  We present a generative model that amortises computation for the field around
e.g. gravitational or magnetic sources. Exact numerical calculation has either
computational complexity $\mathcal{O}(M\times{}N)$ in the number of sources and
field evaluation points, or requires a fixed evaluation grid to exploit fast
Fourier transforms. Using an architecture where a hypernetwork produces an
implicit representation of the field around a source collection, our model
instead performs as $\mathcal{O}(M + N)$, achieves accuracy of $\sim\!4\%-6\%$,
and allows evaluation at arbitrary locations for arbitrary numbers of sources,
greatly increasing the speed of e.g. physics simulations. We also examine a
model relating to the physical properties of the output field and develop
two-dimensional examples to demonstrate its application. The code for these
models and experiments is available at
https://github.com/cmt-dtu-energy/hypermagnetics.
