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The nature of the Fermi gamma-ray Galactic Center Excess (GCE) has remained apersistent mystery for over a decade. Although the excess is broadly compatiblewith emission expected due to dark matter annihilation, an explanation in termsof a population of unresolved astrophysical point sources e.g., millisecondpulsars, remains viable. The effort to uncover the origin of the GCE ishampered in particular by an incomplete understanding of diffuse emission ofGalactic origin. This can lead to spurious features that make it difficult torobustly 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 ofsimulation-based inference, in particular density estimation techniques usingnormalizing flows, in order to characterize the contribution of modeledcomponents, including unresolved point source populations, to the GCE. Comparedto traditional techniques based on the statistical distribution of photoncounts, our machine learning-based method is able to utilize more of theinformation contained in a given model of the Galactic Center emission, and inparticular can perform posterior parameter estimation while accounting forpixel-to-pixel spatial correlations in the gamma-ray map. This makes the methoddemonstrably more resilient to certain forms of model misspecification. Onapplication to Fermi data, the method generically attributes a smaller fractionof the GCE flux to unresolved point sources when compared to traditionalapproaches. We nevertheless infer such a contribution to make up anon-negligible fraction of the GCE across all analysis variations considered,with at least $38^{+9}_{-19}\%$ of the excess attributed to unresolved pointsources in our baseline analysis.

A neural simulation-based inference approach for characterizing the Galactic Center $\gamma$-ray excess