Reduced Order Modelling (ROM) approaches, such as the Proper Orthogonal Decomposition (POD) [1] or the Proper Generalized Decomposition (PGD) [2], provide accelerated solutions for partial differential equations (PDEs). However, their effectiveness often depends on parametrization, which limits their application to fixed geometries, or geometries that can be parameterized by a few control points (often with a constant number of degrees of freedom). In order to overcome this limitation, we propose integrating deep learning with ROM. Hence this contribution discusses recent developments on a new “GNN-PGD” approach initially proposed in [2]. The key idea is to leverage a deep learning model to obtain a reduced basis, tailored to the structure under study, onto which the PDE is projected. The learning model is based on Graph Neural Networks (GNNs), enabling the treatment of meshes with highly varied geometries and topologies---a significant advantage over more traditional methods and one that is well-suited for industrial needs. The architecture of our proposed model has been redesigned to drastically reduce the number of parameters to be learned, thereby improving both training and inference time. This contribution further discusses an extension and subsequent enhancement of the GNN-PGD method towards accommodating simulations of nonlinear dynamic behavior. Such an extension is based on the learning of a second reduced basis that captures the evolution of the internal forces that generally carry the mechanical nonlinearities, inspired by methods like the Discrete Empirical Interpolation Method (DEIM) [1]. The ultimate goal of our approach aims to provide computationally efficient online solutions suitable for industrial pre-design applications. REFERENCES [1] Chaturantabut, S., & Sorensen, D. C. (2010). Nonlinear model reduction via discrete empirical interpolation. SIAM Journal on Scientific Computing, 32(5), 2737-2764 [2] Matray, V., Amlani, F., Feyel, F., & Néron, D. (2024). A hybrid numerical methodology coupling Reduced Order Modeling and Graph Neural Networks for non-parametric geometries: applications to structural dynamics problems, Computer Methods in Applied Mechanics and Engineering, 430 (2024) 117243, https://doi.org/10.1016/j.cma.2024.11724