properties could help the development of social robots.

The need of solving industrial problems using faster and less computationally expensive techniques is becoming a requirement to cope with the present digital transformation of most industries. Recently, data is conquering the domain of engineering with different purposes: (i) defining data-driven models of materials, processes, structures and systems, whose physics-based models, when they exists, remain too inaccurate; (ii) enriching the existing physics-based models within the so-called hybrid paradigm; and (iii) using advanced machine learning and artificial intelligence techniques for scales bridging (upscaling), that is, for creating models that operating at the coarse-grained scale (cheaper in what respect the computational resources) enables integrating the fine-scale richness. The present work addresses the last item, aiming at enhancing standard structural models (defined in 2D shell geometries) for accounting all the fine-scale details (3D with rich through-the-thickness behaviors). For this purpose, two main strategies will be combined: (i) the in-plane-out-of-plane proper generalized decomposition -PGD- serving to provide the fine-scale richness; and (ii) advance machine learning techniques able to learn and extract the regression relating the input parameters with those high-resolution detailed descriptions.

This work retraces the main recent advances in the so-called non-intrusive model order reduction, and more concretely, the construction of parametric solutions related to parametric models, with special emphasis on the technologies enabling allying accuracy, frugality and robustness. Thus, different technologies will be revisited beyond the usual metamodeling techniques making use of polynomial basis or kriging, for addressing multi-parametric models, with sometimes several tens of parameters, while keeping the complexity (DoE size) scaling with the number of parameters. Moreover, sparsity can be profitable for increasing accuracy while avoiding overfitting, and when combined with ANOVA-based decompositions the benefits are potentially huge.

We have seen in Part I of this paper that model order reduction allows the involvement of physics-based models in design, as in the past, but now also in online decision-making, without requiring unreasonable computing resources. On the other hand, machine learning techniques were not ready to cope with the processing speed and the lack of data. It was therefore necessary to adapt a number of techniques, and to create others, capable of operating online and even in the presence of a very small amount of data: the so-called "physics-informed artificial intelligence" techniques. For that purpose, we have adapted and proposed a number of techniques, which have proven and are proving every day in many industrial applications their capabilities and performances. Six major uses of AI in engineering concern: (i) visualization of multidimensional data; (ii) classification and clustering, supervised and unsupervised, where it is assumed that members of the same cluster have similar behaviors; (iii) model extraction, that is, discovering the quantitative relationship between inputs (actions) and outputs (reactions) in a consistent manner with respect to the physical laws. When addressing knowledge extraction, item (iv) above, as well as the need of explaining for certifying, item (v), advances are much limited and both items need for major progresses, as the one enabling discarding useless parameters, or discovering latent variables whose consideration becomes compulsory for explaining experimental findings, or combining parameters that act in a combined manner. Discovering equations is a very timely topic because it finally enables transforming data into knowledge.

Finite element modeling (FEM) has recently become the most attractive computational tool to predict and optimize many industrial problems. However, the FEM becomes ineffective as far as complex multi-physics parameterized problems, such as induction heating process, are concerned because of high computational cost. This work aims at studying the possibility of applying a new approach based on the reduced order modeling (ROM) to obtain approximate solutions of a parametric problem. Basically, the effect of induction heating process parameters on some physical quantities of interest (QoI) will be analyzed under the real-time constraint. To achieve this dimensionality reduction, a set of precomputed solutions is first collected, at some sparse points in the space domain and for a properly selected process parameters, by solving the full-order models implemented in the commercial finite element software FORGE®. A Proper Orthogonal Decomposition (POD) based reducedorder model is then applied to the collected data to find a low dimensional space onto which the solution manifold could be projected and an approximated solution for new process parameters could be efficiently computed in real time. Besides, the POD is applied to build a reduced basis and to compute their corresponding modal coefficients. It is then followed by artificial intelligence techniques for regression purpose, such as sparse Proper Generalized Decomposition, to fit the low dimensional POD modal coefficients. Hence, the problem can be solved with a much lower dimension compared to the initial one. It was shown that a good approximation of the QoI was provided, in low-data limit, using a single POD modal coefficient as a response for the regression methods. However, the obtained approximation accuracy needs to be enhanced.

Additive manufacturing is an appealing solution to produce geometrically complex parts, difficult to manufacture using traditional technologies. The extreme process conditions, in particular the high temperature, complex interactions and couplings, and rich metallurgical transformations that this process entails, are at the origin of numerous process defects. Therefore, the numerical simulation of the process is gaining the interest of both the scientific and the industrial communities. However, simulating that process demands impressive computational resources, limiting high resolution simulations to the microscopic and mesoscopic scales. This paper proposes a thermo-mechanical modeling framework at the process scale as well as its associated reduced order simulation counterpart, enabling the parametric evaluation of the part distortion. It deeply addresses the process calibration using a high-resolution computational procedure based on the use of an in-plane-out-ofplane separated representation at the heart of the so-called Proper Generalized Decomposition (PGD), as well as the analysis of the transient thermal effects, defining the conditions in which the thermal and mechanical analyses can be decoupled., Horizon 2020, Clean Sky 2 Joint Undertaking, grant number 831857, European Union (EU)

International audience; The International Journal of Material Forming -IJMF- was celebrating its 10th anniversary in 2018. With its first issue published in 2008, IJMF continues being a key figure in the science and technology of material forming, covering different approaches (modeling, simulation and experiments), materials (including composites) and forming processes.

The concept of “hybrid twin” (HT) has recently received a growing interest thanks to the availability of powerful machine learning techniques. This twin concept combines physics-based models within a model order reduction framework—to obtain real-time feedback rates—and data science. Thus, the main idea of the HT is to develop on-the-fly data-driven models to correct possible deviations between measurements and physics-based model predictions. This paper is focused on the computation of stable, fast, and accurate corrections in the HT framework. Furthermore, regarding the delicate and important problem of stability, a new approach is proposed, introducing several subvariants and guaranteeing a low computational cost as well as the achievement of a stable time-integration.

International audience; Pipeline structural analysis is a well-developed topic in engineering and research practice. Since water, oil or gas pipeline systems are a key part of modern development, therefore, it is important to ensure an appropriate behavior under seismic action. In this paper, the seismic response of buried pipelines is numerically simulated using a three-dimensional (3D) parametric model of soil-pipeline interaction. The role of several parameters on both soil and pipeline are incorporated into a 2D-1D space separated representation based on the Proper Generalized Decomposition (PGD) framework, which allows addressing 3D parametric problems while reducing the computational complexity of 1D and 2D characteristic problems. These results can be used for design, safety evaluation and protection of buried pipelines crossing seismic area and can be calculated in real time from the parametric solution of the associated problem within the PGD framework.

International audience; Microwave (MW) technology relies on volumetric heating, where thermal energy is induced from an electromagnetic field. Nowadays, the main drawback of this technology is that the complex physics involved in the conversion of electromagnetic energy into thermal energy is not entirely understood and controlled. The main objective of this work is to model, simulate and validate the interactions of microwaves with a composite laminate consisting of a stack of unidirectional layers composed of a resin matrix and carbon fibers, to predict its heating. Once validated, this simulation tool will serve to predict, control and optimize composites forming processes.

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.

International audience; Data-driven modeling provides an efficient approach to compute approximate solutions for complex multiphysics parametrized problems such as induction hardening (IH) process. Basically, some physical quantities of interest (QoI) related to the IH process will be evaluated under real-time constraint, without any explicit knowledge of the physical behavior of the system. Hence, computationally expensive finite element models will be replaced by a parametric solution, called metamodel. Two data-driven models for temporal evolution of temperature and austenite phase transformation, during induction heating, were first developed by using the proper orthogonal decomposition based reduced-order model followed by a nonlinear regression method for temperature field and a classification combined with regression for austenite evolution. Then, data-driven and hybrid models were created to predict hardness, after quenching. It is shown that the results of artificial intelligence models are promising and provide good approximations in the low-data limit case.

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.

[EN] The development of condition monitoring (CM) systems of induction machines (IMs) is essential for the industry because the early fault detection would help engineers to optimise maintenance plans. However, the use of several IMs to test and validate the fault diagnosis methods developed requires also costly test benches that, anyway, often face limitations in the range of faults and operating conditions to be tested. To avoid it, the use of accurate models such as those based on finite element method (FEM) would reduce the major drawbacks of test benches but their inability to execute FEM models in real time largely reduces their application in the development of on-line continuous monitoring systems. To alleviate this problem a hybrid FEM-analytical model has been proposed. It uses an analytical model that can be run in real-time in a hardware in the loop (HIL) system, after its parameters have been computed through FEM simulations. In this way, the proposed model provides high accuracy but at the cost of long simulation times and high computational costs (both computing power and memory resources) to compute the IM parameters. This work aims at reducing these drawbacks. In particular, a model based on sparse identification techniques is proposed. The method balances complexity and accuracy by selecting a sparse model that reduces the number of FEM simulations to accurately compute the coupling parameters of an IM model with different fault severity degrees. Particularly, the proposed methodology has been applied to develop models with abnormal eccentricity levels as this fault is related to development of mechanical faults that produce most of IM breakdowns., This work was supported by the Spanish "Ministerio de Educacion, cultura y Deporte" in the framework of the "Programa Estatal de Promocion del Talento y su Empleabilidad en I+D+i, Subprograma Estatal de Movilidad, del Plan Estatal de Investigacion Cientifica y Tecnica y de Innovacion 2013-2016" in the subframework "Estancias de movilidad en el extranjero Jose Castillejo para jovenes doctores".

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.

Carbon nanotubes (CNTs) belong to a novel class of nanoscale fibers. Their high aspect ratio and superior physical properties make them an appealing candidate to be incorporated into polymeric materials for mechanical reinforcement and conductivity enhancement. This chapter provides an overview of the development of CNT polymer composites. We first discuss the structure and physical properties of CNTs as individual nanoscale entities. We then review different techniques available for processing them into composites and the challenges involved. Two different flow models are introduced, and we conclude this chapter by discussing the performance and potential applications of some CNT polymer composites.

The present work aims at analyzing issues related to the data manifold dimensionality. The interest of the study is twofold: (i) first, when too many measurable variables are considered, manifold learning is expected to extract useless variables; (ii) second, and more important, the same technique, manifold learning, could be utilized for identifying the necessity of employing latent extra variables able to recover single-valued outputs. Both aspects are discussed in the modeling of materials and structural systems by using unsupervised manifold learning strategies. The first, third, and fourth authors are supported by their respective ESI Group research chairs; their support is gratefully acknowledged. The first author is supported by CREATE-ID ESI-ENSAM research chair. The third author is supported by the ESI Group Chair at the University of Zaragoza. The fourth author is supported by CREATE-ID ESI-ENSAM research chair.

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.

We present a novel realtime digital twin based on artificial intelligence to emulate physically sound fluid dynamics, and classify and recognise liquids, with information from video streamings. Results are presented with augmented reality techniques not only for friendly user interaction, but also to provide augmented information in manipulation tasks.

En este trabajo se pretende aplicar inteligencia artificial para predecir la evolución temporal de un sistema físico arbitrario sólo mediante el uso de datos, es decir, sin conocer las ecuaciones que lo rigen. Este método se ha validadado con dos sistemas dinámicos disipativos: uno continuo y otro discreto.