Deep Learning based discovery of Integrable Systems

Shailesh Lal; Suvajit Majumder; Evgeny Sobko

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arXiv · 2503.10469

Deep Learning based discovery of Integrable Systems

Shailesh Lal·Suvajit Majumder·Evgeny Sobko

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Abstract

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.

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hep-th cs.LG math-ph math.MP math.QA quant-ph

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Shailesh Lal, Suvajit Majumder, Evgeny Sobko. 2025-03-13. Deep Learning based discovery of Integrable Systems. https://arxiv.org/abs/2503.10469

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