Verification and validation for and with reduced order modeling

Guest Editors:

• Ludovic Chamoin (LMT (ENS Cachan/CNRS/Université Paris Saclay, Cachan, France)
• Pedro Diez (Laboratori de Calcul Numeric (LaCaN), Universitat Politecnica de Catalunya, Barcelona, Spain)

Reduced Order Models (ROM) are essential tools to address the current challenges in Modeling and Simulation. However, the reduction of the computational complexity is accompanied by a loss of accuracy of the solution. The idea of ROM is to drastically reduce the complexity keeping the quality standards of the numerical solution (error within some prescribed tolerance).

In a more general context, in silico experiments that consist in building a virtual reality with numerical models are growing faster than the classical in vivo, in vitro or in situ versions. However, the numerical result is frequently suspicious of lack of realism. The inception of this suspicion is twofold because one may presume that 1) the underlying mathematical model is exaggeratedly simplifying reality (modeling error, related to validation) and 2) the numerical solver providing an approximate solution is questionable (numerical error, related to verification), for instance using a too coarse discretization. The use of a ROM is introducing a further approximation that could increase the numerical error and aggravate the effect of the second item.

Thus, reducing the order of the model is important, but the reduction has to be kept under control.

A growing synergy has emerged during the last decade between Verification & Validation (V&V) tools and ROM. On the one hand, predictive ROM cannot go without effective V&V procedures; this is currently a fundamental and active research topic. On the other hand, V&V can take great advantage of the flexibility and simplicity brought by reduced-order models.

The objective of the current special issue is therefore to present recent advances on this synergy, state-of-the-art techniques allowing quantifying the accuracy of the ROM solution and illustrative applications of coupled V&V and ROM in engineering activities.