# Time Extrapolation with Graph Convolutional Autoencoder and Tensor Train Decomposition

arXiv: https://arxiv.org/abs/2511.23037 · HTML: https://mlsanity.com/paper/2511.23037/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 89 references that are in the map.
- First posted on arXiv 28 Nov 2025.

## Builds on (most cited first, 25 of 25)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs](https://mlsanity.com/paper/2001.04001/) (2020)
- [Predicting Physics in Mesh-reduced Space with Temporal Attention](https://mlsanity.com/paper/2201.09113/) (2022)
- [POD-DL-ROM: enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition](https://mlsanity.com/paper/2101.11845/) (2021)
- [Physics-informed Autoencoders for Lyapunov-stable Fluid Flow Prediction](https://mlsanity.com/paper/1905.10866/) (2019)
- [Federated Graph Neural Networks: Overview, Techniques and Challenges](https://mlsanity.com/paper/2202.07256/) (2022)
- [A graph convolutional autoencoder approach to model order reduction for parametrized PDEs](https://mlsanity.com/paper/2305.08573/) (2023)
- [Physics-Embedded Neural Networks: Graph Neural PDE Solvers with Mixed Boundary Conditions](https://mlsanity.com/paper/2205.11912/) (2022)
- [Non-intrusive reduced order modeling of natural convection in porous media using convolutional autoencoders: comparison with linear subspace techniques](https://mlsanity.com/paper/2107.11460/) (2021)
- [Non-intrusive reduced-order models for parametric partial differential equations via data-driven operator inference](https://mlsanity.com/paper/2110.07653/) (2021)
- [A Comparison of Neural Network Architectures for Data-Driven Reduced-Order Modeling](https://mlsanity.com/paper/2110.03442/) (2021)
- [Eighty Years of the Finite Element Method: Birth, Evolution, and Future](https://mlsanity.com/paper/2107.04960/) (2021)
- [Learning Reduced-Order Models for Cardiovascular Simulations with Graph Neural Networks](https://mlsanity.com/paper/2303.07310/) (2023)
- [Deep Learning-based surrogate models for parametrized PDEs: handling geometric variability through graph neural networks](https://mlsanity.com/paper/2308.01602/) (2023)
- [DeepGraphONet: A Deep Graph Operator Network to Learn and Zero-shot Transfer the Dynamic Response of Networked Systems](https://mlsanity.com/paper/2209.10622/) (2022)
- [An artificial neural network approach to bifurcating phenomena in computational fluid dynamics](https://mlsanity.com/paper/2109.10765/) (2021)
- [GFN: A graph feedforward network for resolution-invariant reduced operator learning in multifidelity applications](https://mlsanity.com/paper/2406.03569/) (2024)
- [Multi-fidelity physics constrained neural networks for dynamical systems](https://mlsanity.com/paper/2402.02031/) (2024)
- [Neural empirical interpolation method for nonlinear model reduction](https://mlsanity.com/paper/2406.03562/) (2024)

## Built on by (most cited first, 2 of 2)

- [Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs](https://mlsanity.com/paper/2601.11259/) (2026)
- [A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems](https://mlsanity.com/paper/2606.13063/) (2026)

## Abstract (arXiv)

Graph autoencoders have gained attention in nonlinear reduced-order modeling of parameterized partial differential equations defined on unstructured grids. Despite they provide a geometrically consistent way of treating complex domains, applying such architectures to parameterized 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. In particular, high-fidelity snapshots are represented as a combination of parametric, spatial, and temporal cores via TT decomposition, while OpInf is used to learn the evolution of the latter. Moreover, we enhance the generalization performance by developing a multi-fidelity two-stages approach in the framework of Deep Operator Networks (DeepONet), treating the spatial and temporal cores as the trunk networks, and the parametric core as the branch network. Numerical results, including heat-conduction, advection-diffusion and vortex-shedding phenomena, demonstrate great performance in effectively learning the dynamic in the extrapolation regime for complex geometries, also in comparison with state-of-the-art approaches e.g. MeshGraphNets.