Measuring the Dark Matter Self-Interaction Cross-Section with Deep Compact Clustering for Robust Machine Learning Inference

We have developed a machine learning algorithm capable of detecting ``out-of-domain data'' for trustworthy cosmological inference. By using data from two separate suites of cosmological simulations, we show that our algorithm is able to determine whether ``observed'' data is consistent with its training domain, returning confidence estimates as well as accurate parameter estimations. We apply our algorithm to two-dimensional images of galaxy clusters from the BAHAMAS-SIDM and DARKSKIES simulations with the aim to measure the self-interaction cross-section of dark matter. Through deep compact clustering we construct an informative latent space where galaxy clusters are mapped to the latent space forming ``latent-clusters'' for each simulation, with the location of the latent-cluster corresponding to the macroscopic parameters, such as the cross-section, $\sigma_{\rm DM}/m$. We then pass through mock observations, where the location of the observed latent-cluster informs us of which properties are shared with the training data. If the observed latent-cluster shares no similarities with latent-clusters from the known simulations, we can conclude that our simulations do not represent the observations and discard any parameter estimations, thus providing us with a method to measure machine learning confidence. This method serves as a blueprint for transparent and robust inference that is in demand in scientific machine learning.