mlsanityData to 7 Oct 2026

Deep Learning based discovery of Integrable Systems

arXiv 2503.10469 ↗First posted 13 Mar 2025hep-th cs.LG math-phcited by 0

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Abstract (arXiv)

We introduce a novel machine learning based framework for discovering integrable models. Our approach first employs a synchronized ensemble of neural networks to find high-precision numerical solution to the Yang-Baxter equation within a specified class. Then, using an auxiliary system of algebraic equations, [Q_2, Q_3] = 0, and the numerical value of the Hamiltonian obtained via deep learning as a seed, we reconstruct the entire Hamiltonian family, forming an algebraic variety. We illustrate our presentation with three- and four-dimensional spin chains of difference form with local interactions. Remarkably, all discovered Hamiltonian families form rational varieties.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 17 of its 61 references that are in the map. First posted on arXiv 13 Mar 2025.

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References · 17

  1. 2025Agent Laboratory: Using LLM Agents as Research Assistantscited by 405
  2. 2017The Expressive Power of Neural Networks: A View from the Widthcited by 318
  3. 2024ResearchAgent: Iterative Research Idea Generation over Scientific Literature with Large Language Modelscited by 200
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  9. 2020Discovering Symmetry Invariants and Conserved Quantities by Interpreting Siamese Neural Networkscited by 33
  10. 2021Machine-learning hidden symmetriescited by 31
  11. 2023Deep Learning Symmetries and Their Lie Groups, Algebras, and Subalgebras from First Principlescited by 22
  12. 2019Learning Symmetries of Classical Integrable Systemscited by 15
5 more
  1. 2020Machine Learning Lie Structures & Applications to Physicscited by 13
  2. 2024Rigor with Machine Learning from Field Theory to the Poincar'e Conjecturecited by 12
  3. 2023Searching for ribbons with machine learningcited by 11
  4. 2023The R-mAtrIx Netcited by 4
  5. 2024Classical integrability in the presence of a cosmological constant: analytic and machine learning resultscited by 1

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