LD-GCN couples an encoder-free latent-space neural ODE with a graph convolutional decoder, achieving accurate reduced-order modeling of time-dependent parameterized PDEs and detecting bifurcations from the latent trajectories.
Flexible SE(2) graph neural networks with applications to PDE surrogates
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abstract
This paper presents a novel approach for constructing graph neural networks equivariant to 2D rotations and translations and leveraging them as PDE surrogates on non-gridded domains. We show that aligning the representations with the principal axis allows us to sidestep many constraints while preserving SE(2) equivariance. By applying our model as a surrogate for fluid flow simulations and conducting thorough benchmarks against non-equivariant models, we demonstrate significant gains in terms of both data efficiency and accuracy.
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2026 1verdicts
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Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs
LD-GCN couples an encoder-free latent-space neural ODE with a graph convolutional decoder, achieving accurate reduced-order modeling of time-dependent parameterized PDEs and detecting bifurcations from the latent trajectories.