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Figure 1. Workflow of accelerated phase-field framework for Ostwald ripening problem. (A) High-throughput phase-field simulations of
generating database of 2D microstructure images for five coupled fields in Ostwald ripening; (B) Dimensionality reduction of 2D
microstructural images into latent space using autoencoder; (C) LSTM-based machine learning engine to accelerate the microstructure
prediction in latent space; (D) Reconstruction of latent microstructures back to original 2D space using well-trained autoencoder
models, along with machine-learning prediction of feature correlation between the coupled phase fields. 2D: Two-dimensional; LSTM:
long short-term memory.

Phase-field model of the Ostwald ripening
The phase-field modeling of Ostwald ripening involves a system consisting of both ordered and disordered
phases. The solute concentration, c (x, t), is a conservative field that describes the atomic fraction of solute
diffusion within a matrix. The structural order parameter, η, is a non-conservative field that describes
different phases based on order parameters, such that η = 0 represents α phase and η = 1 means β phase. The