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

• Verfasst von: Stammer, Pia [VerfasserIn]
• Verfasst von: Burigo, Lucas Norberto [VerfasserIn]
• Verfasst von: Jäkel, Oliver [VerfasserIn]
• Verfasst von: Frank, Martin [VerfasserIn]
• Verfasst von: Wahl, Niklas [VerfasserIn]
• Titel: Multivariate error modeling and uncertainty quantification using importance (re-)weighting for Monte Carlo simulations in particle transport
• Verf.angabe: Pia Stammer, Lucas Burigo, Oliver Jäkel, Martin Frank, Niklas Wahl
• E-Jahr: 2023
• Jahr: 26 October 2022
• Umfang: 22 S.
• Fussnoten: Gesehen am 18.01.2023
• Titel Quelle: Enthalten in: Journal of computational physics
• Ort Quelle: Amsterdam : Elsevier, 1961
• Jahr Quelle: 2023
• Band/Heft Quelle: 473(2023), Artikel-ID 111725, Seite 1-22
• ISSN Quelle: 1090-2716
• DOI: doi:10.1016/j.jcp.2022.111725
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Boltzmann equation
• Sach-SW: Error modeling
• Sach-SW: Importance sampling
• Sach-SW: Monte Carlo
• Sach-SW: Radiative transport
• Sach-SW: Uncertainty quantification
• K10plus-PPN: 183142150X

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 [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.