Exploring potential of Turing pattern classification through convolution maps

We investigate the classification potential of nonlinear Turing patterns by employing convolutional features. Classifying spatial heterogeneity caused by Turing instability, observed in natural phenomena such as animal coat patterns and neural models, remains a challenging problem due to the difficulty in learning the parameters governing such pattern formation. We consider a minimal structure of a convolutional neural network including convolutional layers, activation functions, and pooling layers to classify patterns based on the reaction-diffusion model. To better capture nonlinear variations while alleviating overfitting, we additionally examine deeper convolutional structures and employ data augmentation methods. By extracting crucial features, pattern diagrams are comprehensively generated to illustrate spatial and structural variations. This approach aims to uncover potential applications of machine learning in understanding pattern formation mechanisms. The training data is generated by performing numerical simulations over a relatively large domain to minimize the influence of boundary conditions, followed by partitioning the computed results into smaller regions. The results and performances demonstrate the effectiveness of this approach.