Sensitivity Analysis and Uncertainty Quantification on Point Defect Kinetics Equations with Perturbation Analysis

TL;DR

This paper develops a perturbation-based method to analyze the sensitivity and uncertainty in point defect kinetics equations, enabling accurate predictions despite large parameter uncertainties in radiation damage modeling.

Contribution

It introduces a third-order correction approach for point defect kinetics equations that accounts for changing rate constants and quantifies uncertainty and sensitivity.

Findings

Accurately predicts defect concentrations with up to 50% parameter deviation.

Provides a framework for sensitivity analysis of input parameters.

Enables uncertainty quantification in defect evolution models.

Abstract

The concentration of radiation-induced point defects in general materials under irradiation is commonly described by the point defect kinetics equations based on rate theory. However, the parametric uncertainty in describing the rate constants of competing physical processes such as recombination and loss to sinks can lead to a large uncertainty in predicting the time-evolving point defect concentrations. Here, based on the perturbation theory, we derived up to the third order correction to the solution of point defect kinetics equations. This new set of equations enable a full description of continuously changing rate constants, and can accurately predict the solution up to $50\%$ deviation in these rate constants. These analyses can also be applied to reveal the sensitivity of solution to input parameters and aggregated uncertainty from multiple rate constants.