  In this paper, we introduce interpretable Siamese Neural Networks (SNN) for
similarity detection to the field of theoretical physics. More precisely, we
apply SNNs to events in special relativity, the transformation of
electromagnetic fields, and the motion of particles in a central potential. In
these examples, the SNNs learn to identify datapoints belonging to the same
events, field configurations, or trajectory of motion. It turns out that in the
process of learning which datapoints belong to the same event or field
configuration, these SNNs also learn the relevant symmetry invariants and
conserved quantities. These SNNs are highly interpretable, which enables us to
reveal the symmetry invariants and conserved quantities without prior
knowledge.
