A hybrid numerical methodology coupling Reduced Order Modeling and Graph Neural Networks for non-parametric geometries: applications to structural dynamics problems

TL;DR

This paper presents a hybrid approach combining reduced-order modeling and graph neural networks to efficiently analyze complex physical systems with non-parametric geometries, demonstrated on aircraft seat design problems.

Contribution

It introduces a novel coupling of ROM and GNNs tailored for non-parametric geometries, enabling faster simulations across diverse topologies.

Findings

Significant reduction in computational time for simulations.

Effective handling of heterogeneous geometries.

Maintained accuracy comparable to traditional methods.

Abstract

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.