  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.
