Accelerating simulations of strained-film growth by deep learning: Finite element method accuracy over long time scales

A convolutional neural network is trained on a large dataset of suitably randomized film profiles and corresponding elastic energy densities ρɛ, computed by the finite element method. The trained model provides quantitative predictions of ρɛ for arbitrary profiles, surrogating its explicit calculation, and is used for the time integration of partial differential equations describing the evolution of strained films. The close match found between the neural network predictions and the “ground-truth” evolutions obtained by the finite element method calculation of ρɛ, even after tens-of-thousands of integration time-steps, validates the approach. A substantial computational speed up without significant loss of accuracy is demonstrated, allowing for million-steps simulations of islands growth and coarsening. The intriguing possibility of extending the domain size is also discussed.