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Learning integrability

AI-assisted maths

We introduce an AI-based framework for finding solutions to the Yang-Baxter equation and discover hundreds of new integrable Hamiltonians.

Deep learning based discovery of integrable systems

Arxiv (2025)

S. Lal, S. Majumder, E. Sobko

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.

Arxiv (2025)

S. Lal, S. Majumder, E. Sobko