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：宇宙空洞蕴含高阶宇宙学信息，对天体粒子物理学具有重要意义。然而，在稀疏星系巡天数据中识别真实的物质低密度区是一个欠约束问题。传统空洞探测算法生成确定性空洞星表，忽略了该问题的概率本质。本文提出一种方法，用于对从星系星表到任意空洞定义的随机映射进行采样。我们的算法采用深度图神经网络，根据流匹配目标演化"测试粒子"。我们在简化示例场景中验证了该方法，并概述了将其推广至实用化空洞探测器的步骤。模型在确定性教师模型上训练后表现良好，但具有显著的随机性，我们将其解释为正则化效应。预测空洞星表中的宇宙学信息优于教师模型。一方面，本方法能够以较低成本模拟现有空洞探测器，并表现出有效的正则化特性；更重要的是，它还能帮助我们寻找观测星系与任意空洞定义之间的贝叶斯最优映射，这包括在模拟物质密度场和速度场层面运作的定义。