Uncertainty Quantification by Convolutional Neural Network Gaussian Process Regression with Image and Numerical Data

Abstract

Uncertainty Quantification (UQ) plays a critical role in engineering analysis and design. Regression is commonly employed to construct surrogate models to replace expensive simulation models for UQ. Classical regression methods suffer from the curse of dimensionality, especially when image data and numerical data coexist, which makes UQ computationally unaffordable. In this work, we propose a Convolutional Neural Network (CNN) based framework, which accommodates both image and numerical data. We first transform numerical data into images and then combine them with existing image data. The combined images are fed to CNN for regression. To obtain the model uncertainty, we integrate CNN with Gaussian Process (GP), which results in the mixed network CNN-GP. The simulation results show that CNN-GP can build accurate surrogate models for UQ with mixed data and that CNN-GP can also provide the uncertainty associated with the model prediction.