Scalable physical source-to-field inference with hypernetworks
This work addresses a bottleneck in physics simulations by enabling faster and more flexible field evaluations, though it appears incremental as it builds on existing hypernetwork and implicit representation techniques.
The paper tackles the computational inefficiency of calculating fields around physical sources by introducing a generative model that uses hypernetworks to produce implicit field representations, achieving a complexity of O(M + N) and accuracy of ~4-6% compared to traditional methods with O(M × N) complexity.
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.