# JFlow: Model-Independent Spherical Jeans Analysis using Equivariant Continuous Normalizing Flows

arXiv: https://arxiv.org/abs/2505.00763 · HTML: https://mlsanity.com/paper/2505.00763/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 62 references that are in the map.
- First posted on arXiv 1 May 2025.

## Builds on (most cited first, 7 of 7)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densities](https://mlsanity.com/paper/2006.02425/) (2020)
- [Equivariant flow-based sampling for lattice gauge theory](https://mlsanity.com/paper/2003.06413/) (2020)
- [Equivariant Flows: sampling configurations for multi-body systems with symmetric energies](https://mlsanity.com/paper/1910.00753/) (2019)
- [Uncovering dark matter density profiles in dwarf galaxies with graph neural networks](https://mlsanity.com/paper/2208.12825/) (2022)

## Abstract (arXiv)

The kinematics of stars in dwarf spheroidal galaxies have been studied to understand the structure of dark matter halos. However, the kinematic information of these stars is often limited to celestial positions and line-of-sight velocities, making full phase space analysis challenging. Conventional methods rely on projected analytic phase space density models with several parameters and infer dark matter halo structures by solving the spherical Jeans equation. In this paper, we introduce an unsupervised machine learning method for solving the spherical Jeans equation in a model-independent way as a first step toward model-independent analysis of dwarf spheroidal galaxies. Using equivariant continuous normalizing flows, we demonstrate that spherically symmetric stellar phase space densities and velocity dispersions can be estimated without model assumptions. As a proof of concept, we apply our method to Gaia challenge datasets for spherical models and measure dark matter mass densities for given velocity anisotropy profiles. Our method can identify halo structures accurately, even with a small number of tracer stars.