Model Order Reduction Augmented by a Neural Network for a Nonlinear Electrostatic Microactuator

Inhalt:
Projection-based model order reduction is a well-established technique to generate highly efficient yet accurate models of microsystems based on, i.e., finite element models. However, the methodology is unsuited for nonlinear effects, which are commonly found in microsystems. Approaches to overcome this gap are referred to as hyperreduction. They typically require access to the mathematical formulation of nonlinear terms. These data are hardly accessible in commercial software. A recent alternative based on easily accessible data are artificial neural networks (ANNs) to efficiently approximate the nonlinear terms. This method operates directly at the reduced level and is therefore associated with significant computational efficiency. Furthermore, its automatic differentiation provides inexpensive access to the nonlinear terms’ Jacobian matrix, which is commonly required for nonlinear solvers. This contribution demonstrates hyperreduction by an ANN for an electrostatic microactuator modeled in commercial finite element software. In addition, a modified snapshot-based scheme to compute the reduced basis using not only snapshots of states but also of forces is proposed.