Master's thesis submission talk (Informatics). Maternus is advised by Friedrich Menhorn and Mathias Lesjak.

# Previous talks at the SCCS Colloquium

# Maternus Herold: Projection-based Model Order Reduction using Autoencoders in Nonlinear Finite Element Analysis

SCCS Colloquium |

Computer simulations are a core element of today’s engineering toolboxes. Especially high-fidelity simulations allow to obtain detailed insights into the object under consideration. Besides the observations obtained from a single simulation, several simulations can be used for Uncertainty Quantification and Robustness Analysis.

Due to their high-fidelity, those simulations also tend to have a very long runtime, limiting their applicability in the mentioned scenarios. Therefore, methods developed in the field of Model Order Reduction try to reduce a simulation’s complexity and achieving an improved runtime. Projection-based approaches assume that the data of a simulation lies close to a manifold, embedded in the high dimensional space, on to which the data can be projected to reduce computational costs.

Common approaches to find the lower dimensional manifold included linear methods, such as Singular Value Decomposition. However, such linear methods do yield less accurate reductions for the usually highly nonlinear equations of motions, which describe the simulation. Therefore, the goal of this thesis was to identify ways to utilize Deep Autoencoder for nonlinear projection-based model order reduction.

The talk will briefly motivate the idea and necessity of model order reduction and conclude by describing the idea of using Deep Autoencoder for nonlinear projective model order reduction. Also, the computation of the critical timestep for the simulation as well as solutions to numerical instabilities in the reduced simulation will be discussed.