用深度学习找可积模型，自动发现带理式结构的哈密顿量族。
Deep Learning based discovery of Integrable Systems
- 用同步神经网络高精度求解杨-巴克斯特方程
- 从数值哈密顿量重建出整个有理数域的哈密顿量族
- 适用于具有局域相互作用的差分型自旋链模型
我们提出一种基于机器学习的新框架，用于发现可积模型。方法首先利用同步神经网络集合，在特定类别中高精度求解杨-巴克斯特方程；随后，结合代数方程组 [Q_2, Q_3] = 0 及深度学习得到的哈密顿量数值作为种子，重构出完整的哈密顿量族，形成代数簇。我们在具有局域相互作用的三、四维差分型自旋链模型上进行了演示，发现所有新发现的哈密顿量族均为有理簇。
原文摘要 · Abstract (English)
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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