Model and system learners, optimal process constructors and kinetic theory-based goal-oriented design: a new paradigm in materials and processes informatics

Traditionally, Simulation-Based Engineering Sciences (SBES) has relied on the use of static data inputs (model parameters, initial or boundary conditions, ... obtained from adequate experiments) to perform simulations. A new paradigm in the field of Applied Sciences and Engineering has emerged in the last decade. Dynamic Data-Driven Application Systems [9, 10, 11, 12, 22] allow the linkage of simulation tools with measurement devices for real-time control of simulations and applications, entailing the ability to dynamically incorporate additional data into an executing application, and in reverse, the ability of an application to dynamically steer the measurement process. It is in that context that traditional "digital-twins" are giving raise to a new generation of goal-oriented data-driven application systems, also known as "hybrid-twins", embracing models based on physics and models exclusively based on data adequately collected and assimilated for filling the gap between usual model predictions and measurements. Within this framework new methodologies based on model learners, machine learning and kinetic goal-oriented design are defining a new paradigm in materials, processes and systems engineering

Virtual, Digital and Hybrid Twins: A New Paradigm in Data-Based Engineering and Engineered Data

Engineering is evolving in the same way than society is doing. Nowadays, data is acquiring a prominence never imagined. In the past, in the domain of materials, processes and structures, testing machines allowed extract data that served in turn to calibrate state-of-the-art models. Some calibration procedures were even integrated within these testing machines. Thus, once the model had been calibrated, computer simulation takes place. However, data can offer much more than a simple state-of-the-art model calibration, and not only from its simple statistical analysis, but from the modeling and simulation viewpoints. This gives rise to the the family of so-called twins: the virtual, the digital and the hybrid twins. Moreover, as discussed in the present paper, not only data serve to enrich physically-based models. These could allow us to perform a tremendous leap forward, by replacing big-data-based habits by the incipient smart-data paradigm

Hybrid constitutive modeling: data-driven learning of corrections to plasticity models

In recent times a growing interest has arose on the development of data-driven techniques to avoid the employ of phenomenological constitutive models. While it is true that, in general, data do not fit perfectly to existing models, and present deviations from the most popular ones, we believe that this does not justify (or, at least, not always) to abandon completely all the acquired knowledge on the constitutive characterization of materials. Instead, what we propose here is, by means of machine learning techniques, to develop correction to those popular models so as to minimize the errors in constitutive modeling

A Manifold Learning Approach to Data-Driven Computational Elasticity and Inelasticity

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

Data-Driven Computational Plasticity

The use of constitutive equations calibrated from data collected from adequate testing has been implemented successfully into standard solvers for successfully addressing a variety of problems encountered in SBES (simulation based engineering sciences). However, the complexity remains constantly increasing due to the more and more fine models being considered as well as the use of engineered materials. Data-Driven simulation constitutes a potential change of paradigm in SBES. 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. Data-driven simulation consists of directly linking data to computers in order to perform numerical simulations. These simulations will use universal laws while minimizing the need of explicit, often phenomenological, models. This work revisits our former work on data-driven computational linear and nonlinear elasticity and the rationale is extended for addressing computational inelasticity (viscoelastoplasticity)

A manifold learning approach for integrated computational materials engineering

Image-based simulation is becoming an appealing technique to homogenize properties of real microstructures of heterogeneous materials. However fast computation techniques are needed to take decisions in a limited time-scale. Techniques based on standard computational homogenization are seriously compromised by the real-time constraint. The combination of model reduction techniques and high performance computing contribute to alleviate such a constraint but the amount of computation remains excessive in many cases. In this paper we consider an alternative route that makes use of techniques traditionally considered for machine learning purposes in order to extract the manifold in which data and fields can be interpolated accurately and in real-time and with minimum amount of online computation. Locallly Linear Embedding is considered in this work for the real-time thermal homogenization of heterogeneous microstructures

A Physically-Based Fractional Diffusion Model for Semi-Dilute Suspensions of Rods in a Newtonian Fluid

[EN] The rheological behaviour of suspensions involving interacting (functionalized) rods remains nowadays incompletely understood, in particular with regard to the evolution of the elastic modulus with the applied frequency in small-amplitude oscillatory flows. In a previous work, we addressed this issue by assuming a fractional diffusion mechanism, however the approach followed was purely phenomenological. The present work revisits the topic from a phys ical viewpoint, with the aim of justifying the fractional nature of diffusion. After accomplishing this first objective, we explore by means of numerical ex periments the consequences of the proposed fractional modelling approach in linear and non-linear rheology.Nadal, E.; Aguado-López, JV.; Abisset-Chavanne, E.; Chinesta Soria, FJ.; Keunings, R.; Cueto, E. (2017). A Physically-Based Fractional Diffusion Model for Semi-Dilute Suspensions of Rods in a Newtonian Fluid. Applied Mathematical Modelling. 51:58-67. https://doi.org/10.1016/j.apm.2017.06.009S58675

“Savages Who Speak French”: Folklore, Primitivism and Morals in Robert Hertz

Hertz's analysis of the Alpine cult of Saint Besse apparently marks a break from his studies of death, sin and the left to folkloric studies. This analysis helps one to understand the personality of Robert Hertz. His sociological curiosity about folklore reveals his ambiguous position in social sciences at the beginning of the twentieth century. His text appears to be a variation from the Durkheimian norm, but another reading could suggest that Hertz continued and went beyond Durkheimian thought to something between sociology of the modern world and engaged socialism. Through this study, Hertz linked his political ideals, his work in ethnology and his desire for social involvement. The cult of Saint Besse perpetuated as much religious tradition as local identity. The Alpine people were presented in the text as wilful perpetuators of an ideal social order, whose loss for his contemporary city dwellers Hertz feared. The alpine Other, marked by a material and moral backwardness, represented for activist and socialist Hertz one of the paths of balanced social organization that stabilized the identity of a group across time if it fit rather well into the folkloric stereotypes of the beginning of the twentieth century. Finally, by linking events in Herz's life (e.g., the accidental Alpine death of his father), this article suggests that the legend of Saint Besse embodied several recurring motifs in Hertz' career: the accidental deaths of saint and father by falls, the military role of the saint and of Hertz himself

A Virtual Testing Approach for Laminated Composites Based on Micromechanics

International audienceThe chapter deals with a crucial question for the design of composite structures: how can one predict the evolution of damage up to and including final fracture? Virtual testing, whose goal is to drastically reduce the huge number of industrial tests involved in current characterization procedures, constitutes one of today’s main industrial challenges. In this work, one revisits our multiscale modeling answer through its practical aspects. Some complements regarding identification, kinking, and crack initiation are also given. Finally, the current capabilities and limits of this approach are discussed, as well as the computational challenges that are inherent to “Virtual Structural Testing.

Efficient Stabilization of Advection Terms Involved in Separated Representations of Boltzmann and Fokker-Planck Equations

The fine description of complex fluids can be carried out by describing the evolution of each individual constituent (e.g. each particle, each macromolecule, etc.). This procedure, despite its conceptual simplicity, involves many numerical issues, the most challenging one being that related to the computing time required to update the system configuration by describing all the interactions between the different individuals. Coarse grained approaches allow alleviating the just referred issue: the system is described by a distribution function providing the fraction of entities that at certain time and position have a particular conformation. Thus, mesoscale models involve many different coordinates, standard space and time, and different conformational coordinates whose number and nature depend on the particular system considered. Balance equation describing the evolution of such distribution function consists of an advection-diffusion partial differential equation defined in a high dimensional space. Standard mesh-based discretization techniques fail at solving high-dimensional models because of the curse of dimensionality. Recently the authors proposed an alternative route based on the use of separated representations. However, until now these approaches were unable to address the case of advection dominated models due to stabilization issues. In this paper this issue is revisited and efficient procedures for stabilizing the advection operators involved in the Boltzmann and Fokker-Planck equation within the PGD framework are proposed.The fine description of complex fluids can be carried out by describing the evolution of each individual constituent (e.g. each particle, each macromolecule, etc.). This procedure, despite its conceptual simplicity, involves many numerical issues, the most challenging one being that related to the computing time required to update the system configuration by describing all the interactions between the different individuals. Coarse grained approaches allow alleviating the just referred issue: the system is described by a distribution function providing the fraction of entities that at certain time and position have a particular conformation. Thus, mesoscale models involve many different coordinates, standard space and time, and different conformational coordinates whose number and nature depend on the particular system considered. Balance equation describing the evolution of such distribution function consists of an advection-diffusion partial differential equation defined in a high dimensional space. Standard mesh-based discretization techniques fail at solving high-dimensional models because of the curse of dimensionality. Recently the authors proposed an alternative route based on the use of separated representations. However, until now these approaches were unable to address the case of advection dominated models due to stabilization issues. In this paper this issue is revisited and efficient procedures for stabilizing the advection operators involved in the Boltzmann and Fokker-Planck equation within the PGD framework are proposed