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Figure 5. Comparison of microstructural evolution predicted by LSTM models trained with different time frames. The microstructural
evolution of composition field c in reduced 4 × 4 space and autoencoder-reconstructed 2D space predicted by LSTM models using (B)
70 time frames, (C) 50 time frames, and (D) 30 time frames. The original phase-field-simulated microstructure images at each timestep
are shown in panel (A) for comparing the performance of each LSTM model. In panels (B-D), the third rows are pointwise error plots to
visualize the differences between the LSTM-predicted microstructure images and original images as a result of the autoencoder (training
and predicted frames) and LSTM (predicted frames only). LSTM: Long short-term memory; 2D: two-dimensional.

compared to original one [Figure 5A]. This finding aligns well with our prior analysis, where the LSTM-
predicted feature values have perfect agreement with true feature values when time frame is above 60
[Figure 4B]. Moreover, we also adopt LSTM models with 70 training time frames to predict the evolution of
four η fields, and the near-perfect match between LSTM-predicted microstructures and true phase-field
simulations shown in Supplementary Figure 4 further demonstrates the superior performance of LSTM
models in accurately predicting the microstructure evolution of Ostwald ripening problem.