Fig. 2: Training and validation of the neural network system.

a Typical magnetic domain images calculated using micromagnetic simulations (the images are used for training). Dark and bright contrast represents the magnetization direction along the film normal. The DM exchange constant is varied from 0 to 0.90 mJ m⁻²: the corresponding value is indicated at the bottom right corner of each image. b The DM exchange constant (\(D^{{\mathrm{est}}}\)) estimated from the testing images are plotted as a function of D set in the simulations (\(D^{{\mathrm{set}}}\)). c Histograms of the \(D^{{\mathrm{est}}}\) for \(D^{{\mathrm{set}}} = 0.2,\,0.4,\,0.6,\,0.8,\,1.0\) mJ m⁻². a–c \(\sigma\) is fixed to 0.15 in the simulations to generate the training/testing images. d Same with (a) except that, in addition to D, \(\sigma\) is randomly varied in the process of creating training images. The images shown are randomly chosen from a set of training images with fixed D but various \(\sigma\). The corresponding value of D is indicated at the bottom right corner of each image. e \(D^{{\mathrm{est}}}\) vs. \(D^{{\mathrm{set}}}\). f \(\sigma ^{{\mathrm{est}}}\) vs. \(\sigma ^{{\mathrm{set}}}\). d–f Both D and \(\sigma\) are varied in the simulations to generate the training/testing images. See Table 1 for the values of all material parameters.