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Title: Uncertainty Analysis and Order-by-Order Optimization of Chiral Nuclear Interactions

Abstract

Chiral effective field theory ( ΧEFT) provides a systematic approach to describe low-energy nuclear forces. Moreover, EFT is able to provide well-founded estimates of statistical and systematic uncertainties | although this unique advantage has not yet been fully exploited. We ll this gap by performing an optimization and statistical analysis of all the low-energy constants (LECs) up to next-to-next-to-leading order. Our optimization protocol corresponds to a simultaneous t to scattering and bound-state observables in the pion-nucleon, nucleon-nucleon, and few-nucleon sectors, thereby utilizing the full model capabilities of EFT. Finally, we study the effect on other observables by demonstrating forward-error-propagation methods that can easily be adopted by future works. We employ mathematical optimization and implement automatic differentiation to attain e cient and machine-precise first- and second-order derivatives of the objective function with respect to the LECs. This is also vital for the regression analysis. We use power-counting arguments to estimate the systematic uncertainty that is inherent to EFT and we construct chiral interactions at different orders with quantified uncertainties. Statistical error propagation is compared with Monte Carlo sampling showing that statistical errors are in general small compared to systematic ones. In conclusion, we find that a simultaneous t to different setsmore » of data is critical to (i) identify the optimal set of LECs, (ii) capture all relevant correlations, (iii) reduce the statistical uncertainty, and (iv) attain order-by-order convergence in EFT. Furthermore, certain systematic uncertainties in the few-nucleon sector are shown to get substantially magnified in the many-body sector; in particlar when varying the cutoff in the chiral potentials. The methodology and results presented in this Paper open a new frontier for uncertainty quantification in ab initio nuclear theory.« less

Authors:
; ; ; ; ; ; ; ;
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1239437
Alternate Identifier(s):
OSTI ID: 1261377
Grant/Contract Number:  
SC0008499; AC05-00OR22725; FP7/2007-2013; DEFG02-96ER40963
Resource Type:
Published Article
Journal Name:
Physical Review. X
Additional Journal Information:
Journal Name: Physical Review. X Journal Volume: 6 Journal Issue: 1; Journal ID: ISSN 2160-3308
Publisher:
American Physical Society
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Citation Formats

Carlsson, B. D., Ekström, A., Forssén, C., Strömberg, D. Fahlin, Jansen, G. R., Lilja, O., Lindby, M., Mattsson, B. A., and Wendt, K. A. Uncertainty Analysis and Order-by-Order Optimization of Chiral Nuclear Interactions. United States: N. p., 2016. Web. doi:10.1103/PhysRevX.6.011019.
Carlsson, B. D., Ekström, A., Forssén, C., Strömberg, D. Fahlin, Jansen, G. R., Lilja, O., Lindby, M., Mattsson, B. A., & Wendt, K. A. Uncertainty Analysis and Order-by-Order Optimization of Chiral Nuclear Interactions. United States. doi:10.1103/PhysRevX.6.011019.
Carlsson, B. D., Ekström, A., Forssén, C., Strömberg, D. Fahlin, Jansen, G. R., Lilja, O., Lindby, M., Mattsson, B. A., and Wendt, K. A. Wed . "Uncertainty Analysis and Order-by-Order Optimization of Chiral Nuclear Interactions". United States. doi:10.1103/PhysRevX.6.011019.
@article{osti_1239437,
title = {Uncertainty Analysis and Order-by-Order Optimization of Chiral Nuclear Interactions},
author = {Carlsson, B. D. and Ekström, A. and Forssén, C. and Strömberg, D. Fahlin and Jansen, G. R. and Lilja, O. and Lindby, M. and Mattsson, B. A. and Wendt, K. A.},
abstractNote = {Chiral effective field theory ( ΧEFT) provides a systematic approach to describe low-energy nuclear forces. Moreover, EFT is able to provide well-founded estimates of statistical and systematic uncertainties | although this unique advantage has not yet been fully exploited. We ll this gap by performing an optimization and statistical analysis of all the low-energy constants (LECs) up to next-to-next-to-leading order. Our optimization protocol corresponds to a simultaneous t to scattering and bound-state observables in the pion-nucleon, nucleon-nucleon, and few-nucleon sectors, thereby utilizing the full model capabilities of EFT. Finally, we study the effect on other observables by demonstrating forward-error-propagation methods that can easily be adopted by future works. We employ mathematical optimization and implement automatic differentiation to attain e cient and machine-precise first- and second-order derivatives of the objective function with respect to the LECs. This is also vital for the regression analysis. We use power-counting arguments to estimate the systematic uncertainty that is inherent to EFT and we construct chiral interactions at different orders with quantified uncertainties. Statistical error propagation is compared with Monte Carlo sampling showing that statistical errors are in general small compared to systematic ones. In conclusion, we find that a simultaneous t to different sets of data is critical to (i) identify the optimal set of LECs, (ii) capture all relevant correlations, (iii) reduce the statistical uncertainty, and (iv) attain order-by-order convergence in EFT. Furthermore, certain systematic uncertainties in the few-nucleon sector are shown to get substantially magnified in the many-body sector; in particlar when varying the cutoff in the chiral potentials. The methodology and results presented in this Paper open a new frontier for uncertainty quantification in ab initio nuclear theory.},
doi = {10.1103/PhysRevX.6.011019},
journal = {Physical Review. X},
number = 1,
volume = 6,
place = {United States},
year = {2016},
month = {2}
}

Journal Article:
Free Publicly Available Full Text
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DOI: 10.1103/PhysRevX.6.011019

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Cited by: 30 works
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