# Robust field-level inference with dark matter halos

arXiv: https://arxiv.org/abs/2209.06843 · HTML: https://mlsanity.com/paper/2209.06843/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 44 references that are in the map.
- First posted on arXiv 14 Sep 2022.

## Builds on (most cited first, 4 of 4)

- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [The CAMELS Multifield Dataset: Learning the Universe's Fundamental Parameters with Artificial Intelligence](https://mlsanity.com/paper/2109.10915/) (2021)
- [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)

## Built on by (most cited first, 5 of 5)

- [Domain Adaptive Graph Neural Networks for Constraining Cosmological Parameters Across Multiple Data Sets](https://mlsanity.com/paper/2311.01588/) (2023)
- [Field-level simulation-based inference with galaxy catalogs: the impact of systematic effects](https://mlsanity.com/paper/2310.15234/) (2023)
- [Learning from Topology: Cosmological Parameter Estimation from the Large-scale Structure](https://mlsanity.com/paper/2308.02636/) (2023)
- [Cosmology with Persistent Homology: Parameter Inference via Machine Learning](https://mlsanity.com/paper/2412.15405/) (2024)
- [Galaxy Phase-Space and Field-Level Cosmology: The Strength of Semi-Analytic Models](https://mlsanity.com/paper/2512.10222/) (2025)

## Abstract (arXiv)

We train graph neural networks on halo catalogues from Gadget N-body simulations to perform field-level likelihood-free inference of cosmological parameters. The catalogues contain lesssim5,000 halos with masses gtrsim 1010~h-1M_odot in a periodic volume of (25~h-1rm Mpc)3; every halo in the catalogue is characterized by several properties such as position, mass, velocity, concentration, and maximum circular velocity. Our models, built to be permutationally, translationally, and rotationally invariant, do not impose a minimum scale on which to extract information and are able to infer the values of Omegarm m and σ8 with a mean relative error of ~6%, when using positions plus velocities and positions plus masses, respectively. More importantly, we find that our models are very robust: they can infer the value of Omegarm m and σ8 when tested using halo catalogues from thousands of N-body simulations run with five different N-body codes: Abacus, CUBEP3M, Enzo, PKDGrav3, and Ramses. Surprisingly, the model trained to infer Omegarm m also works when tested on thousands of state-of-the-art CAMELS hydrodynamic simulations run with four different codes and subgrid physics implementations. Using halo properties such as concentration and maximum circular velocity allow our models to extract more information, at the expense of breaking the robustness of the models. This may happen because the different N-body codes are not converged on the relevant scales corresponding to these parameters.