IS20 - Complexity reduction of large-scale parametric problems: domain decomposition, reduced order models and machine learning
M. Giacomini , G. Stabile and M. Discacciati
Coupled problems such as fluid-structure interaction, thermo-mechanics, thermo-fluids,
electro-magneto-mechanics and aerodynamic noise are ubiquitous in engineering
applications and they require complex interdisciplinary modelling skills. The numerical
discretisation of these problems, e.g. via finite element or finite volume methods, leads
to large systems of (non)linear equations for which monolithic solvers struggle to provide
solutions in a reasonable computing time.
This issue becomes especially critical when multiple queries of the same problem need to
be solved for different configurations of the system (e.g. geometry of the domain, material
parameters, …). This is the case of many sensitivity and parametric studies performed on
a daily basis by engineers and scientists in the framework of optimal control and
optimisation, inverse analysis, data assimilation and uncertainty quantification.
This session aims to gather contributions on the most recent advances in domain
decomposition, partitioned iterative solvers, preconditioning, reduced order models,
scientific machine learning and physics-informed deep learning to address the current
challenge of solving large-scale parametric problems arising from the discretisation of
(possibly coupled) high-dimensional partial differential equations.
Contributions on emerging techniques in physics-based surrogate and data-assisted
models bridging the above topics towards the construction of hybrid models and digital
twins of large-scale industrial problems are particularly welcome.