Discovering symmetry invariants and conserved quantities by interpreting siamese neural networks

We introduce interpretable siamese neural networks (SNNs) 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, SNNs learn to identify data points belonging to the same event, field configuration, or trajectory of motion. We demonstrate that in the process of learning which data points belong to the same event or field configuration, these SNNs also learn the relevant symmetry invariants and conserved quantities. Such SNNs are highly interpretable, which enables us to reveal the symmetry invariants and conserved quantities without prior knowledge.