Model-Specific to Model-General Uncertainty for Physical Properties

Abstract

Many physical properties are derived from models, and we would like to be able to report the property with its uncertainty in an interpretable way. Different frameworks for interpreting uncertainty have been proposed. For example, “aleatoric” refers to randomness in the experiment or observations, while “epistemic” refers to ignorance about the best model. In addition, there are many ways to calculate uncertainty, including the frequentist confidence interval and the Bayesian probability distribution. In this work, we improve the understanding of which sources of uncertainty are captured by different methods. We use an example of obtaining physical properties based on function derivatives from an equation of state for Pd and Au. We obtain uncertainties using three methods: the delta method and nonlinear regression, Bayesian nonlinear regression, and Gaussian process regression. We develop a Gaussian process with joint covariance over a function and its first and second derivatives. The delta method and Bayesian regression uncertainties are consistent with each other and capture epistemic uncertainty, specifically model parameter uncertainty. The Gaussian process extends this to uncertainties arising from model selection.

Clarifying trust of materials property predictions using neural networks with distribution-specific uncertainty quantification

“…ML-guided studies of catalysts that apply uncertainty have already been performed, but these studies historically rely on GPR [22][23][24][25]. GPR is formulated from Bayesian statistics and directly outputs uncertainty estimates of the predictions [26,27]. However, the computational cost of training a GPR model typically scales O(N 3 ) and thus grows unfavorably with dataset size, which is an open challenge for big-data applications [28].…”

Machine Learning and Data Science in Chemical Engineering

“…This special issue of Industrial & Engineering Chemistry Research presents an excellent collection of articles from internationally renowned researchers from all around the world to showcase the application of machine learning and data science in the aforementioned chemical engineering problems. − We truly appreciate the efforts from all contributing authors to make it happen. We hope these articles provide new insights and perspectives as to how machine learning can be used in a wide variety of chemical engineering problems, and stimulate more creative solutions to existing and future challenges.…”