Quantifying Model Uncertainties in the Space of Probability Measures

TL;DR

This paper introduces a novel method for quantifying model uncertainties by analyzing the evolution of probability distributions, providing a new approach to estimate uncertain parameters in complex scientific models.

Contribution

The paper proposes a new technique to quantify model uncertainties in the space of probability measures using experimental distribution data, with analytical and numerical demonstrations.

Findings

Method successfully estimates uncertain parameters from distribution data.

Analytical and numerical examples validate the approach.

Provides a new perspective on uncertainty quantification in complex systems.

Abstract

Due to lack of scientific understanding, some mechanisms may be missing in mathematical modeling of complex phenomena in science and engineering. These mathematical models thus contain some uncertainties such as uncertain parameters. One method to estimate these parameters is based on pathwise observations, i.e., quantifying model uncertainty in the space of sample paths for system evolution. Another method is devised here to estimate uncertain parameters, or unknown system functions, based on experimental observations of probability distributions for system evolution. This is called the quantification of model uncertainties in the space of probability measures. A few examples are presented to demonstrate this method, analytically or numerically.