A hybrid numerical methodology coupling Reduced Order Modeling and Graph Neural Networks for non-parametric geometries: applications to structural dynamics problems
This work addresses the problem of rapid design iteration for engineers dealing with non-parametric geometries in structural dynamics, though it is incremental as it hybridizes existing methods.
The paper tackles the computational burden of simulating time-domain PDEs for complex physical systems with non-parametric geometries by combining reduced-order modeling and graph neural networks, achieving significant efficiency gains while maintaining reasonable accuracy in applications like aircraft seat design.
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.