https://popups.uliege.be/esaform21/index.php?id=2013 Publications of Auteurs Francisco Chinesta fr 0 https://popups.uliege.be/esaform21/index.php?id=2050 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. Tue, 23 Mar 2021 12:33:56 +0100 Mon, 12 Apr 2021 10:26:50 +0200 https://popups.uliege.be/esaform21/index.php?id=2050 https://popups.uliege.be/esaform21/index.php?id=2017 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. Tue, 23 Mar 2021 12:27:29 +0100 Mon, 12 Apr 2021 10:24:45 +0200 https://popups.uliege.be/esaform21/index.php?id=2017 https://popups.uliege.be/esaform21/index.php?id=2004 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. Tue, 23 Mar 2021 12:23:56 +0100 Mon, 12 Apr 2021 10:22:59 +0200 https://popups.uliege.be/esaform21/index.php?id=2004 https://popups.uliege.be/esaform21/index.php?id=1572 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. Mon, 22 Mar 2021 20:13:16 +0100 Fri, 02 Apr 2021 17:05:46 +0200 https://popups.uliege.be/esaform21/index.php?id=1572