Physics-Guided CNN Predicts Domain Growth in Complex Systems

This research introduces a novel deep learning approach for modeling complex physical, chemical, and biological systems. The proposed method utilizes an attention-based, physics-guided convolutional neural network (CNN) to act as a surrogate model, learning and predicting the microstructural evolution described by nonlinear partial differential equations. This offers a computationally efficient alternative to traditional numerical solvers. The model was specifically trained and tested on the Cahn-Hilliard equation, which governs phase separation in binary mixtures. It demonstrated remarkable stability and accuracy in predicting the full time-evolution, even over extended periods, while consistently preserving the mixture's composition. Furthermore, the CNN accurately captured domain size growth, aligning with the well-known Lifshitz-Slyozov law.