Bayesian Entropy Neural Networks for Physics-Aware Prediction
This addresses the need for more reliable surrogate models in physics and engineering applications, though it is incremental as it builds on existing Bayesian neural network and constraint methods.
The paper tackles the problem of integrating constraints into deep learning models for physics-aware prediction by introducing Bayesian Entropy Neural Networks (BENN), which improves robustness and reliability in applications like beam deflection modeling and microstructure generation.
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.