Cosmic voids contain higher-order cosmological information and are of interest for astroparticle physics. Finding genuine matter underdensities in sparse galaxy surveys is, however, an underconstrained problem. Traditional void finding algorithms produce deterministic void catalogs, neglecting the probabilistic nature of the problem. We present a method to sample from the stochastic mapping from galaxy catalogs to arbitrary void definitions. Our algorithm uses a deep graph neural network to evolve "test particles" according to a flow-matching objective. We demonstrate the method in a simplified example setting but outline steps to generalize it towards practically usable void finders. Trained on a deterministic teacher, the model performs well but has considerable stochasticity which we interpret as regularization. Cosmological information in the predicted void catalogs outperforms the teacher. On the one hand, our method can cheaply emulate existing void finders with apparently useful regularization. More importantly, it also allows us to find the Bayes-optimal mapping between observed galaxies and any void definition. This includes definitions operating at the level of simulated matter density and velocity fields.

翻译：宇宙空洞包含高阶宇宙学信息，对天体粒子物理学具有重要意义。然而，在稀疏星系巡天中寻找真实物质欠密度区域是一个欠约束问题。传统空洞发现算法生成确定性的空洞目录，忽略了问题的概率性质。我们提出了一种从星系目录到任意空洞定义的随机映射采样方法。该算法利用深度图神经网络，根据流匹配目标演化"测试粒子"。我们在一个简化示例场景中演示了该方法，但概述了将其推广到实际可用空洞发现工具的步骤。在确定性教师模型上训练后，模型表现良好，但具有显著随机性，我们将此解释为正则化。预测空洞目录中的宇宙学信息优于教师模型。一方面，我们的方法可以通过看似有用的正则化高效模拟现有空洞发现算法。更重要的是，它使我们能够找到观测星系与任何空洞定义之间的贝叶斯最优映射，这包括在模拟物质密度和速度场层面运行的各类定义。