Session: CIE-04-01 - AMS: Uncertainty Quantification in Simulation and Model Verification & Validation

Paper Number: 97788

97788 - Physics-Constrained Bayesian Neural Network to Quantify Uncertainty in Physics-Informed Machine Learning 

Neural networks have been widely applied to solve engineering problems. For complex problems with high-dimensional inputs, the lack of training data can make the neural network predictions unreliable. To tackle this issue, physics-constrained neural networks were developed to integrate physical models in training the neural networks in order to improve the training efficiency. However, the model-form and parameter uncertainty associated with the neural networks can still cause prediction errors. The sources of model-form uncertainty are the choices of architecture for neural networks and physical models. The parameter uncertainty comes from the quantity and quality of the training data as well as the training algorithms. Traditional neural networks do not have inherent uncertainty quantification mechanisms. In this work, a new physics-constrained Bayesian neural network (PCBNN) framework is proposed to quantify the uncertainty in physics-constrained neural networks. The bias and variance of predictions are considered simultaneously during the PCBNN training process. A new loss term associated with the variance of neural network parameters is introduced in the total loss function to regulate the training. As a result, the prediction accuracy and precision are improved simultaneously. Similarly, the Kullback-Leibler divergence of parameters between training iterations is incorporated in the total loss function. This additional regularization term slows down the convergence of the parameter variance and avoid unreasonably narrow confidence intervals that miss the true output. Two training methods are also introduced. The first one is the adaptive weight scheme, where the weights associated with the different losses are adjusted adaptively based on the losses in each iteration. The second method is to formulate the training as a minimax problem where the total loss function for the worst-case scenario is minimized. A Dual-Dimer algorithm is used to search the saddle points of the total loss function for the minimax problem. The new PCBNN framework is demonstrated with engineering examples of heat transfer and phase transition. It is seen that the accuracy and precision of predictions can be both improved in the new PCBNN framework.

Presenting Author: Yan Wang Georgia Institute of Technology

Presenting Author Biography: Yan Wang is a Professor of Mechanical Engineering and leads the Multiscale Systems Engineering Research Group at Georgia Institute of Technology.

Authors:

Luka Malashkhia Georgia Institute of Technology
Dehao Liu State University of New York at Binghamton
Yan Wang Georgia Institute of Technology