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.

本研究提出了一种新颖的神经网络结构，可以用于输出给定量子可积自旋链的 R - 矩阵，搜索对称性或其他限制条件下的可积哈密顿量和相应的 R - 矩阵，以及探索已学习模型周围哈密顿量的空间并重构它们所属的自旋链族。