In this paper, we introduce interpretable Siamese Neural Networks (SNN) for similarity detectionto the field of theoretical physics. More precisely, we apply SNNs to events in special relativity, thetransformation of electromagnetic fields, and the motion of particles in a central potential. In theseexamples, these 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 andconserved quantities. These SNNs are highly interpretable, which enables us to reveal the symmetry invariants and conserved quantities without prior knowledge.

本文在理论物理学领域引入可解释的孪生神经网络 (SNN) 用于相似性检测。具体而言，我们将 SNN 应用于特殊相对论事件、电磁场的变形以及中心势场中粒子的运动，在这些例子中，SNN 学习识别属于同一事件、同一场配置或相同运动轨迹的数据点。结果表明，在学习哪些数据点属于同一事件或场配置的过程中，这些 SNN 还可以学习相关的对称不变量和守恒量。这些 SNN 高度可解释，使我们能够揭示对称不变量和守恒量而无需预先知识。

解释Siamese神经网络中的对称性不变量和守恒量