Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs

• URL: http://arxiv.org/abs/2601.11259v1
• Date: Fri, 16 Jan 2026 13:10:00 GMT
• Title: Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs
• Authors: Lorenzo Tomada, Federico Pichi, Gianluigi Rozza,
• Abstract summary: We introduce Latent Dynamics Graph Conal Network (LD-GCN), a purely data-driven, encoder-free architecture.<n>LD-GCN learns a global, low-dimensional representation of dynamical systems conditioned on external inputs and parameters.<n>Our framework enhances interpretability by enabling the analysis of the reduced dynamics and supporting zero-shot prediction.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Graph Neural Networks (GNNs) are emerging as powerful tools for nonlinear Model Order Reduction (MOR) of time-dependent parameterized Partial Differential Equations (PDEs). However, existing methodologies struggle to combine geometric inductive biases with interpretable latent behavior, overlooking dynamics-driven features or disregarding spatial information. In this work, we address this gap by introducing Latent Dynamics Graph Convolutional Network (LD-GCN), a purely data-driven, encoder-free architecture that learns a global, low-dimensional representation of dynamical systems conditioned on external inputs and parameters. The temporal evolution is modeled in the latent space and advanced through time-stepping, allowing for time-extrapolation, and the trajectories are consistently decoded onto geometrically parameterized domains using a GNN. Our framework enhances interpretability by enabling the analysis of the reduced dynamics and supporting zero-shot prediction through latent interpolation. The methodology is mathematically validated via a universal approximation theorem for encoder-free architectures, and numerically tested on complex computational mechanics problems involving physical and geometric parameters, including the detection of bifurcating phenomena for Navier-Stokes equations. Code availability: https://github.com/lorenzotomada/ld-gcn-rom

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