Stochastic deep learning surrogate models for uncertainty propagation in microstructure–properties of ceramic aerogels

This study presents an integrated computational framework that, given synthesis parameters, predicts the resulting microstructural morphology and mechanical response of ceramic aerogel porous materials by combining physics-based simulations with deep learning surrogate models. Lattice Boltzmann simulations are employed to model microstructure formation during material synthesis process, while a finite element model is used to compute the corresponding mechanical properties. To overcome the prohibitive computational demands of repeated physics-based simulations required for characterizing the impact of microstructure randomness on mechanical properties, surrogate models are developed using Convolutional Neural Networks (CNNs) for both microstructure generation and microstructure–property mapping. CNN training is formulated as a Bayesian inference problem to enable uncertainty quantification and provide confidence estimates in surrogate model predictions, under limited training data furnished by physics-based simulations. Numerical results demonstrate that the microstructure surrogate model effectively generates microstructural images consistent with the morphology of training data across larger domains. The Bayesian CNN surrogate accurately predicts strain energy for in-distribution microstructures and its generalization capability to interpolated morphologies are further investigated. Finally, the surrogate models are employed for efficient uncertainty propagation, quantifying the influence of microstructural variability on macroscopic mechanical property.