Scalable physical source-to-field inference with hypernetworks

We present a generative model that amortises computation for the field and potential around e.g.~gravitational or electromagnetic sources. Exact numerical calculation has either computational complexity O(M×N) in the number of sources M and evaluation points N, or requires a fixed evaluation grid to exploit fast Fourier transforms. Using an architecture where a hypernetwork produces an implicit representation of the field or potential around a source collection, our model instead performs as O(M + N), achieves relative error of ~!4%-6%, and allows evaluation at arbitrary locations for arbitrary numbers of sources, greatly increasing the speed of e.g.~physics simulations. We compare with existing models and develop two-dimensional examples, including cases where sources overlap or have more complex geometries, to demonstrate its application.