Machine learning for reduced-order-models and surrogate models of elastoplasticity

Projection-based model-order-reduction (MOR) accelerates computations of physical systems in case the same computation must be performed many times for different load parameters (e.g.~parameters, geometries, initial conditions, boundary conditions). It therefore finds its use in application domains such as inverse modelling, optimization, uncertainty quantification and computational homogenization. Projection-based MOR uses the solutions of an initial set of (training/offline) computations to construct the solutions of the remaining (online) computations. For finite element computations of hyperelastic solids, projection-based MOR is accurate and fast. However, for finite element computations of hyperelastoplastic solids, conventional projection-based MOR is far from accurate and fast. This thesis explores different numerical approaches to improve projection-based MOR for hyperelastoplastic finite element simulations. The first investigated innovation focuses on enhancing the interpolation employed in projection-based MOR with an additional interpolation associated with a coarse finite element discretization. Because inconsistent results are obtained with this approach, the second innovation focuses on equipping the projection-based MOR with a neural network. This substantially accelerates the online computations, and although the reported accuracy can be argued to be reasonable, it is definitely not excellent. To this end, the third innovation investigates the use of machine learning to adaptively select the interpolation functions of projection-based MOR during the course of a simulation.