We provide a novel Neural Network architecture that can: i) output R-matrix for a given quantum integrable spin chain, ii) search for an integrable Hamiltonian and the corresponding R-matrix under assumptions of certain symmetries or other restrictions, iii) explore the space of Hamiltonians around already learned models and reconstruct the family of integrable spin chains which they belong to. The neural network training is done by minimizing loss functions encoding Yang-Baxter equation, regularity and other model-specific restrictions such as hermiticity. Holomorphy is implemented via the choice of activation functions. We demonstrate the work of our Neural Network on the two-dimensional spin chains of difference form. In particular, we reconstruct the R-matrices for all 14 classes. We also demonstrate its utility as an \textit{Explorer}, scanning a certain subspace of Hamiltonians and identifying integrable classes after clusterisation. The last strategy can be used in future to carve out the map of integrable spin chains in higher dimensions and in more general settings where no analytical methods are available.

翻译：我们提出了一种新颖的神经网络架构，该架构能够：i) 针对给定的量子可积自旋链输出R矩阵，ii) 在特定对称性或其他约束条件下搜索可积哈密顿量及对应的R矩阵，iii) 探索已学习模型周围哈密顿量的参数空间，并重构其所属的可积自旋链族。通过最小化编码杨-巴克斯特方程、正则性及其他模型特定约束（如厄米性）的损失函数来完成神经网络训练，并利用激活函数的选择实现全纯性。我们以差形式的两维自旋链为例展示了该网络的工作性能，特别地，重构了全部14个类别的R矩阵。此外，我们论证了其作为“探索者”工具的实用性——通过扫描哈密顿量的特定子空间并在聚类后识别可积类别。该策略未来可用于勾勒更高维度及缺乏解析方法的一般设定下可积自旋链的图谱。