Exploring potential of Turing pattern classification through convolution maps.

Area of Science:

• Computational biology
• Pattern formation
• Machine learning applications

Background:

• Turing patterns exhibit spatial heterogeneity, crucial in biological systems (e.g., animal coats, neural models).
• Classifying these patterns is challenging due to difficulties in learning governing parameters.

Purpose of the Study:

• To explore the classification potential of nonlinear Turing patterns using convolutional neural networks (CNNs).
• To apply machine learning for understanding pattern formation mechanisms in reaction-diffusion systems.

Main Methods:

• Utilized a minimal CNN structure with convolutional, activation, and pooling layers.
• Employed deeper convolutional structures and data augmentation to capture nonlinear variations and prevent overfitting.
• Generated training data via numerical simulations on large domains, minimizing boundary effects.

Main Results:

• Successfully classified spatial heterogeneity caused by Turing instability.
• Extracted crucial features to generate pattern diagrams illustrating spatial and structural variations.
• Demonstrated the effectiveness of the CNN approach in analyzing pattern formation.

Conclusions:

• Convolutional features offer significant potential for classifying nonlinear Turing patterns.
• This machine learning methodology provides a powerful tool for studying complex pattern formation mechanisms.