Uncertainty-aware generation of spinodal decomposition microstructures via conditional variational autoencoders

Spinodal decomposition can give rise to distinct microstructural realizations, even with nominally identical processing conditions, due to the intrinsic stochasticity of the initial microstructures. As a result, deterministic process-structure surrogates that predict a single outcome collapse physically meaningful variability and provide limited insight for uncertainty-aware design. In this work, we develop a probabilistic surrogate modeling framework that targets the full conditional distribution of microstructure descriptors rather than their mean. Microstructures generated by elastochemical phase-field simulations are quantified using two-point spatial statistics and reduced via principal component analysis to obtain a compact, physically interpretable representation. A conditional β -variational autoencoder, conditioned on 18 simulation (process) parameters, is then trained to model the conditional distribution of principal components. Model architecture and regularization are selected using multi-objective Bayesian optimization to balance reconstruction fidelity and latent-space regularization. The resulting surrogate accurately reconstructs reduced microstructure descriptors, generalizes robustly to held-out data, and reproduces the distributional structure of principal component scores through both posterior predictive and generative sampling. Conditional ensemble predictions recover structured microstructural variability at fixed processing conditions, while modifying the processing conditions reveals physically consistent process-structure trends and associated uncertainty without additional high-fidelity simulations. These results demonstrate that probabilistic framing is important for surrogate modeling of stochastic process-structure relationships and provide a scalable foundation for uncertainty-aware microstructure design and exploration.