C3NN-SBI: 从宇宙场中利用物理指导神经网络学习N点统计的层次结构
C3NN-SBI: Learning Hierarchies of $N$-Point Statistics from Cosmological Fields with Physics-Informed Neural Networks
AI总结：
C3NN-SBI通过物理指导神经网络学习宇宙场中N点统计的层次结构，结合高效优化与NPCF程序，提升宇宙学分析的效率与物理意义。
摘要：
宇宙学分析正在从已知的2点统计向更复杂的统计信息提取迈进。在扩展推理管道以包含其他汇总统计时，一个自然的步骤是包括更高阶的N点相关函数（NPCFs），这些函数计算成本高且难以建模。同时，不清楚需要包括多少NPCFs才能合理地穷尽可观测场中的宇宙学信息。一个高效的替代方法是通过神经网络进行学习和优化的汇总统计，主要通过神经网络的过参数化来实现。然而，这在很大程度上放弃了我们对NPCF形式的物理直觉，信息提取变得对实践者来说变得模糊。我们设计了一个基于模拟的推理管道，它不仅受益于通过优化获得的机器学习汇总统计的效率，还保持了NPCF程序。我们采用了受严格约束的宇宙相关卷积神经网络（C3NN），该网络能够提取可以直接与给定阶次NPCF相关联的汇总统计。我们展示了我们的框架在模拟的弱引力透镜收敛图上的应用，并研究了在不同阶次NPCF中我们学习的汇总统计的信息含量。我们将我们的方法视为一种令人兴奋的新途径，用于物理指导的模拟基于推理。
英文摘要：
Cosmological analyses are moving past the well understood 2-point statistics to extract more information from cosmological fields. A natural step in extending inference pipelines to other summary statistics is to include higher order N-point correlation functions (NPCFs), which are computationally expensive and difficult to model. At the same time it is unclear how many NPCFs one would have to include to reasonably exhaust the cosmological information in the observable fields. An efficient alternative is given by learned and optimized summary statistics, largely driven by overparametrization through neural networks. This, however, largely abandons our physical intuition on the NPCF formalism and information extraction becomes opaque to the practitioner. We design a simulation-based inference pipeline, that not only benefits from the efficiency of machine learned summaries through optimization, but also holds on to the NPCF program. We employ the heavily constrained Cosmological Correlator Convolutional Neural Network (C3NN) which extracts summary statistics that can be directly linked to a given order NPCF. We present an application of our framework to simulated lensing convergence maps and study the information content of our learned summary at various orders in NPCFs for this idealized example. We view our approach as an exciting new avenue for physics-informed simulation-based inference.
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