Bayesian Entropy Neural Networks for Physics-Aware Prediction

This paper addresses the need for deep learning models to integrate well-defined constraints into their outputs, driven by their application in surrogate models, learning with limited data and partial information, and scenarios requiring flexible model behavior to incorporate non-data sample information. We introduce Bayesian Entropy Neural Networks (BENN), a framework grounded in Maximum Entropy (MaxEnt) principles, designed to impose constraints on Bayesian Neural Network (BNN) predictions. BENN is capable of constraining not only the predicted values but also their derivatives and variances, ensuring a more robust and reliable model output. To achieve simultaneous uncertainty quantification and constraint satisfaction, we employ the method of multipliers approach. This allows for the concurrent estimation of neural network parameters and the Lagrangian multipliers associated with the constraints. Our experiments, spanning diverse applications such as beam deflection modeling and microstructure generation, demonstrate the effectiveness of BENN. The results highlight significant improvements over traditional BNNs and showcase competitive performance relative to contemporary constrained deep learning methods.

B-BACN: Bayesian Boundary-Aware Convolutional Network for Crack Characterization

The accurate detection of crack boundaries is crucial for various purposes, such as condition monitoring, prognostics, and maintenance scheduling. To address this issue, we introduce a Bayesian Boundary-Aware Convolutional Network (B-BACN) that emphasizes the significance of both uncertainty quantification and boundary refinement to generate precise and reliable defect boundary detections. Our inspection model employs a multi-task learning approach, where we use Monte Carlo Dropout to learn the epistemic uncertainty and a Gaussian sampling function to predict each sample's aleatoric uncertainty. Moreover, we include a boundary refinement loss to B-BACN to enhance the determination of defect boundaries. The experimental results illustrate the effectiveness of our proposed approach in identifying crack boundaries with high accuracy, minimizing misclassification rate, and improving model calibration capabilities.