A latent space assimilation framework for quasicrystal growth prediction using β-VAE–Transformer and Ensemble Kalman Filter

Accurately forecasting microstructural evolution under uncertain parameters and initial conditions presents a significant challenge. In this study, we consider an eighth-order quasicrystal model and develop a framework combining a β-Variational Autoencoder (β-VAE), a Transformer network, and the Ensemble Kalman Filter (EnKF) for efficient prediction and data assimilation. The β-VAE compresses high-dimensional crystal field data into a compact latent representation, while the Transformer captures complex temporal dependencies in the latent space for multi-step forecasting. By performing EnKF-based data assimilation in the latent space, the framework can efficiently integrate observational data, simultaneously refining predictions of evolving crystal states and estimating model parameters. Extensive numerical experiments demonstrate the scalability and efficiency of the proposed framework. This study highlights the effectiveness of combining deep learning and data assimilation techniques for accurate modeling and prediction of complex, high-dimensional crystal structures.