Machine Learning (ML) based Reduced Order Modeling (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 required high level knowledge involved in the construction and usage of these techniques. Moreover, the computation time benefit is compromised for highly nonlinear problems. On the other hand, non-intrusive methods often struggle with accuracy in nonlinear cases, typically requiring a large design of experiment and a large number of snapshots achieve a reliable performance. However, generating the stiffness matrix in a non-intrusive approach presents an optimal way to align accuracy with efficiency, allying the advantages of both intrusive and non-intrusive methods.This work introduces a lightly 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 has the possibility to approximate linear non affine as well as non linear terms. It is showcased for linear and nonlinear structural mechanics problems.