Deep Learning based discovery of Integrable Systems
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.
Cite
@article{arxiv.2503.10469,
title = {Deep Learning based discovery of Integrable Systems},
author = {Shailesh Lal and Suvajit Majumder and Evgeny Sobko},
journal= {arXiv preprint arXiv:2503.10469},
year = {2025}
}
Comments
11 pages, 2 column text, 3 figures, Mathematica notebook with example Hamiltonians. Typos fixed