  Based on the DUSTGRAIN-pathfinder suite of simulations, we investigate
observational degeneracies between nine models of modified gravity and massive
neutrinos. Three types of machine learning techniques are tested for their
ability to discriminate lensing convergence maps by extracting dimensional
reduced representations of the data. Classical map descriptors such as the
power spectrum, peak counts and Minkowski functionals are combined into a joint
feature vector and compared to the descriptors and statistics that are common
to the field of digital image processing. To learn new features directly from
the data we use a Convolutional Neural Network (CNN). For the mapping between
feature vectors and the predictions of their underlying model, we implement two
different classifiers; one based on a nearest-neighbour search and one that is
based on a fully connected neural network. We find that the neural network
provides a much more robust classification than the nearest-neighbour approach
and that the CNN provides the most discriminating representation of the data.
It achieves the cleanest separation between the different models and the
highest classification success rate of 59% for a single source redshift. Once
we perform a tomographic CNN analysis, the total classification accuracy
increases significantly to 76% with no observational degeneracies remaining.
Visualising the filter responses of the CNN at different network depths
provides us with the unique opportunity to learn from very complex models and
to understand better why they perform so well.
