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

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...

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Main Authors: Stammer, Pia (Author) , Burigo, Lucas Norberto (Author) , Jäkel, Oliver (Author) , Frank, Martin (Author) , Wahl, Niklas (Author)
Format: Article (Journal)
Language:English
Published: 26 October 2022
In: Journal of computational physics
Year: 2023, Volume: 473, Pages: 1-22
ISSN:1090-2716
DOI:10.1016/j.jcp.2022.111725
Online Access:Verlag, Volltext: https://doi.org/10.1016/j.jcp.2022.111725
Verlag, Volltext: https://www.sciencedirect.com/science/article/pii/S0021999122007884
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Author Notes:Pia Stammer, Lucas Burigo, Oliver Jäkel, Martin Frank, Niklas Wahl

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520 |a 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 [61], 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. 
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