用拓扑方法提升宇宙学参数推断精度，尤其擅长捕捉原始非高斯信号。
Cosmology with Persistent Homology: Parameter Inference via Machine Learning
- 用持久同调生成图像，替代传统功率谱与三体相关函数。
- 在Ωₘ、σ₈、nₛ、f_NL^loc参数上，拓扑图像表现优于传统方法。
- 揭示星系团与空洞对Ωₘ敏感，丝状结构则贡献于f_NL^loc识别。
基于[2308.02636]，我们研究持久同调在无似然推断框架下对宇宙学参数及原始非高斯性的约束能力，结合机器学习方法。评估了持久同调图像（PIs）在参数推断中的表现，并与联合功率谱和三体相关函数（PS/BS）进行比较。结果显示，在可约束参数如{Ωₘ, σ₈, nₛ, f_NL^loc}上，PIs始终优于PS/BS；尤其在f_NL^loc的估计中表现突出，凸显持久同调在原始非高斯性探测方面的潜力。进一步发现，将PIs与PS/BS结合仅带来边际增益，表明两者信息重叠度高。最后，可视化显示：对于f_NL^loc，1-循环（丝状结构）具有关键作用；而Ωₘ主要由0-循环（星系团）和2-循环（空洞）主导。
原文摘要 · Abstract (English)
Building upon [2308.02636], we investigate the constraining power of persistent homology on cosmological parameters and primordial non-Gaussianity in a likelihood-free inference pipeline utilizing machine learning. We evaluate the ability of Persistence Images (PIs) to infer parameters, comparing them to the combined Power Spectrum and Bispectrum (PS/BS). We also compare two classes of models: neural-based and tree-based. PIs consistently lead to better predictions compared to the combined PS/BS for parameters that can be constrained, i.e., for $\{Ω_{\rm m}, σ_8, n_{\rm s}, f_{\rm NL}^{\rm loc}\}$. PIs perform particularly well for $f_{\rm NL}^{\rm loc}$, highlighting the potential of persistent homology for constraining primordial non-Gaussianity. Our results indicate that combining PIs with PS/BS provides only marginal gains, indicating that the PS/BS contains little additional or complementary information to the PIs. Finally, we provide a visualization of the most important topological features for $f_{\rm NL}^{\rm loc}$ and for $Ω_{\rm m}$. This reveals that clusters and voids (0-cycles and 2-cycles) are most informative for $Ω_{\rm m}$, while $f_{\rm NL}^{\rm loc}$ is additionally informed by filaments (1-cycles).
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