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Learning linear and nonlinear dynamical systems from available data is a timely topic in scientific machine learning. Learning must be performed while enforcing the numerical stability of the learned model, the existing knowledge within an informed or augmented setting, or by taking into account the multiscale dynamics—for both linear and nonlinear dynamics. However, when the final objective of such a learned dynamical system is to be used for control purposes, learning transformed dynamics can be advantageous. Therefore, many alternatives exists, and the present paper focuses on two of them: the first based on the discovery and use of the so-called flat control and the second one based on the use of the Koopman theory. The main contributions when addressing the first is the discovery of the flat output transformation by using an original neural framework. Moreover, when using the Koopman theory, this paper proposes an original procedure for learning parametric dynamics in the latent space, which is of particular interest in control-based engineering applications.

The efficient solution (fast and accurate) of parametric partial differential equations (pPDE) is of major interest in many domains of science and engineering, enabling evaluations of the quantities of interest, optimization, control, and uncertainty propagation—all them under stringent real-time constraints. Different methodologies have been proposed in the past within the model order reduction (MOR) community, based on the use of reduced bases (RB) or the separated representation at the heart of the so-called proper generalized decompositions (PGD). In PGD, an alternate-direction strategy is employed to circumvent the integration issues of operating in multi-dimensional domains. Recently, physics informed neural networks (PINNs), a particular collocation schema where the unknown field is approximated by a neural network (NN), have emerged in the domain of scientific machine learning. PNNs combine the versatility of NN-based approximation with the ease of collocating pPDE. The present paper proposes a combination of both procedures to find an efficient solution for pPDE, that can either be viewed as an efficient collocation procedure for PINN, or as a monolithic PGD that bypasses the use of the fixed-point alternated directions.

Monitoring a deep geological repository for radioactive waste during the operational phases relies on a combination of fit-for-purpose numerical simulations and online sensor measurements, both producing complementary massive data, which can then be compared to predict reliable and integrated information (e.g., in a digital twin) reflecting the actual physical evolution of the installation over the long term (i.e., a century), the ultimate objective being to assess that the repository components/processes are effectively following the expected trajectory towards the closure phase. Data prediction involves using historical data and statistical methods to forecast future outcomes, but it faces challenges such as data quality issues, the complexity of real-world data, and the difficulty in balancing model complexity. Feature selection, overfitting, and the interpretability of complex models further contribute to the complexity. Data reconciliation involves aligning model with in situ data, but a major challenge is to create models capturing all the complexity of the real world, encompassing dynamic variables, as well as the residual and complex near-field effects on measurements (e.g., sensors coupling). This difficulty can result in residual discrepancies between simulated and real data, highlighting the challenge of accurately estimating real-world intricacies within predictive models during the reconciliation process. The paper delves into these challenges for complex and instrumented systems (multi-scale, multi-physics, and multi-media), discussing practical applications of machine and deep learning methods in the case study of thermal loading monitoring of a high-level waste (HLW) cell demonstrator (called ALC1605) implemented at Andra’s underground research laboratory.

There was an error in the original publication, section data availability, stating “Data is available upon request” [...]

Machine learning approaches are currently used to understand or model complex physical systems. In general, a substantial number of samples must be collected to create a model with reliable results. However, collecting numerous data is often relatively time-consuming or expensive. Moreover, the problems of industrial interest tend to be more and more complex, and depend on a high number of parameters. High-dimensional problems intrinsically involve the need for large amounts of data through the curse of dimensionality. That is why new approaches based on smart sampling techniques have been investigated to minimize the number of samples to be given to train the model, such as active learning methods. Here, we propose a technique based on a combination of the Fisher information matrix and sparse proper generalized decomposition that enables the definition of a new active learning informativeness criterion in high dimensions. We provide examples proving the performances of this technique on a theoretical 5D polynomial function and on an industrial crash simulation application. The results prove that the proposed strategy outperforms the usual ones.

When training a parametric surrogate to represent a real-world complex system in real time, there is a common assumption that the values of the parameters defining the system are known with absolute confidence. Consequently, during the training process, our focus is directed exclusively towards optimizing the accuracy of the surrogate’s output. However, real physics is characterized by increased complexity and unpredictability. Notably, a certain degree of uncertainty may exist in determining the system’s parameters. Therefore, in this paper, we account for the propagation of these uncertainties through the surrogate using a standard Monte Carlo methodology. Subsequently, we propose a novel regression technique based on optimal transport to infer the impact of the uncertainty of the surrogate’s input on its output precision in real time. The OT-based regression allows for the inference of fields emulating physical reality more accurately than classical regression techniques, including advanced ones.

A deep geological repository for radioactive waste, such as Andra’s Cigéo project, requires long-term (persistent) monitoring. To achieve this goal, data from a network of sensors are acquired. This network is subject to deterioration over time due to environmental effects (radioactivity, mechanical deterioration of the cell, etc.), and it is paramount to assess each sensor’s integrity and ensure data consistency to enable the precise monitoring of the facilities. Graph neural networks (GNNs) are suitable for detecting faulty sensors in complex networks because they accurately depict physical phenomena that occur in a system and take the sensor network’s local structure into consideration in the predictions. In this work, we leveraged the availability of the experimental data acquired in Andra’s Underground Research Laboratory (URL) to train a graph neural network for the assessment of data integrity. The experiment considered in this work emulated the thermal loading of a high-level waste (HLW) demonstrator cell (i.e., the heating of the containment cell by nuclear waste). Using real experiment data acquired in Andra’s URL in a deep geological layer was one of the novelties of this work. The used model was a GNN that inputted the temperature field from the sensors (at the current and past steps) and returned the state of each individual sensor, i.e., faulty or not. The other novelty of this work lay in the application of the GraphSAGE model which was modified with elements of the Graph Net framework to detect faulty sensors, with up to half of the sensors in the network being faulty at once. This proportion of faulty sensors was explained by the use of distributed sensors (optic fiber) and the environmental effects on the cell. The GNNs trained on the experimental data were ultimately compared against other standard classification methods (thresholding, artificial neural networks, etc.), which demonstrated their effectiveness in the assessment of data integrity.

Many engineering systems can be described by using differential models whose solutions, generally obtained after discretization, can exhibit a noticeable deviation with respect to the response of the physical systems that those models are expected to represent. In those circumstances, one possibility consists of enriching the model in order to reproduce the physical system behavior. The present paper considers a dynamical system and proposes enriching the model solution by learning the dynamical model of the gap between the system response and the model-based prediction while ensuring that the time integration of the learned model remains stable. The proposed methodology was applied in the simulation of the top-oil temperature evolution of a power transformer, for which experimental data provided by the RTE, the French electricity transmission system operator, were used to construct the model enrichment with the hybrid rationale, ensuring more accurate predictions.

System components are often regarded as part of a whole system, especially when it comes to data-driven modeling. Thus, subsystem modeling is disregarded in general when building a data-driven response, especially since multiple subsystem outputs are never measured in real applications. However, subsystem knowledge and accurate modeling are of utmost importance when aiming to repair, tune or troubleshoot a system. This work proposes a holistic modeling of subsystems in an embedded system setting. A hybrid modeling starting from the physics-based model is proposed in this work, correcting or enhancing the model, and predicting output variables, even when a measurement is never available for some of those variables. The process relies on the variables’ history, and employs an adjoint-free neural ordinary differential equation technique, along with evanescent regularization to enhance the convergence on the unmeasurable variables. The updated model converges to the exact measurements, for both the measurable and the unmeasurable variables. Multiple examples are presented using synthetic data, to allow an easy evaluation of the hidden or unmeasurable variables. The relative error offered by the updated model is around 0.001% for the measurable quantities and 0.1% for the unmeasurable ones.

Inverse problems can be challenging and interesting to study in the context of metallurgical processes. This work aims to carry out a method for inverse modeling for simultaneous double-frequency induction hardening process. In this investigation, the experimental measured hardness profiles were considered as input data, while the output data were the process parameters. For this purpose experiments were carried out on C45 steel spur-gear. The method is based on machine learning algorithms and data treatment for dealing with inverse approach issues. In addition to the inverse modeling, a forward problem-based verification completes the study. It was found that according to promising results that this method is suitable and applicable for inverse problem of hardness modeling.

This paper presents a data-driven structural health monitoring (SHM) method by the use of so-called reduced-order models relying on an offline training/online use for unidirectional fiber and matrix failure detection in a 3D woven composite plate. During the offline phase (or learning) a dataset of possible damage localization, fiber and matrix failure ratios is generated through high-fidelity simulations (ABAQUS software). Then, a reduced model in a lower-dimensional approximation subspace based on the so-called sparse proper generalized decomposition (sPGD) is constructed. The parametrized approach of the sPGD method reduces the computational burden associated with a high-fidelity solver and allows a faster evaluation of all possible failure configurations. However, during the testing phase, it turns out that classical sPGD fails to capture the influence of the damage localization on the solution. To alleviate the just-referred difficulties, the present work proposes an adaptive sPGD. First, a change of variable is carried out to place all the damage areas on the same reference region, where an adapted interpolation can be done. During the online use, an optimization algorithm is employed with numerical experiments to evaluate the damage localization and damage ratio which allow us to define the health state of the structure.

In industrial settings, engineering products are often divided into separate components for detailed conception. They often require iterative corrections between different designers/teams to optimize the final product with all components assembled into a system. This article proposes a surrogate modeling approach with functional descriptions of parts in the model and aims to accelerate the design and optimization phase in real projects. The approach is applied to a vibration problem of a two-component plate structure, where the model estimates the dynamic behavior of the assembled system when only the properties of each individual part are available. A database is built using high-fidelity numerical simulations, and neural-network-based regressions provide reliable predictions on unseen data.

In many contexts of scientific computing and engineering science, phenomena are monitored over time and data are collected as time-series. Plenty of algorithms have been proposed in the field of time-series data mining, many of them based on deep learning techniques. High-fidelity simulations of complex scenarios are truly computationally expensive and a real-time monitoring and control could be efficiently achieved by the use of artificial intelligence. In this work we build accurate data-driven models of a two-phase transient flow in a heated channel, as usually encountered in heat exchangers. The proposed methods combine several artificial neural networks architectures, involving standard and transposed deep convolutions. In particular, a very accurate real-time integrator of the system has been developed.

Many models assumed to be able to predict the response of structural systems fail to efficiently accomplish that purpose because of two main reasons. First, some structures in operation undergo localized damage that degrades their mechanical performances. To reflect this local loss of performance, the stiffness matrix associated with the structure should be locally corrected. Second, the nominal model is sometimes too coarse grained for reflecting all structural details, and consequently, the predictions are expected to deviate from the measurements. In that case, there is no small region of the model that needs to be repaired, but the entire domain needs to be repaired; therefore, the entire structure-stiffness matrix should be corrected. In the present work, we propose a methodology for locally correcting or globally enriching the models from collected data, which is, upon its turn, completed beyond the sensor’s location. The proposed techniques consist in the first case of an L1-minimization procedure that, with the support of data, aims at the same time period to detect the damaged zone in the structure and to predict the correct solution. For the global enrichment, instead, the methodology consists of an L2-minimization procedure with the support of measurements. The results obtained showed, for the local problem, a correction up to 90% with respect to the initially incorrectly predicted displacement of the structure, and for the global one, a correction up to 60% was observed (this results concern the problems considered in the present study, but they depend on different factors, such as the number of data used, the geometry or the intensity of the damage). The benefits and potential of such techniques are illustrated on four different problems, showing the large generality and adaptability of the methodology.

Characterizing complex material consists in establishing the relationship between flow rheology during forming processes and the induced micro-structural state that affects directly the final mechanical properties of the formed parts [...]

Ti-6Al-4V titanium is considered a difficult-to-cut material used in critical applications in the aerospace industry requiring high reliability levels. An appropriate selection of cutting conditions can improve the machinability of this alloy and the surface integrity of the machined surface, including the generation of compressive residual stresses. In this paper, orthogonal cutting tests of Ti-6Al-4V titanium were performed using coated and uncoated tungsten carbide tools. Suitable design of experiments (DOE) was used to investigate the influence of the cutting conditions (cutting speed Vc, uncut chip thickness h, tool rake angle γn, and the cutting edge radius rn) on the forces, chip compression ratio, and residual stresses. Due to the time consumed and the high cost of the residual stress measurements, they were only measured for selected cutting conditions of the DOE. Then, the machine learning method based on mathematical regression analysis was applied to predict the residual stresses for other cutting conditions of the DOE. Finally, the optimal cutting conditions that minimize the machining outcomes were determined. The results showed that when increasing the compressive residual stresses at the machined surface by 40%, the rake angle should be increased from negative (−6°) to positive (5°), the cutting edge radius should be doubled (from 16 µm to 30 µm), and the cutting speed should be reduced by 67% (from 60 to 20 m/min).

Electromagnetic field propagation inside composite materials represents a challenge where fiber-scale simulation remains intractable using classical simulation methods. The present work proposes an original 3D simulation with a mesh resolution fine enough to resolve the fiber scale, thanks to the use of Proper Generalized Decomposition (PGD)-based space decomposition, which avoids the necessity of considering homogenized properties and considers the richest description of the involved physics from the solution of the Maxwell equations. This high-resolution simulation enables comparing the electromagnetic field propagation in a composite part, depending on the considered frequency and the fiber’s/wave polarization’s relative orientation. The electromagnetic fields are then post-processed to identify the heat generation terms and- the resulting induced thermal field. The results prove the ability of the PGD-based discretization to attain extremely high levels of resolution, the equivalent of 1010 finite-element degrees of freedom. The obtained results show an enhanced wave penetration when the electric field polarization coincides with the fiber orientation. On the contrary, when the electric field is polarized along the normal to the fiber orientation, both the penetration and the associated heating reduce significantly, compromising the use of homogenized models, rendering them unable to reproduce the observed behaviors.

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.

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.

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.

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.

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.

We are interested in evaluating the state of drivers to determine whether they are attentive to the road or not by using motion sensor data collected from car driving experiments. That is, our goal is to design a predictive model that can estimate the state of drivers given the data collected from motion sensors. For that purpose, we leverage recent developments in topological data analysis (TDA) to analyze and transform the data coming from sensor time series and build a machine learning model based on the topological features extracted with the TDA. We provide some experiments showing that our model proves to be accurate in the identification of the state of the user, predicting whether they are relaxed or tense.

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.

Efficient and optimal design of radar-based Advanced Driver Assistant Systems (ADAS) needs the evaluation of many different electromagnetic solutions for evaluating the impact of the radome on the electromagnetic wave propagation. Because of the very high frequency at which these devices operate, with the associated extremely small wavelength, very fine meshes are needed to accurately discretize the electromagnetic equations. Thus, the computational cost of each numerical solution for a given choice of the design or operation parameters, is high (CPU time consuming and needing significant computational resources) compromising the efficiency of standard optimization algorithms. In order to alleviate the just referred difficulties the present paper proposes an approach based on the use of reduced order modeling, in particular the construction of a parametric solution by employing a non-intrusive formulation of the Proper Generalized Decomposition, combined with a powerful phase-angle unwrapping strategy for accurately addressing the electric and magnetic fields interpolation, contributing to improve the design, the calibration and the operational use of those systems.

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.

Mesh-based solution of 3D models defined in plate or shell domains remains a challenging issue nowadays due to the fact that the needed meshes generally involve too many degrees of freedom. When the considered problem involves some parameters aiming at computing its parametric solution the difficulty is twofold. The authors proposed, in some of their former works, strategies for solving both, however they suffer from a deep intrusiveness. This paper proposes a totally novel approach that from any existing discretization is able to reduce the 3D parametric complexity to the one characteristic of a simple 2D calculation. Thus, the 3D complexity is reduced to 2D, the parameters included naturally into the solution, and the procedure applied on a discretization performed with a standard software, which taken together enable real-time engineering.

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.

This paper analyzes the ability of different machine learning techniques, able to operate in the low-data limit, for constructing the model linking material and process parameters with the properties and performances of parts obtained by reactive polymer extrusion. The use of data-driven approaches is justified by the absence of reliable modeling and simulation approaches able to predict induced properties in those complex processes. The experimental part of this work is based on the in situ synthesis of a thermoset (TS) phase during the mixing step with a thermoplastic polypropylene (PP) phase in a twin-screw extruder. Three reactive epoxy/amine systems have been considered and anhydride maleic grafted polypropylene (PP-g-MA) has been used as compatibilizer. The final objective is to define the appropriate processing conditions in terms of improving the mechanical properties of these new PP materials by reactive extrusion.

In this work, we begin by considering the qualitative modeling of biological regulatory systems using process hitting, from which we define its probabilistic counterpart by considering the chemical master equation within a kinetic theory framework. The last equation is efficiently solved by considering a separated representation within the proper generalized decomposition framework that allows circumventing the so-called curse of dimensionality. Finally, model parameters can be added as extra-coordinates in order to obtain a parametric solution of the model.

Fiber−fiber interaction plays an important role in the evolution of fiber orientation in semi-concentrated suspensions. Flow induced orientation in short-fiber reinforced composites determines the anisotropic properties of manufactured parts and consequently their performances. In the case of dilute suspensions, the orientation evolution can be accurately described by using the Jeffery model; however, as soon as the fiber concentration increases, fiber−fiber interactions cannot be ignored anymore and the final orientation state strongly depends on the modeling of those interactions. First modeling frameworks described these interactions from a diffusion mechanism; however, it was necessary to consider richer descriptions (anisotropic diffusion, etc.) to address experimental observations. Even if different proposals were considered, none of them seem general and accurate enough. In this paper we do not address a new proposal of a fiber interaction model, but a data-driven methodology able to enrich existing models from data, that in our case comes from a direct numerical simulation of well resolved microscopic physics.

This paper concerns engineered composites integrating metallic particles to enhance thermal and electrical properties. However, these properties are strongly dependent on the forming process itself that determines the particle distribution and orientation. At the same time, the resulting enhanced thermal properties affect the reinforced resin viscosity whose flow is involved in the intimate contact evolution. Thus, a subtle and intricate coupling appears, and the process cannot be defined by ignoring it. In this paper, we analyze the effects of particle concentration and orientation on the process and processability. For this purpose, three main models are combined: (i) a multi-scale surface representation and its evolution, by using an appropriate numerical model; (ii) flow-induced orientation, and (iii) the impact of the orientation state on the homogenized thermal conductivity.

When suspensions involving rigid rods become too concentrated, standard dilute theories fail to describe their behavior. Rich microstructures involving complex clusters are observed, and no model allows describing its kinematics and rheological effects. In previous works the authors propose a first attempt to describe such clusters from a micromechanical model, but neither its validity nor the rheological effects were addressed. Later, authors applied this model for fitting the rheological measurements in concentrated suspensions of carbon nanotubes (CNTs) by assuming a rheo-thinning behavior at the constitutive law level. However, three major issues were never addressed until now: (i) the validation of the micromechanical model by direct numerical simulation; (ii) the establishment of a general enough multi-scale kinetic theory description, taking into account interaction, diffusion and elastic effects; and (iii) proposing a numerical technique able to solve the kinetic theory description. This paper focuses on these three major issues, proving the validity of the micromechanical model, establishing a multi-scale kinetic theory description and, then, solving it by using an advanced and efficient separated representation of the cluster distribution function. These three aspects, never until now addressed in the past, constitute the main originality and the major contribution of the present paper.

Enhancing thermal conductivity of simple fluids is of major interest in numerous applicative systems. One possibility of enhancing thermal properties consists of dispersing small conductive particles inside. However, in general, aggregation effects occur and then one must address systems composed of dispersed clusters composed of particles as well as the ones related to percolated networks. This papers analyzes the conductivity enhancement of different microstructures scaling from clusters dispersed into a simple matrix to the ones related to percolated networks exhibiting a fractal morphology.