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, ${\sigma }_{\mathrm{D}\mathrm{M}}\mathrm{/}m$. 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.