Extreme time extrapolation capabilities and thermodynamic consistency of physics-inspired Neural Networks for the 3D microstructure evolution of materials

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 closely 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, 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 late coarsening stages, providing an example of a data-driven, physically consistent and high-accuracy Machine Learning method for the long timescale simulation of materials.

Learning and accurate generation of stochastic dynamics based on multi-model Generative Adversarial Networks

Generative Adversarial Networks (GANs) have shown immense potential in fields far from physics, such as in text and image generation. Here we use GANs to learn a prototypical stochastic process on a lattice. By suitably adding noise to the original data we succeed in bringing both the Generator and the Discriminator loss functions close to their ideal value. However, as typical for adversarial approaches, oscillations persist. This undermines model selection and the quality of the generated trajectory. We demonstrate that a suitable multi-model procedure where stochastic trajectories are advanced at each step upon randomly selecting a Generator leads to a remarkable increase in accuracy. Based on the reported findings GANs appears as a promising tool to tackle complex statistical dynamics.