Microstructural evolution prediction in the phase field crystal model with VAE-LSTM and ensemble Kalman filtering

Accurately predicting microstructural evolution under uncertain parameters and initial conditions is a significant challenge. In this work, we present a data assimilation framework that integrates the phase field crystal model with a Variational Autoencoder-Long Short-Term Memory (VAE-LSTM) neural network and the Ensemble Kalman Filter (EnKF). The VAE-LSTM framework effectively reduces the dimensionality of high-fidelity simulations and captures complex temporal dependencies, enabling fast and accurate predictions of microstructural evolution. The EnKF further enhances the capabilities of the framework by assimilating observational data, allowing for precise estimation of key parameters. Extensive numerical experiments demonstrate the scalability and efficiency of the proposed framework, where it significantly reduces computational costs compared to traditional methods. This study highlights the potential of combining deep learning and data assimilation techniques to address complex, high-dimensional problems in materials science.