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Gesch et al. J. Mater. Inf. 2025, 5, 42 https://dx.doi.org/10.20517/jmi.2025.23 Page 9 of 20

Figure 2. Microstructural evolutions for Ostwald ripening. The screenshots of representative microstructure images of five coupled
fields, including one compositional field (c) and four structural order parameters (η, i = 1-4) with distinct microstructure features. The
i
input parameters include mobility (M), average initial composition (c ), and final composition (c ) for four panels are: (A) M = 4.811, c =
a f a
0.545, c = 0.276; (B) M = 4.864, c = 0.500, c = 0.279; (C) M = 4.993, c = 0.481, c = 0.344; (D) M = 4.717, c = 0.499, c = 0.187.
f a f a f a f
To further evaluate the performance of autoencoder to capture microstructural evolution in latent space, we
plot the first four feature values of the autoencoder-reduced microstructures as a function of total 100 time
frames in Figure 3D. As illustrated in the left panel for the c field, these feature values exhibit smooth and
continuous variation over time and eventually converge after approximately 80 time frames. This behavior
indicates that the autoencoder effectively learns the microstructural evolution of the c field in the reduced
space. A similar continuous variation is also observed for the four η fields [Figure 3D], further
demonstrating the autoencoder’s strong performance in capturing the dynamic evolution of Ostwald
ripening with coupled fields in latent space. This finding not only aligns with the manifold hypothesis ,
[60]
which suggests that the latent representation of microstructures can effectively mirror its dynamic behaviors
over temporal space, but is also consistent with the prior work by Desai et al. . That work demonstrated
[61]
that autoencoders are efficient in representing 2D microstructure images in a relatively smaller dimension,
while these reduced features are able to maintain smooth trajectories within this latent space.

It is important to note that the autoencoder-reduced microstructure features do not follow the rule that the
sum of four η fields is identical to the c field. This is because the autoencoder is a nonlinear reduction
technique, which means it cannot preserve the linear additive relationships of the microstructural features
for the five fields in the reduced spaces. Next, we use these reduced features as input parameters for the
microstructure-learning engine to accelerate the prediction of evolutionary behavior in Ostwald ripening.

LSTM prediction of microstructure evolution
The LSTM model is chosen as the microstructure-learning engine for Ostwald ripening due to its excellent
performance to capture dynamic features of spinodal decomposition in latent space [46,47,49] . Notably, prior