Leveraging Autoencoders

Abstract

The computational demands of finite element simulations, particularly in predicting the time-dependent response of high-dimensional non-linear dynamical systems, pose significant challenges. To overcome these challenges, researchers have developed model order reduction (MOR) methods, which aim to reduce computational complexity by utilizing lower-dimensional models. This thesis proposes a MOR technique that simultaneously learns both the projection to, and the reduced dynamics on, a lower-dimensional manifold using autoencoders, a type of neural network. During training, the known linear part of the reduced dynamics is used to aid the optimization process, leading to an effective method of simultaneous projection and linear informed training (SPLIT). SPLIT demonstrates outstanding performance on the test case of a 2D cantilever beam, and is capable of making non-linear forced response predictions, even though being trained on unforced decaying trajectories. Even in scenarios involving highly non-linear behaviour, such as when the beam folds over itself, SPLIT continues to make accurate predictions, while other MOR techniques fail. This work highlights the potential of autoencoders to advance the field of MOR and improve the efficiency and reliability of simulations for complex dynamical systems.