Abstract
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.
Highlights
Machine learning (ML) algorithms have experienced a surge in the physical sciences
The following are the contributions we make in this paper. (i) We introduce the siamese neural network (SNN) to the field of theoretical physics. (ii) We demonstrate its usage in the well known contexts of special relativity, electromagnetism, and the motion of particles in a central potential
While it is often difficult to decide if neural networks learn to understand physical concepts to make decisions, here we argue that our SNN does so
Summary
Machine learning (ML) algorithms have experienced a surge in the physical sciences. This is based on the introduction of ML methods to fulfill tasks beyond the scope for which they were originally designed. The simplest way to interpret a neural network is to examine the weights and biases of individual neurons, which can only yield successful results in shallow ANNs. In the field of explainable artificial intelligence, there are different methods that determine which features of the given input are responsible for a learned model’s classification [28,29]. Instead of training a traditional neural network to distinguish between a fixed number of classes, an SNN can probe the similarity of one data point with another prototypical data point for a certain class. In the case of motion of particles, these SNNs discover whether or not two observations of position and momenta describe the same particle. (iii) Further, we successfully interpret the intermediate output representations of the SNN and recover the mathematical formulations of known physical conserved quantities and invariants, e.g., the space-time interval or the angular momentum. (iv) Since the interpretation of the SNN yields signatures of known physical equations, we argue that our SNN has learned to understand physical concepts instead of merely performing basic pattern matching
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