Fig. 3.

The trained neural network predicts novel patterns. We used the neural network to screen 10⁸ parameter combinations to search for three-ring patterns. We then used the mechanism-based model to test accuracy of predicted patterns. We tested 1284 three-ring patterns and the mean value of the RMSEs between neural network predicted distributions and PDE simulations is 0.079 and the standard deviation is 0.008. The distributions shown in red are from training data set. The other distributions are from the screening process (top) and the corresponding results generated by the mechanism-based model for validation (bottom). In four examples, the neural network predictions are validated. In one, the neural prediction is incorrect. The RMSE values of these distributions (from left to right) are: 0.0099, 0.015, 0.0097, 0.039, 0.031, and 0.41