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Deep Learning based discovery of Integrable Systems
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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.
Forward citations
Cited by 2 Pith papers
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A Simple Necessary and Sufficient Condition for Yang--Baxter Integrability
The Reshetikhin condition on a nearest-neighbour spin-chain Hamiltonian is sufficient (and necessary) for the existence of a regular difference-form Yang–Baxter R-matrix, resolving a 1980s conjecture.
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Dichotomy theorem separating complete integrability and non-integrability of isotropic spin chains
For SU(2)-invariant nearest-neighbor spin chains of any spin S, the single condition D3=0 decides between complete integrability and complete non-integrability.
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