A hyperreduced manifold learning approach to nonlinear model order reduction for the homogenisation of hyperelastic RVEs

In a recent work, we proposed a graph-based manifold learning scheme for the nonlinear Galerkin-reduction of quasi-static solid mechanical problems [1]. The resulting nonlinear approximation spaces can closely and flexibly represent nonlinear solution manifolds. The present work discusses how this nonlinear model order reduction (MOR) approach can be employed to reduce online computational costs by multiple orders of magnitude while retaining high levels of accuracy. We integrate two popular hyperreduction methods into the nonlinear MOR framework and discuss how we achieve an algorithmic complexity which is independent from the original system size. Furthermore, improvements are made to the local online linearisation scheme for the sake of performance and robustness. On an example RVE problem, the MOR scheme accelerates computations by more than two orders of magnitude with little training data and negligible loss of accuracy. Additionally, the algorithm Pareto-dominates alternative approaches in the trade-off between accuracy and runtime on the considered example.