Technology Category
Machine Learning: Learning with ManifoldsIntelligent Robots: State EstimationReasoning under Uncertainty: Stochastic Optimization
Machine Learning (ML) based Reduced Order Modeling (ROM) for linear and non-linear solid and structural mechanics
🤖 AI Summary
Existing reduced-order models (ROMs) for solid mechanics face a trade-off between accuracy and usability: intrusive methods require expert knowledge and are computationally expensive, while non-intrusive approaches suffer from insufficient accuracy for nonlinear or non-affine problems.
Method: This paper proposes a lightweight intrusive ML-POD co-modeling framework that leverages only black-box outputs from commercial finite element solvers. It employs machine learning to accurately surrogate non-affine terms—particularly the stiffness matrix—enabling ROM construction without expert intervention, extensive snapshot collections, or formal design-of-experiments (DoE).
Contribution/Results: For the first time, the stiffness-matrix-driven mechanism is integrated into POD-ML joint modeling, preserving non-intrusive usability while substantially improving nonlinear ROM accuracy. Numerical experiments across multiple benchmark cases demonstrate 40–65% error reduction over conventional non-intrusive methods, confirming superior accuracy, generalizability, and engineering practicality.
Technology Category
Application Category
📝 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.
Problem
Research questions and friction points this paper is trying to address.
Combining accuracy and efficiency in reduced-order modeling for mechanics
Addressing limitations of intrusive and non-intrusive model reduction techniques
Enabling reliable nonlinear analysis without expert intervention via ML
Innovation
Methods, ideas, or system contributions that make the work stand out.
Machine Learning in Proper Orthogonal Decomposition
Lightly intrusive model order reduction technique
Leverages commercial full-order model outputs
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