# Cosmology with Persistent Homology: Parameter Inference via Machine Learning

arXiv: https://arxiv.org/abs/2412.15405 · HTML: https://mlsanity.com/paper/2412.15405/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 119 references that are in the map.
- First posted on arXiv 19 Dec 2024.

## Builds on (most cited first, 22 of 22)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Why do tree-based models still outperform deep learning on tabular data?](https://mlsanity.com/paper/2207.08815/) (2022)
- [PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures](https://mlsanity.com/paper/1904.09378/) (2019)
- [Truncated Marginal Neural Ratio Estimation](https://mlsanity.com/paper/2107.01214/) (2021)
- [Solving high-dimensional parameter inference: marginal posterior densities & Moment Networks](https://mlsanity.com/paper/2011.05991/) (2020)
- [Learning cosmology and clustering with cosmic graphs](https://mlsanity.com/paper/2204.13713/) (2022)
- [The Cosmic Graph: Optimal Information Extraction from Large-Scale Structure using Catalogues](https://mlsanity.com/paper/2207.05202/) (2022)
- [Inferring halo masses with Graph Neural Networks](https://mlsanity.com/paper/2111.08683/) (2021)
- [Multifield Cosmology with Artificial Intelligence](https://mlsanity.com/paper/2109.09747/) (2021)
- [Robust Field-level Likelihood-free Inference with Galaxies](https://mlsanity.com/paper/2302.14101/) (2023)
- [LtU-ILI: An All-in-One Framework for Implicit Inference in Astrophysics and Cosmology](https://mlsanity.com/paper/2402.05137/) (2024)
- [Robust marginalization of baryonic effects for cosmological inference at the field level](https://mlsanity.com/paper/2109.10360/) (2021)
- [Robust field-level inference with dark matter halos](https://mlsanity.com/paper/2209.06843/) (2022)
- [Cosmology from Galaxy Redshift Surveys with PointNet](https://mlsanity.com/paper/2211.12346/) (2022)
- [Field-level simulation-based inference with galaxy catalogs: the impact of systematic effects](https://mlsanity.com/paper/2310.15234/) (2023)
- [Hybrid Summary Statistics](https://mlsanity.com/paper/2410.07548/) (2024)
- [Constraining cosmological parameters from N-body simulations with Variational Bayesian Neural Networks](https://mlsanity.com/paper/2301.03991/) (2023)
- [Learning from Topology: Cosmological Parameter Estimation from the Large-scale Structure](https://mlsanity.com/paper/2308.02636/) (2023)
- [mathttemuflow: Normalising Flows for Joint Cosmological Analysis](https://mlsanity.com/paper/2409.01407/) (2024)
- [Topological Echoes of Primordial Physics in the Universe at Large Scales](https://mlsanity.com/paper/2012.03616/) (2020)

## Abstract (arXiv)

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 Omegarm m, σ8, nrm s, frm NLrm loc. PIs perform particularly well for frm NLrm 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 frm NLrm loc and for Omegarm m. This reveals that clusters and voids (0-cycles and 2-cycles) are most informative for Omegarm m, while frm NLrm loc is additionally informed by filaments (1-cycles).