PREDICTING MICROSTRUCTURE-PROPERTY OF SILICA AEROGEL MATERIALS VIA BAYESIAN CONVOLUTIONAL NEURAL NETWORKS SURROGATE MODEL

Deep neural networks have become essential for developing data-driven surrogate models of complex multiscale and multiphysics simulations. Trained with high-fidelity simulation data, these surrogate models enable computational predictions with significantly reduced time and resources compared to physics-based simulations. Surrogate models based on Convolutional Neural Networks (CNNs) are emerging as powerful tools for learning the complex relationships between microstructural images and the corresponding macroscopic properties of materials, facilitating tasks once computationally prohibitive, such as optimal design and synthesizing materials with target properties. However, the common neural network training method, relying on maximum likelihood parameter estimation, limits CNNs’ ability to handle uncertainty due to sparse and limited high-fidelity data generated by physics-based simulations. This often leads to overfitting and overly confident predictions, compromising the reliability of CNNs, especially in high-consequence tasks such as model-based material design. This contribution proposes a Bayesian CNN for surrogate modeling by treating the network’s training as statistical inference to overcome the formidable challenge of uncertainty assessment in predictions provided by neural network-based models. We employ Variational Inference to introduce probability distributions over the CNN’s weights, ensuring accurate uncertainty estimation. The proposed Bayesian CNN surrogate model is applied to learn microstructure image-mechanical property relations in silica aerogel porous materials, known for its superior insulation properties but suffer from low mechanical strength. Training data is obtained from elastic deformation simulations of the solid phase in the porous materials governed by stochastic partial differential equations. Results demonstrate the effectiveness of the Bayesian CNN in predicting the strain energy corresponding to a given microstructure image while considering confidence levels in predictions. The impact of training data points on prediction accuracy and reliability is also investigated using Bayesian CNN.