Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915735303880704 |
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| author | Tomada, Lorenzo Pichi, Federico Rozza, Gianluigi |
| author_facet | Tomada, Lorenzo Pichi, Federico Rozza, Gianluigi |
| contents | 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 |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_11259 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Tomada, Lorenzo Pichi, Federico Rozza, Gianluigi Machine Learning Numerical Analysis 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 |
| title | Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs |
| topic | Machine Learning Numerical Analysis |
| url | https://arxiv.org/abs/2601.11259 |