Edward Berman, Luisa Li, Jung Yeon Park, Robin Walters
This paper introduces relaxed unitary convolutions for graph neural networks to improve performance in dynamics modeling by balancing smoothness preservation with natural physical system requirements.
Graph neural networks are often used to solve equations on surfaces by treating them as a mesh. However, they can suffer from oversmoothing, where the features of nodes become too similar to their neighbors. This can be problematic in physical systems where some degree of smoothing is natural. The authors propose a new approach called relaxed unitary convolutions that better balances the need for smoothness with the natural dynamics of physical processes. Their method shows improved performance over existing techniques in experiments involving complex systems like weather forecasting.
