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Page 10 of 20 Gesch et al. J. Mater. Inf. 2025, 5, 42 https://dx.doi.org/10.20517/jmi.2025.23

Figure 3. Performance of autoencoder in reducing and reconstructing coupled microstructures. Reduced and reconstructed
microstructure of five coupled fields for a representative Oswald ripening simulation at (A) t = t , (B) t = t , and (C) t = t ; (D) Four
1 10 100
selected feature values of reduced microstructures are plotted as a function of 100 time frames for each field. The variations of these
feature values in the latent space can reflect the real microstructural evolution in the original space based on manifold hypothesis. For
instance, the microstructural stability at a certain time frame (e.g., flat curves) in the latent space is equivalent to the stability at that
same time frame in the original 2D space. 2D: Two-dimensional.

studies [45,46] have shown that LSTM models achieve best performance in predicting the microstructure of
spinodal decomposition when trained on 80 time frames. However, in the case of Ostwald ripening, we
found that most of the coupled fields reach a converged state after approximately 75 time frames, with no
significant changes thereafter. As a result, training LSTM models with 80 time frames becomes less
meaningful for the Ostwald ripening problem. This can be clearly seen in Figure 4A, where the feature
values (dotted lines) predicted by the LSTM models trained on 80 frames remain nearly constant from
frames 81 to 100 frames, meaning that the microstructures have already converged and no longer evolves
during this period. Therefore, our next objective is to identify the optimal training time frames for
developing the most efficient LSTM models.

To achieve this, we trained LSTM models using 20, 40, 60, and 80 time frames to study their performance in
predicting the latent microstructural features. As shown in Figure 4B, the top four feature values predicted
by the LSTM models trained on 60 time frames exhibit perfect agreement with the true feature values from
original 2D microstructure images. This suggests that the LSTM models can effectively leverage 60 training
frames to predict the future microstructure sequences in Ostwald ripening. When the number of training
time frames is reduced to 40, some discrepancies begin to appear between the LSTM-predicted feature
values and true values [Figure 4C]. This difference becomes even more pronounced with 20 training time
frames [Figure 4D], where the LSTM-predicted feature value curves deviate significantly from the true