Multivariate error modeling and uncertainty quantification using importance (re-)weighting for Monte Carlo simulations in particle transport

TL;DR

This paper presents a generalized, non-intrusive uncertainty quantification method for Monte Carlo particle transport simulations, capable of modeling complex correlated errors to improve dose prediction accuracy in radiation therapy.

Contribution

It introduces a new multivariate importance re-weighting framework for uncertainty quantification, with theoretical analysis and support for complex error correlation models.

Findings

Supports modeling of auto-correlated errors

Provides theoretical analysis of bias and convergence

Enhances efficiency in uncertainty quantification

Abstract

Fast and accurate predictions of uncertainties in the computed dose are crucial for the determination of robust treatment plans in radiation therapy. This requires the solution of particle transport problems with uncertain parameters or initial conditions. Monte Carlo methods are often used to solve transport problems especially for applications which require high accuracy. In these cases, common non-intrusive solution strategies that involve repeated simulations of the problem at different points in the parameter space quickly become infeasible due to their long run-times. Intrusive methods however limit the usability in combination with proprietary simulation engines. In our previous paper [51], we demonstrated the application of a new non-intrusive uncertainty quantification approach for Monte Carlo simulations in proton dose calculations with normally distributed errors on realistic patient data. In this paper, we introduce a generalized formulation and focus on a more in-depth theoretical analysis of this method concerning bias, error and convergence of the estimates. The multivariate input model of the proposed approach further supports almost arbitrary error correlation models. We demonstrate how this framework can be used to model and efficiently quantify complex auto-correlated and time-dependent errors.