# An interpretable machine learning framework for dark matter halo formation

## TL;DR

This paper develops an interpretable machine learning framework to analyze dark matter halo formation, finding that initial density fields are more predictive of halo mass than tidal shear, with models generalizing across simulations.

## Contribution

The study introduces a generalized, interpretable machine learning approach to understand the physical factors influencing dark matter halo formation, emphasizing the role of density versus tidal shear.

## Key findings

- Density contrast alone predicts halo mass effectively.
- Tidal shear does not significantly improve predictions.
- Models generalize well across different simulations.

## Abstract

We present a generalization of our recently proposed machine learning framework, aiming to provide new physical insights into dark matter halo formation. We investigate the impact of the initial density and tidal shear fields on the formation of haloes over the mass range $11.4 \leq \log(M/M_{\odot}) \leq 13.4$. The algorithm is trained on an N-body simulation to infer the final mass of the halo to which each dark matter particle will later belong. We then quantify the difference in the predictive accuracy between machine learning models using a metric based on the Kullback-Leibler divergence. We first train the algorithm with information about the density contrast in the particles' local environment. The addition of tidal shear information does not yield an improved halo collapse model over one based on density information alone; the difference in their predictive performance is consistent with the statistical uncertainty of the density-only based model. This implies that our machine learning setup does not identify any significant role for the tidal shear in determining halo masses. This result is confirmed as we verify the ability of the initial conditions-to-halo mass mapping learnt from one simulation to generalize to independent simulations. Our work illustrates the broader potential of developing interpretable machine learning frameworks to gain physical understanding of non-linear large-scale structure formation.