Teaching dark matter simulations to speak the halo language

TL;DR

This paper introduces GOTHAM, a transformer-based generative model that accurately predicts dark matter halo properties in cosmological simulations, enabling faster and scalable large-volume simulations with high statistical fidelity.

Contribution

The paper presents the first transformer-based model for generating dark matter halos conditioned on approximate simulations, improving small-scale statistical accuracy and scalability.

Findings

Achieves better than 3% accuracy in small-scale halo statistics

Enables large-volume simulations with reduced computational cost

Provides a differentiable model for end-to-end cosmological simulations

Abstract

We develop a transformer-based conditional generative model for discrete point objects and their properties. We use it to build a model for populating cosmological simulations with gravitationally collapsed structures called dark matter halos. Specifically, we condition our model with dark matter distribution obtained from fast, approximate simulations to recover the correct three-dimensional positions and masses of individual halos. This leads to a first model that can recover the statistical properties of the halos at small scales to better than 3% level using an accelerated dark matter simulation. This trained model can then be applied to simulations with significantly larger volumes which would otherwise be computationally prohibitive with traditional simulations, and also provides a crucial missing link in making end-to-end differentiable cosmological simulations. The code, named GOTHAM (Generative cOnditional Transformer for Halo's Auto-regressive Modeling) is publicly available at \url{https://github.com/shivampcosmo/GOTHAM}.