  We propose the use of group convolutional neural network architectures
(GCNNs) equivariant to the 2D Euclidean group, $E(2)$, for the task of galaxy
morphology classification by utilizing symmetries of the data present in galaxy
images as an inductive bias in the architecture. We conduct robustness studies
by introducing artificial perturbations via Poisson noise insertion and
one-pixel adversarial attacks to simulate the effects of limited observational
capabilities. We train, validate, and test GCNNs equivariant to discrete
subgroups of $E(2)$ - the cyclic and dihedral groups of order $N$ - on the
Galaxy10 DECals dataset and find that GCNNs achieve higher classification
accuracy and are consistently more robust than their non-equivariant
counterparts, with an architecture equivariant to the group $D_{16}$ achieving
a $95.52 \pm 0.18\%$ test-set accuracy. We also find that the model loses
$<6\%$ accuracy on a $50\%$-noise dataset and all GCNNs are less susceptible to
one-pixel perturbations than an identically constructed CNN. Our code is
publicly available at https://github.com/snehjp2/GCNNMorphology.
