Our ICLR’24 paper on learning Fourier-based convolutions (SFBC) for particle and unstructured data is online now on arXiv: https://arxiv.org/abs/2403.16680
A first version of the SFBC source code is also up at https://github.com/tum-pbs/SFBC , the approach is especially interesting as an inductive bias for accurate neural networks, e.g. to replace graph-nets.
The graph above shows a quantitative evaluation of different network architectures for a fixed layout with four message-passing steps and 32 features per layer. It’s noticeable that the Fourier-convolutions (SFBC) clearly outperform the graph-net based methods (MLPCConv, GNS and MP-PDE on the right). We noticed this is many settings: for a given parameter budget, the inductive bias of the convolutions helps the network to correlate spatial features, and to give more accurate results.
