Efficient and Scalable Physics-Guided Fully Convolutional Spatiotemporal Learning for 3D Microstructure Evolution Prediction

Michael Trimboli; Wenxi Liu; Xianqi Li

cs.LGSep 29, 2026

Efficient and Scalable Physics-Guided Fully Convolutional Spatiotemporal Learning for 3D Microstructure Evolution Prediction

Authors: Michael Trimboli, Wenxi Liu, Xianqi Li

Organizations: Department of Mathematics and Systems Engineering, Florida Institute of Technology, Melbourne, FL, 32901, USA

Abstract

Accurate prediction of three-dimensional (3D) microstructure evolution remains computationally demanding because high-fidelity phase-field simulations require repeated numerical integration over large volumetric domains and long temporal horizons. This study develops an efficient and scalable physics-guided fully convolutional spatiotemporal framework for direct multi-frame prediction of complete 3D microstructure sequences. The model combines shared 3D spatial encoding and decoding with a factorized latent translator that integrates temporal, local 3D spatial, and channel interactions. A discrete Cahn--Hilliard (CH) residual is incorporated during training to regularize the learned evolution toward the governing dynamics without altering the inference pathway. The framework is evaluated on high-resolution 3D spinodal-decomposition trajectories under nominal, long-horizon, and reduced-temporal-context forecasting. Under full temporal context, the model accurately reproduces volumetric evolution, with average 3D structural similarity remaining above 0.97 over the nominal prediction horizon. Physics guidance becomes increasingly beneficial as temporal information is reduced, improving predictive robustness and preservation of interface-level morphology. The framework also achieves more than a 30-fold wall-clock speedup relative to the reference spectral phase-field solver, while physics guidance introduces no additional inference cost. These results establish direct multi-frame, physics-guided fully convolutional learning as a high-throughput surrogate strategy for dense 3D phase-field dynamics and repeated microstructure forecasting.

Figures & tables

Fig. 1 : Flowchart of proposed architecture: A 3D microstructure sequence of temporal length $T$ serves as input to the model. The 3D convolutional spatial encoder extracts spatial correlations and phase distributions, producing downsampled latent representations. These latent features are propagated through the 4D latent translator, encoding temporal evolution patterns and phase separation dynamics. The convolutional spatial decoder then reconstructs the forecast microstructure fields at future timesteps $T+1$ through $2T$ . Before the final decoder layer, features from the first encoder layer are added as a residual to the predicted field, represented as a green arrow. To further enhance training, a physics-guided regularization term is incorporated to encourage phase-field-consistent spinodal decomposition dynamics, penalizing deviations from the governing properties.

Fig. 2 : Physics-guided model total training losses: Loss contribution to model training is reported at every epoch on the data-driven model.

Fig. 3 : Spinodal decomposition input (10 input frames, 10 output frames): Input sequence corresponding to the results shown in Fig. 4 , displayed at timesteps $t=1,10$ .

Fig. 4 : Spinodal decomposition prediction (10 input frames, 10 output frames) comparison: Predictions from the proposed model are shown alongside the ground-truth at timesteps $t=11,14,17,20$ . The right column reports the RMSE, 3D SSIM, and PSNR computed between the predicted and ground-truth sequences at each timestep. The bottom row displays the interface curvature distributions for both the prediction and ground-truth at $t=14,20$ , with the corresponding total variation distance between the distributions provided beneath each distribution.

Fig. 5 : Spinodal decomposition prediction 2D slice visualization (10 input frames, 10 output frames): Predictions from the proposed model are displayed alongside the ground-truth at timesteps $t=11,20$ . For each timestep, central slices of the volume are shown in the axial, coronal, and sagittal planes.

Fig. 6 : Spinodal decomposition average visual metrics (10 input frames, 10 output frames): Dataset-averaged RMSE ( A ), 3D SSIM ( B ), and PSNR ( C ), evaluated at each timestep over the prediction horizon across all 370 samples in the experiment.

Fig. 7 : Physics-guided model total training losses: Loss contribution to model training is reported at every epoch, illustrating the contribution of data loss and physics-guided loss. Physics guidance hs a regularizer value of $\lambda_{phy}=10^{-8}$ .

Fig. 8 : Spinodal decomposition input (10 input frames, 40 output frames): Input sequence corresponding to the results shown in Fig. 9 , displayed at timesteps $t=1,10$ .

Fig. 9 : Spinodal decomposition prediction (10 input frames, 40 output frames) comparison: Predictions from the physics-guided and baseline models are shown alongside the ground-truth at timesteps $t=11,31,50$ . The right column reports the RMSE, 3D SSIM, and PSNR computed between the predicted and ground-truth sequences for both models at each timestep. The bottom row displays the interface curvature distributions for each model compared with the ground-truth at $t=31,50$ , with the corresponding total variation distance provided beneath each distribution.

Fig. 10 : Spinodal decomposition prediction 2D slice visualization (10 input frames, 40 output frames): Predictions from the physics-guided model are displayed alongside the ground-truth at timesteps $t=11,31,50$ . For each timestep, central slices of the volume are shown in the axial, coronal, and sagittal planes.

Fig. 11 : Spinodal decomposition average visual metrics (10 input frames, 40 output frames): Dataset-averaged RMSE ( A ), 3D SSIM ( B ), and PSNR ( C ), evaluated at each timestep over the prediction horizon across all 270 samples in the experiment.

Fig. 12 : Spinodal decomposition input (5 input frames): Input sequence corresponding to the results shown in Fig. 13 , displayed at timesteps $t=1,5$ .

Fig. 13 : Spinodal decomposition prediction (5 input frames, 15 output frames) comparison: Predictions from the physics-guided and baseline models are shown alongside the ground-truth at timesteps $t=11,16,20$ . The right column reports the RMSE, 3D SSIM, and PSNR computed between the predicted and ground-truth sequences for both models at each timestep. The bottom row displays the interface curvature distributions for each model compared with the ground-truth at $t=16,20$ , with the corresponding total variation distance provided beneath each distribution.

Fig. 14 : Spinodal decomposition prediction 2D slice visualization (5 input frames, 15 output frames): Predictions from the physics-guided model are displayed alongside the ground-truth at timesteps $t=11,20$ . For each timestep, central slices of the volume are shown in the axial, coronal, and sagittal planes.

Fig. 15 : Spinodal decomposition average visual metrics (5 input frames, 15 output frames): Dataset-averaged RMSE ( A ), 3D SSIM ( B ), and PSNR ( C ), evaluated at each timestep over the prediction horizon across all 370 samples in the experiment.

Fig. 16 : Spinodal decomposition input (1 input frame): Input frame corresponding to the results shown in Fig. 17 , displayed at timestep $t=1$ .

Fig. 17 : Spinodal decomposition prediction (19 output frames) comparison: Predictions from the physics-guided and baseline models are shown alongside the ground-truth at timesteps $t=9,16,$ and $20$ . The right column reports the RMSE, 3D SSIM, and PSNR computed between the predicted and ground-truth sequences for both models at each timestep. The bottom row displays the interface curvature distributions for each model compared with the ground-truth at $t=9,20$ , with the corresponding total variation distance provided beneath each distribution.

Fig. 18 : Spinodal decomposition prediction 2D slice visualization (1 input frame, 19 output frames): Predictions from the physics-guided model are displayed alongside the ground-truth at timesteps $t=9,20$ . For each timestep, central slices of the volume are shown in the axial, coronal, and sagittal planes.

Fig. 19 : Spinodal decomposition average visual metrics (1 input frame, 19 output frames): Dataset-averaged RMSE ( A ), 3D SSIM ( B ), and PSNR ( C ), evaluated at each timestep over the prediction horizon across all 370 samples in the experiment.

Models (200 Epochs, batch size 1)	Training Time (hours)	Average Inference Time (40 frames $64^{3}$ )	Average Inference Time (40 frames $96^{3}$ )	Average Inference Time (40 frames $128^{3}$ )
The Proposed Model	46.1561	0.0582	0.1823	0.3682
Physics-Guided Model	48.4778	0.0582	0.1823	0.3682
SpectralETD	X	9.0483	9.129	11.896

Table 1: Inference efficiency comparison across deep spatiotemporal models and computational models on spinodal decomposition prediction . Training time and inference time for 3D spinodal decomposition prediction.

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