Clifford-Steerable Convolutional Neural Networks
This provides a novel method for handling equivariance in physics simulations, addressing challenges in domains like fluid dynamics and relativistic systems.
The paper tackled the problem of developing equivariant convolutional neural networks for pseudo-Euclidean spaces, resulting in CS-CNNs that significantly outperform baseline methods on fluid dynamics and relativistic electrodynamics forecasting tasks.
We present Clifford-Steerable Convolutional Neural Networks (CS-CNNs), a novel class of $\mathrm{E}(p, q)$-equivariant CNNs. CS-CNNs process multivector fields on pseudo-Euclidean spaces $\mathbb{R}^{p,q}$. They cover, for instance, $\mathrm{E}(3)$-equivariance on $\mathbb{R}^3$ and Poincaré-equivariance on Minkowski spacetime $\mathbb{R}^{1,3}$. Our approach is based on an implicit parametrization of $\mathrm{O}(p,q)$-steerable kernels via Clifford group equivariant neural networks. We significantly and consistently outperform baseline methods on fluid dynamics as well as relativistic electrodynamics forecasting tasks.