Conditioned Clifford-Steerable Kernels

Clifford-Steerable CNNs (CSCNNs) provide a unified framework that allows incorporating equivariance to arbitrary pseudo-Euclidean groups, including $\mathrm{E}(n)$ and Poincaré-equivariance on Minkowski spacetime. In this work, we analyze the shortcomings of the approach. We demonstrate that the kernel basis used in CSCNNs is not complete. Furthermore, we suggest to restore missing degrees of freedom by using an extra information obtained directly from data at virtually no cost. Our approach significantly and consistently outperforms baseline methods on PDE forecasting tasks, specifically fluid dynamics and relativistic electrodynamics.