Figure 2
From: Learning physical properties of liquid crystals with deep convolutional neural networks
Predicting the order parameter of liquid crystals with convolutional neural networks. (A) Dependence of the order parameter p on the reduced temperature Tr for a simulated nematic liquid crystal (gray line). The vertical dashed line indicates the critical temperature Tc = 1.1075 separating the nematic (Tr < Tc) and isotropic (Tr > Tc) phases. The insets show typical textures of each phase. (B) Schematic representation of the network architecture used for the regression task of predicting the order parameter p from the textures. This network has the same general structure used for phase classification and comprises four blocks of convolutional (red) and max-pooling (green) layers followed by two fully connected layers (yellow) and an output layer. The only difference is in the last layer, where we use a linear activation function for estimating the order parameter p. (C) Coefficient of determination (between actual and predicted values) estimated from the training and validation sets as a function of the number of epochs used during the training stage. We separate 15% of data as test set, and the remaining is divided into training (80%) and validation (20%) sets (all obtained in a stratified manner). The trained network yields a coefficient of determination of ≈0.997 when applied to the test set, and the red line in panel A illustrates the accuracy of the network predictions. (D) Coefficient of determination obtained from the test set as a function of the number of convolution (and max-pooling) blocks nb in the architecture (panel B corresponds to nb = 4). The circles are average values over ten realizations of the training procedures, and the error bars are 95% confidence intervals.
