No abstract

This paper aims at introducing the main building blocks of a digital twin, embracing physics-based and data-driven functionalities, both enriching mutually. Both should proceed in almost real-time, and the last being able to proceed in the scarce data limit. When applied to materials and processes, model order reduction technologies enable the construction of the so-called “computational vademecum”, whereas data-driven modelling, based in advanced regressions, must be informed by the physics to encompass rapidity and accuracy, in the low data limit. Despite of the recent advances, a lot of functionalities are needed and are under progress, some of them representing real scientific challenges. A number of them, the ones that we estimate being the most crucial, will be discussed in the present work.

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.