Accelerating phase-field predictions via recurrent neural networks learning the microstructure evolution in latent space

The phase-field method is a popular modeling technique used to describe the dynamics of microstructures and their physical properties at the mesoscale. However, because in these simulations the microstructure is described by a system of continuous variables evolving both in space and time, phase-field models are computationally expensive. They require refined spatio-temporal discretization and a parallel computing approach to achieve a useful degree of accuracy. As an alternative, we present and discuss an accelerated phase-field approach which uses a recurrent neural network (RNN) to learn the microstructure evolution in latent space. We perform a comprehensive analysis of different dimensionality-reduction methods and types of recurrent units in RNNs. Specifically, we compare statistical functions combined with linear and nonlinear embedding techniques to represent the microstructure evolution in latent space. We also evaluate several RNN models that implement a gating mechanism, including the long short-term memory (LSTM) unit and the gated recurrent unit (GRU) as the microstructure-learning engine. We analyze the different combinations of these methods on the spinodal decomposition of a two-phase system. Our comparison reveals that describing the microstructure evolution in latent space using an autocorrelation-based principal component analysis (PCA) method is the most efficient. We find that the LSTM and GRU RNN implementations provide comparable accuracy with respect to the high-fidelity phase-field predictions, but with a considerable computational speedup relative to the full simulation. This study not only enhances our understanding of the performance of dimensionality reduction on the microstructure evolution, but it also provides insights on strategies for accelerating phase-field modeling via machine learning techniques.