  Different models of dark matter can alter the distribution of mass in galaxy
clusters in a variety of ways. However, so can uncertain astrophysical feedback
mechanisms. Here we present a Machine Learning method that ''learns'' how the
impact of dark matter self-interactions differs from that of astrophysical
feedback in order to break this degeneracy and make inferences on dark matter.
We train a Convolutional Neural Network on images of galaxy clusters from
hydro-dynamic simulations. In the idealised case our algorithm is 80% accurate
at identifying if a galaxy cluster harbours collisionless dark matter, dark
matter with ${\sigma}_{\rm DM}/m = 0.1$cm$^2/$g or with ${\sigma}_{DM}/m =
1$cm$^2$/g. Whilst we find adding X-ray emissivity maps does not improve the
performance in differentiating collisional dark matter, it does improve the
ability to disentangle different models of astrophysical feedback. We include
noise to resemble data expected from Euclid and Chandra and find our model has
a statistical error of < 0.01cm$^2$/g and that our algorithm is insensitive to
shape measurement bias and photometric redshift errors. This method represents
a new way to analyse data from upcoming telescopes that is an order of
magnitude more precise and many orders faster, enabling us to explore the dark
matter parameter space like never before.
