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Gesch et al. J. Mater. Inf. 2025, 5, 42 https://dx.doi.org/10.20517/jmi.2025.23 Page 17 of 20

over time sequences. This also indicates the high potential of this accelerated phase-field framework for
adapting to new phase-field problems.

CONCLUSIONS
In this work, we developed an accelerated phase-field framework for Ostwald ripening problems. This
framework integrates the high-throughput phase-field simulations for generating large datasets of 2D
microstructure images, autoencoder-based image reduction techniques, and LSTM models as machine-
learning engine for predicting the microstructural evolutions in latent space. A high-quality database of
microstructure evolution containing 200 Ostwald ripening trajectories was developed. Based on this large
database, we found that the autoencoder can efficiently capture the key features of Ostwald ripening
microstructure images in the low-dimensional dimensions for five different fields: including one solute
compositional field and four structural order parameter fields. The reduced microstructures were
subsequently fed into the LSTM models to predict the evolution of microstructures for all five fields. These
models do not only exhibit high performance in accurately predicting the dynamics of coupled
5
microstructures, but also achieve a significant speedup of 3.35 × 10 compared to high-fidelity phase-field
simulations. Additionally, the SVM models were implemented to successfully predict the correlation
between the difference fields, further improving the computational efficiency of our accelerated framework.
The accelerated frameworks developed in this study are not only applicable to the 2D Ostwald ripening
problems, but also have the potential to predict microstructural evolution in more complex systems
involving multiple coupled fields in 3D space. As the datasets for microstructure evolutions continue to
grow, the framework developed in this work may become less efficient. Therefore, the development of
physics-informed PSDMs could represent a potentially future research direction for accelerating coupled
phase-field problems.

DECLARATIONS
Acknowledgments
The authors thank Dr. Remi Dingreville and Dr. Daniel Vizoso for valuable discussions regarding the use of
the MEMPHIS code.

Authors’ contributions
Data curation (lead); formal analysis (lead); investigation (lead); methodology (lead); visualization (lead);
writing - original draft (lead); writing - review and editing (lead): Gesch, A.
Conceptualization; supervision; formal analysis (lead); investigation (lead); methodology (lead);
visualization (lead); writing - original draft (lead); writing - review and editing (lead): Hu, C.

Availability of data and materials
The data and codes are available on publicly accessible platforms. All microstructure databases can be
[59]
accessed through the MDF website using following link . The machine-learning codes developed for the
accelerated framework are available on GitHub website: https://github.com/huhuhhhh/AcceleratePF.

Financial support and sponsorship
This work was supported by the University of Alabama startup fund. Computational resources were
provided by the Alabama Supercomputer Authority (ASA). This work was partially conducted using the
resources at the National Energy Research Scientific Computing Center, a DOE Office of Science User
Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-
05CH11231 using NERSC award BES-ERCAP0031213.