SUPG-based stabilization using a separated representations approach

We have developed a new method for the construction of Streamline Upwind Petrov Galerkin (SUPG) stabilization techniques for the resolution of convection-diffusion equations based on the use of separated representations inside the Proper Generalized Decompositions (PGD) framework. The use of SUPG schemes produces a consistent stabilization adding a parameter to all the terms of the equation (not only the convective one). SUPG obtains an exact solution for problems in 1D, nevertheless, a generalization does not exist for elements of high order or for any system of convection-diffusion equations. We introduce in this paper a method that achieves stabilization in the context of Proper Generalzied Decomposition (PGD). This class of approximations use a representation of the solution by means of the sum of a finite number of terms of separable functions. Thus it is possible to use the technique of separation of variables in the context of problems of convection-diffusion that will lead to a sequence of problems in 1D where the parameter of stabilization is well known.Postprint (published version

Data-driven correction of models for deformable solids

Unveiling physical laws from data is seen as the ultimate sign of human intelligence. While there is a growing interest in this sense around the machine learning community, some recent works have attempted to simply substitute physical laws by data. We believe that getting rid of centuries of scientific knowledge is simply nonsense. There are models whose validity and usefulness is out of any doubt, so try to substitute them by data seems to be a waste of knowledge. While it is true that fitting well-known physical laws to experimental data is sometimes a painful process, a good theory continues to be practical and provide useful insights to interpret the phenomena taking place. That is why we present here a method to construct, based on data, automatic corrections to existing models. Emphasis is put in the correct thermodynamic character of these corrections, so as to avoid violations of first principles such as the laws of thermodynamics. These corrections are sought under the umbrella of the GENERIC framework [M. Grmela and H. Ch. Oettinger, Dynamics and thermodynamics of complex fluids. I. Development of a general formalism. Phys. Rev. E 56, 6620, 1997], a generalization of Hamiltonian mechanics to non-equilibrium thermodynamics. This framework ensures the satisfaction of the first and second laws of thermodynamics, while providing a very appealing context for the proposed automated correction of existing laws. In this work we focus on solid mechanics, particularly large strain (visco-) hyperelasticity

Empowering materials processing and performance from data and AI

[No abstract available

Scientific machine learning for coarse-grained constitutive 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

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

Parametric numerical solutions of additive manufacturing processes

Additive manufacturing is the more and more considered in industry, however efficient simulation tools able to perform accurate predictions are still quite limited. The main difficulties for an efficient simulation are related to the multiple scales, the multiple and complex physics involved, as well as the strong dependency on the process trajectory. In [21] authors proposed the use of advanced model reduction techniques for performing parametric simulations of additive manufacturing processes, where deposition trajectory, the intensity of the thermal shrinkage and the deposited layers were considered as model parameters. The resulting simulation tool allowed evaluating in real-time the impact of the parameters just referred on the part distortion, and proceed to the required geometrical compensation. In the present work we address the use of that parametric solution with three different purposes: (i) evaluating the parameters leading to the minimal part distortion; (ii) evaluating the solution sensitivity to the different parameters, and in particular to the ones related to the deposition trajectory; and (iii) propagating the uncertainty related to the intensity of the thermal shrinkage

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

Smart-GFEM for welding simulation

In this paper, a new and efficient method for welding simulation is proposed. This method, known as Smart-GFEM introduces in a GFEM framework an enrichment function which is capable of adapting the approximation space optimally. The enrichment function can be seen as a computational vademecum which depends on technological and material parameters of the process and it is completely computed off-line. In this work we present how to perform the thermal analysis of the welding and a general strategy to address the mechanical analysis

A combined reduced order‐full order methodology for the solution of 3D magneto‐mechanical problems with application to magnetic resonance imaging scanners

The design of a new magnetic resonance imaging (MRI) scanner requires multiple numerical simulations of the same magneto‐mechanical problem for varying model parameters, such as frequency and electric conductivity, in order to ensure that the vibrations, noise, and heat dissipation are minimized. The high computational cost required for these repeated simulations leads to a bottleneck in the design process due to an increased design time and, thus, a higher cost. To alleviate these issues, the application of reduced order modeling techniques, which are able to find a general solution to high‐dimensional parametric problems in a very efficient manner, is considered. Building on the established proper orthogonal decomposition technique available in the literature, the main novelty of this work is an efficient implementation for the solution of 3D magneto‐mechanical problems in the context of challenging MRI configurations. This methodology provides a general solution for varying parameters of interest. The accuracy and efficiency of the method are proven by applying it to challenging MRI configurations and comparing with the full‐order solution

Nonintrusive reduced order model for parametric solutions of inertia relief problems

The Inertia Relief (IR) technique is widely used by industry and produces equilibrated loads allowing to analyze unconstrained systems without resorting to the more expensive full dynamic analysis. The main goal of this work is to develop a computational framework for the solution of unconstrained parametric structural problems with IR and the Proper Generalized Decomposition (PGD) method. First, the IR method is formulated in a parametric setting for both material and geometric parameters. A reduced order model using the encapsulated PGD suite is then developed to solve the parametric IR problem, circumventing the so-called curse of dimensionality. With just one offline computation, the proposed PGD-IR scheme provides a computational vademecum that contains all the possible solutions for a predefined range of the parameters. The proposed approach is nonintrusive and it is therefore possible to be integrated with commercial finite element (FE) packages. The applicability and potential of the developed technique is shown using a three-dimensional test case and a more complex industrial test case. The first example is used to highlight the numerical properties of the scheme, whereas the second example demonstrates the potential in a more complex setting and it shows the possibility to integrate the proposed framework within a commercial FE package. In addition, the last example shows the possibility to use the generalized solution in a multi-objective optimization setting