The development of efficient reduced order models (ROMs) from a deep learning perspective enables users to overcome the limitations of traditional approaches [1]. One drawback of convolutional autoencoders-based techniques is the lack of geometrical information when dealing with complex domains defined on unstructured meshes. The present work proposes a framework for nonlinear model order reduction based on Graph Convolutional Autoencoders (GCA) to exploit emergent patterns in different physical problems, including those showing bifurcating behavior, high-dimensional parameter space, slow Kolmogorov-decay, and varying domains [2]. Our methodology extracts the latent space’s evolution while introducing geometric priors, possibly alleviating the learning process through up- and down-sampling operations, enabling high generalizability in the low-data regime and great speedup. Moreover, we will present a novel graph feedforward network (GFN), extending the GCA approach to exploit multifidelity data, leveraging graph-adaptive weights, and providing large savings and computable error bounds for the predictions [3]. This way, we overcome the limitations of the up- and down-sampling procedures by building a resolution-invariant GFN-ROM strategy capable of training and testing on different mesh sizes, resulting in a more lightweight and flexible architecture.