Extreme time extrapolation capabilities and thermodynamic consistency of physics-inspired neural networks for the 3D microstructure evolution of materials via Cahn–Hilliard flow

A Convolutional Recurrent Neural Network (CRNN) is trained to reproduce the evolution of the spinodal decomposition process in three dimensions as described by the Cahn-Hilliard equation. A specialized, physics-inspired architecture is proven to provide close accordance between the predicted evolutions and the ground truth ones obtained via conventional integration schemes. The method can accurately reproduce the evolution of microstructures not represented in the training set at a fraction of the computational costs. Extremely long-time extrapolation capabilities are achieved, up to reaching the theoretically expected equilibrium state of the system, consisting of a layered, phase-separated morphology, despite the training set containing only relatively-short, initial phases of the evolution. Quantitative accordance with the decay rate of the free energy is also demonstrated up to the late coarsening stages, proving that this class of machine learning approaches can become a new and powerful tool for the long timescale and high throughput simulation of materials, while retaining thermodynamic consistency and high-accuracy.