Deep Learning based discovery of Integrable Systems

I will present 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 - known as a Reshetikhin condition - 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. Remarkably, all the discovered Hamiltonian families form rational varieties, making it compelling to initiate their systematic analysis using tools from algebraic geometry. I will conclude by outlining how our approach can be used to perform the Integrable S-matrix Bootstrap for two-dimensional integrable QFTs and integrable strings on AdS backgrounds.