  Modelling the propagation of electromagnetic signals is critical for
designing modern communication systems. While there are precise simulators
based on ray tracing, they do not lend themselves to solving inverse problems
or the integration in an automated design loop. We propose to address these
challenges through differentiable neural surrogates that exploit the geometric
aspects of the problem. We first introduce the Wireless Geometric Algebra
Transformer (Wi-GATr), a generic backbone architecture for simulating wireless
propagation in a 3D environment. It uses versatile representations based on
geometric algebra and is equivariant with respect to E(3), the symmetry group
of the underlying physics. Second, we study two algorithmic approaches to
signal prediction and inverse problems based on differentiable predictive
modelling and diffusion models. We show how these let us predict received
power, localize receivers, and reconstruct the 3D environment from the received
signal. Finally, we introduce two large, geometry-focused datasets of wireless
signal propagation in indoor scenes. In experiments, we show that our
geometry-forward approach achieves higher-fidelity predictions with less data
than various baselines.
