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.

翻译：我们提出了一种生成模型，用于摊销计算引力或电磁源周围的场和势能。精确数值计算的计算复杂度在源数量$M$和评估点$N$上为$\mathcal{O}(M\times{}N)$，或者需要固定评估网格以利用快速傅里叶变换。通过采用超网络生成源集合周围场或势能的隐式表示的架构，我们的模型实现了$\mathcal{O}(M + N)$的计算性能，达到约$4\%-6\%$的相对误差，并允许对任意数量的源在任意位置进行评估，从而显著提高了物理模拟等应用的速度。我们与现有模型进行了比较，并开发了二维示例（包括源重叠或具有更复杂几何结构的情况）以展示其应用。