Graph autoencoders have gained attention in nonlinear reduced-order modeling of parameterized partial differential equations defined on unstructured grids [1,2]. Despite providing a geometrically consistent way of treating complex domains, applying such architectures to parametrized dynamical systems for temporal prediction beyond the training data, i.e.\ the extrapolation regime, is still a challenging task due to the simultaneous need of temporal causality and generalizability in the parametric space. In this work, we explore the integration of graph convolutional autoencoders (GCAs) with tensor train (TT) decomposition and operator inference (OpInf) to develop a time-consistent reduced-order model [3]. In particular, high-fidelity snapshots are represented as a combination of parametric, spatial, and temporal cores via tensor train decomposition, while operator inference is used to learn the evolution of the latter. By decoupling the cores, the training of GCA is only performed for a few time instances within the training range, enabling the computation of new parametric cores during the online stage. Moreover, we enhance the generalization performance by developing a multi-fidelity approach in the framework of Deep Operator Networks (DeepONet), treating the spatial and temporal cores as the trunk network, and the parametric core as the branch network. Numerical results, including heat-conduction, advection-diffusion, and vortex-shedding phenomena, demonstrate that the proposed approach effectively learns the dynamic responses defined on parametric unstructured grids and accurately predicts solutions in the extrapolation regime. REFERENCES [1] Pichi, F., Moya, B. and Hesthaven, J.S. (2024) ’A graph convolutional autoencoder approach to model order reduction for parametrized PDEs’, Journal of Computational Physics, https://doi.org/10.1016/j.jcp.2024.112762. [2] Morrison, O.M., Pichi, F. and Hesthaven, J.S. (2024) ’GFN: A graph feedforward network for resolution-invariant reduced operator learning in multifidelity applications’, Computer Methods in Applied Mechanics and Engineering, https://doi.org/10.1016/j.cma.2024.117458. [3] Chen, Y., Pichi, F., Gao, Z., and Rozza, G. (2025) ’Multi-fidelity reduced-order model based on graph convolutional autoencoder for parameterized time-dependent partial differential equations’, In preparation