# A neural simulation-based inference approach for characterizing the Galactic Center γ-ray excess

arXiv: https://arxiv.org/abs/2110.06931 · HTML: https://mlsanity.com/paper/2110.06931/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 72 references that are in the map.
- First posted on arXiv 13 Oct 2021.

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

- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [DeepSphere: Efficient spherical Convolutional Neural Network with HEALPix sampling for cosmological applications](https://mlsanity.com/paper/1810.12186/) (2018)
- [Mining gold from implicit models to improve likelihood-free inference](https://mlsanity.com/paper/1805.12244/) (2018)
- [MadMiner: Machine learning-based inference for particle physics](https://mlsanity.com/paper/1907.10621/) (2019)

## Built on by (most cited first, 12 of 12)

- [Sampling-Based Accuracy Testing of Posterior Estimators for General Inference](https://mlsanity.com/paper/2302.03026/) (2023)
- [Simulation-Based Inference: A Practical Guide](https://mlsanity.com/paper/2508.12939/) (2025)
- [sbi reloaded: a toolkit for simulation-based inference workflows](https://mlsanity.com/paper/2411.17337/) (2024)
- [Simulator-Based Inference with Waldo: Confidence Regions by Leveraging Prediction Algorithms and Posterior Estimators for Inverse Problems](https://mlsanity.com/paper/2205.15680/) (2022)
- [Uncertain Evidence in Probabilistic Models and Stochastic Simulators](https://mlsanity.com/paper/2210.12236/) (2022)
- [Embed and Emulate: Contrastive representations for simulation-based inference](https://mlsanity.com/paper/2409.18402/) (2024)
- [Amortized Bayesian Inference of GISAXS Data with Normalizing Flows](https://mlsanity.com/paper/2210.01543/) (2022)
- [Extracting the gamma-ray source-count distribution below the Fermi-LAT detection limit with deep learning](https://mlsanity.com/paper/2302.01947/) (2023)
- [BitHEP -- The Limits of Low-Precision ML in HEP](https://mlsanity.com/paper/2504.03387/) (2025)
- [A Real-Time Digital Twin for Type 1 Diabetes using Simulation-Based Inference](https://mlsanity.com/paper/2507.01740/) (2025)
- [A deep learning framework for jointly extracting spectra and source-count distributions in astronomy](https://mlsanity.com/paper/2401.03336/) (2024)
- [Misspecification-robust amortised simulation-based inference using variational methods](https://mlsanity.com/paper/2509.05724/) (2025)

## Abstract (arXiv)

The nature of the Fermi gamma-ray Galactic Center Excess (GCE) has remained a persistent mystery for over a decade. Although the excess is broadly compatible with emission expected due to dark matter annihilation, an explanation in terms of a population of unresolved astrophysical point sources e.g., millisecond pulsars, remains viable. The effort to uncover the origin of the GCE is hampered in particular by an incomplete understanding of diffuse emission of Galactic origin. This can lead to spurious features that make it difficult to robustly differentiate smooth emission, as expected for a dark matter origin, from more "clumpy" emission expected for a population of relatively bright, unresolved point sources. We use recent advancements in the field of simulation-based inference, in particular density estimation techniques using normalizing flows, in order to characterize the contribution of modeled components, including unresolved point source populations, to the GCE. Compared to traditional techniques based on the statistical distribution of photon counts, our machine learning-based method is able to utilize more of the information contained in a given model of the Galactic Center emission, and in particular can perform posterior parameter estimation while accounting for pixel-to-pixel spatial correlations in the gamma-ray map. This makes the method demonstrably more resilient to certain forms of model misspecification. On application to Fermi data, the method generically attributes a smaller fraction of the GCE flux to unresolved point sources when compared to traditional approaches. We nevertheless infer such a contribution to make up a non-negligible fraction of the GCE across all analysis variations considered, with at least 38+9-19% of the excess attributed to unresolved point sources in our baseline analysis.