mlsanityData to 7 Oct 2026

Discovering Symmetry Invariants and Conserved Quantities by Interpreting Siamese Neural Networks

arXiv 2003.04299 ↗First posted 9 Mar 2020physics.comp-ph cond-mat.dis-nn cs.LGcited by 33

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Abstract (arXiv)

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.

Key facts. Cited by 33 papers in the map (data through 7 Oct 2026). First posted on arXiv 9 Mar 2020.

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Citing papers per year: 2021: 4; 2022: 8; 2023: 10; 2024: 4; 2025: 6; 2026: 1.

33 papers.

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  5. 2023Deep Learning Symmetries and Their Lie Groups, Algebras, and Subalgebras from First Principlescited by 22
  6. 2022AI Poincar'e 2.0: Machine Learning Conservation Laws from Differential Equationscited by 20
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  8. 2025Interpretable Machine Learning in Physics: A Reviewcited by 11
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  12. 2022A Review of Machine Learning Methods Applied to Structural Dynamics and Vibroacousticcited by 7
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  7. 2022Rotationally Equivariant Super-Resolution of Velocity Fields in Two-Dimensional Fluids Using Convolutional Neural Networkscited by 3
  8. 2024Closed-Form Interpretation of Neural Network Classifiers with Symbolic Gradientscited by 3
  9. 2024Data-Driven Discovery of Conservation Laws from Trajectories via Neural Deflationcited by 3
  10. 2025Adiabatic Fine-Tuning of Neural Quantum States Enables Detection of Phase Transitions in Weight Spacecited by 3
  11. 2023Fluctuation based interpretable analysis scheme for quantum many-body snapshotscited by 2
  12. 2023A Bayesian framework for discovering interpretable Lagrangian of dynamical systems from datacited by 2
  13. 2025Learning finite symmetry groups of dynamical systems via equivariance detectioncited by 2
  14. 2022A tradeoff between universality of equivariant models and learnability of symmetriescited by 1
  15. 2023Discovering New Interpretable Conservation Laws as Sparse Invariantscited by 1
  16. 2024Closed-Form Interpretation of Neural Network Latent Spaces with Symbolic Gradientscited by 1
  17. 2025Uncertainties in Physics-informed Inverse Problems: The Hidden Risk in Scientific AIcited by 1
  18. 2021Improving Simulations with Symmetry Control Neural Networkscited by 0
  19. 2022Learning quantum symmetries with interactive quantum-classical variational algorithmscited by 0
  20. 2025Deep Learning based discovery of Integrable Systemscited by 0
  21. 2026TetrisCNN for interpretable detection of phases of matter from experimental quantum simulator datacited by 0