New convolutions improve neural networks for solving PDEs on surfaces

Researchers have identified and addressed smoothness errors in neural network models used for solving partial differential equations over surfaces. Traditional graph neural networks can suffer from oversmoothing, where node features become too similar, hindering performance in tasks like diffusion processes. While unitary graph convolutions were proposed to mitigate this, they can be overly restrictive for systems that naturally smooth over time. The paper introduces relaxed unitary convolutions, which balance smoothness preservation with the necessary natural smoothing for physical systems, and extends these concepts to meshes. Experiments show this new method outperforms existing baselines on tasks including the heat and wave equations and weather forecasting. AI

IMPACT Introduces a novel convolution method that enhances the accuracy of neural networks for modeling physical systems and solving complex equations.

RANK_REASON The cluster contains a research paper detailing a new method for improving neural network performance on specific tasks. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv cs.LG →

• arXiv
• Edward Berman
• graph neural networks
• heat equation
• Mesh-aware transformers
• Relaxed unitary convolutions
• Unitary graph convolutions
• wave equation

• paper
• model release

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