Discovering Symmetry Invariants and Conserved Quantities by Interpreting Siamese Neural Networks
This provides a novel method for physicists to uncover fundamental physical laws from data, though it is incremental as it adapts existing neural network techniques to a new domain.
The paper tackles the problem of discovering symmetry invariants and conserved quantities in theoretical physics by applying interpretable Siamese Neural Networks to events in special relativity, electromagnetic fields, and particle motion, resulting in the networks learning these invariants without prior knowledge.
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.