Uncertainty Quantification of Physics-Based Label-Free Deep Learning and Probabilistic Prediction of Extreme Events

Abstract

Abstract Surrogate models from machine learning regression have been increasingly used in engineering analysis and design. Since surrogate models are usually built using data from solving expensive physical models, label-free machine learning methodologies have been developed to reduce the computational cost. Understanding and quantifying the model (epistemic) uncertainty of surrogate models is critical for their applications with quantified confidence. It is, however, much more computationally expensive, or even impossible to quantifying the model uncertainty for label-free machine learning. In this work we propose an uncertainty quantification method for the epistemic uncertainty of physics-based label-free regression. The method is used after a surrogate model has already been built by deep neural network based on the data of only input variables without labels (data of responses) and a system of physical equations. A surrogate model of the neural network regression model error is built with Gaussian Process regression using the existing training points and the derivatives of the system of physical equations at the training points. The error model is then used to compensate the error of the neural network surrogate model, therefore producing more accurate predictions. With higher accuracy, the proposed method is applied to probabilistic prediction of extreme events where both (aleatory) data uncertainty and model uncertainty coexist, and higher accuracy is required. Its application to time-dependent reliability prediction of a four-bar linkage mechanism demonstrates the high accuracy of the proposed method.