Figure 1

Deep learning for Heisenberg model. a Spin configurations for training data preparation. \(\sigma _i\) is initial spin configuration, \(\sigma _{i}^{(10^{-1})}\) is spin configuration after one time step of \({\uptau _{1}=10^{-1}}\) from \(\sigma _i\), and \(\sigma _{i}^{(10^{-3})}\) is spin configuration after 100 time steps of \({\uptau _{3}=10^{-3}}\) from \(\sigma _i\). \(\sigma _{i}^{(res)}\) is residue of \(\sigma _{i}^{(10^{-3})}\) and \(\sigma _{i}^{(10^{-1})}\). b Illustration of the U-Net architecture. Each vertical black line represents a multi-channel feature map. The number of channels is denoted on the top of the straight vertical black line and each map’s dimension is indicated on the left edge. Vertical dashed black lines correspond on the copied feature maps from each encoder layer. c, A sequence of spin dynamics for testing the trained U-Net model: (a) conduct one time step \(\uptau _{1} = 10^{-1}\) of spin dynamics simulation; (b) use \(\sigma _{i}^{(10^{-1})}\) to predict the spin configuration \({\sigma }_i^{(10^{-3})}\) by estimating predicted residue \({\hat{\sigma }}^{(res)}_i\) using Eq. (6); Steps (a) and (b) are repeated up to t\(_{max}\) time.