Deep Learning based discovery of Integrable Systems
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916653324828672 |
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| author | Lal, Shailesh Majumder, Suvajit Sobko, Evgeny |
| author_facet | Lal, Shailesh Majumder, Suvajit Sobko, Evgeny |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_10469 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Deep Learning based discovery of Integrable Systems Lal, Shailesh Majumder, Suvajit Sobko, Evgeny High Energy Physics - Theory Machine Learning Mathematical Physics Quantum Algebra Quantum Physics 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. |
| title | Deep Learning based discovery of Integrable Systems |
| topic | High Energy Physics - Theory Machine Learning Mathematical Physics Quantum Algebra Quantum Physics |
| url | https://arxiv.org/abs/2503.10469 |