Scalable physical source-to-field inference with hypernetworks

TL;DR

This paper introduces a hypernetwork-based generative model that efficiently computes fields from sources with linear complexity, enabling fast, accurate, and flexible physics simulations for gravitational and electromagnetic scenarios.

Contribution

The paper presents a novel hypernetwork architecture that reduces computational complexity from quadratic to linear for source-to-field inference, allowing arbitrary evaluation points and source configurations.

Findings

Achieves 4-6% relative error in field predictions.

Performs inference with linear complexity in sources and evaluation points.

Demonstrates effectiveness on 2D examples with complex source geometries.

Abstract

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 $\mathcal{O}(M\times{}N)$ 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 $\mathcal{O}(M + N)$, achieves relative error 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 compare with existing models and develop two-dimensional examples, including cases where sources overlap or have more complex geometries, to demonstrate its application.