Machine learning (ML) based reduced order modelling (ROM) for linear and non-linear solid and structural mechanics

Abstract

Multiple model reduction techniques have been proposed to tackle linear and non-linear problems. Intrusive model order reduction techniques exhibit high accuracy levels; however, they are rarely used as a standalone industrial tool because of the high level of expertise required in the construction and usage of these techniques. Moreover, the computation time benefit is compromised for highly non-linear problems. On the other hand, non-intrusive methods often struggle with accuracy in non-linear cases, typically requiring a large design of experiments and a large number of snapshots in order to achieve reliable performance. However, generating the stiffness matrix in a non-intrusive approach presents an optimal way to align accuracy with efficiency, combining the advantages of both intrusive and non-intrusive methods. This work introduces a minimally intrusive model order reduction technique that employs machine learning within a Proper Orthogonal Decomposition framework to achieve this alliance. By leveraging outputs from commercial full-order models, this method constructs a reduced-order model that operates effectively without requiring expert user intervention. The proposed technique is capable of approximating linear non-affine as well as non-linear terms. It is showcased for linear and non-linear structural mechanics problems.