Discovering Symmetry Invariants and Conserved Quantities by Interpreting Siamese Neural Networks

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.

References in corpus (28)

• Methods for Interpreting and Understanding Deep Neural Networks
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Machine learning phases of matter
• Learning phase transitions by confusion
• Discovering Phase Transitions with Unsupervised Learning
• Unsupervised learning of phase transitions: from principal component analysis to variational autoencoders
• Discovering physical concepts with neural networks
• Machine learning quantum phases of matter beyond the fermion sign problem
• Discovering Phases, Phase Transitions and Crossovers through Unsupervised Machine Learning: A critical examination
• Machine Learning Topological States
• Quantum Loop Topography for Machine Learning
• Recurrent Neural Network Wave Functions
• Deep autoregressive models for the efficient variational simulation of many-body quantum systems
• Learning Thermodynamics with Boltzmann Machines
• Machine Learning Phases of Strongly Correlated Fermions
• Machine Learning of Explicit Order Parameters: From the Ising Model to SU(2) Lattice Gauge Theory
• Probing many-body localization with neural networks
• Kernel methods for interpretable machine learning of order parameters
• Identifying Quantum Phase Transitions with Adversarial Neural Networks
• Neural Gutzwiller-projected variational wave functions
• Parameter diagnostics of phases and phase transition learning by neural networks
• Probing hidden spin order with interpretable machine learning
• Deep Learning the Quantum Phase Transitions in Random Electron Systems: Applications to Three Dimensions
• Smallest Neural Network to Learn the Ising Criticality
• Towards Novel Insights in Lattice Field Theory with Explainable Machine Learning
• Interpreting machine learning of topological quantum phase transitions
• Projective quantum Monte Carlo simulations guided by unrestricted neural network states
• Emergent Quantum Mechanics in an Introspective Machine Learning Architecture

Cited by in corpus (29)

• On scientific understanding with artificial intelligence
• A Review of Machine Learning Methods Applied to Structural Dynamics and Vibroacoustic
• Machine Learning for Quantum Matter
• AI Poincaré: Machine Learning Conservation Laws from Trajectories
• Unsupervised machine learning of topological phase transitions from experimental data
• AI Poincaré 2.0: Machine Learning Conservation Laws from Differential Equations
• Towards glueball masses of large-$N$ $\mathrm{SU}(N)$ pure-gauge theories without topological freezing
• Scientific intuition inspired by machine learning generated hypotheses
• Phase Detection with Neural Networks: Interpreting the Black Box
• Entanglement-guided architectures of machine learning by quantum tensor network
• Discovering Conservation Laws using Optimal Transport and Manifold Learning
• Twin Neural Network Regression
• Surrogate- and invariance-boosted contrastive learning for data-scarce applications in science
• Hessian-based toolbox for reliable and interpretable machine learning in physics
• Confinement in non-Abelian lattice gauge theory via persistent homology
• Observing a topological phase transition with deep neural networks from experimental images of ultracold atoms
• Quantum Similarity Testing with Convolutional Neural Networks
• Discovering Sparse Representations of Lie Groups with Machine Learning
• Discover the GellMann-Okubo formula with machine learning
• Unsupervised Learning of Rydberg Atom Array Phase Diagram with Siamese Neural Networks
• Machine-assisted discovery of integrable symplectic mappings
• Characterizing out-of-distribution generalization of neural networks: application to the disordered Su-Schrieffer-Heeger model
• Deep learning in bifurcations of particle trajectories
• Regimes of charged particle dynamics in current sheets: the machine learning approach
• Fluctuation based interpretable analysis scheme for quantum many-body snapshots
• Digital Discovery of a Scientific Concept at the Core of Experimental Quantum Optics
• Deep Quantum Graph Dreaming: Deciphering Neural Network Insights into Quantum Experiments
• Learning quantum symmetries with interactive quantum-classical variational algorithms
• Deep learning of thermodynamic laws from microscopic dynamics