A hybrid numerical methodology coupling reduced order modeling and Graph Neural Networks for non-parametric geometries: Applications to structural dynamics problems

• Published in: Computer methods in applied mechanics and engineering Vol. 430; p. 117243
• Main Authors: Matray, Victor, Amlani, Faisal, Feyel, Frédéric, Néron, David
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01-10-2024; Elsevier
• Subjects: Analysis of PDEs; Artificial Intelligence; Computer Science; Deep learning; Finite element methods; Graph Neural Networks; Mathematics; Mechanical engineering; Mechanics; Non-parametric geometries; Numerical Analysis; Physics; Proper generalized decomposition; Reduced-order modeling; Structural mechanics; Deep learning; Non-parametric geometries; Proper generalized decomposition; Finite element methods; Reduced-order modeling; Graph Neural Networks; Proper Generalized Decomposition; Finite Element Methods; Reduced-Order Modeling; Non-Parametric Geometries; Deep Learning
• ISSN: 0045-7825
• DOI: 10.1016/j.cma.2024.117243

This work introduces a new approach for accelerating the numerical analysis of time-domain partial differential equations (PDEs) governing complex physical systems. The methodology is based on a combination of a classical reduced-order modeling (ROM) framework and recently-introduced Graph Neural Networks (GNNs), where the latter is trained on highly heterogeneous databases of varying numerical discretization sizes. The proposed techniques are shown to be particularly suitable for non-parametric geometries, ultimately enabling the treatment of a diverse range of geometries and topologies. Performance studies are presented in an application context related to the design of aircraft seats and their corresponding mechanical responses to shocks, where the main motivation is to reduce the computational burden and enable the rapid design iteration for such problems that entail non-parametric geometries. The methods proposed here are straightforwardly applicable to other scientific or engineering problems requiring a large-number of finite element-based numerical simulations, with the potential to significantly enhance efficiency while maintaining reasonable accuracy.