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.

翻译：我们提出一种生成模型，该模型可摊销计算引力或磁源等物理源周围场的计算成本。精确数值计算要么在源和场评估点数量上具有计算复杂度$\mathcal{O}(M\times{}N)$，要么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隐式表示的架构，我们的模型的计算复杂度仅为$\mathcal{O}(M + N)$，精度达到约4%-6%，并且允许在任意位置对任意数量的源进行评估，从而显著提升了物理模拟等应用的速度。我们还研究了一个与输出场物理特性相关的模型，并通过二维示例展示了其应用。这些模型和实验的代码可在https://github.com/cmt-dtu-energy/hypermagnetics获取。