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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:
 [1];  [1];  [1];  [2];  [1];  [1];  [1]
  1. Chalmers Univ. of Technology, Goteborg (Sweden)
  2. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
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:  
AC05-00OR22725; SC0008499; FP7/2007-2013; DEFG02-96ER40963
Resource Type:
Published Article
Journal Name:
Physical Review. X
Additional Journal Information:
Journal Volume: 6; 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, Boris, Forssen, Christian, Fahlin Strömberg, D., Jansen, Gustav R., Lilja, O., Lindby, M., and Mattsson, B. 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, Boris, Forssen, Christian, Fahlin Strömberg, D., Jansen, Gustav R., Lilja, O., Lindby, M., & Mattsson, B. A. Uncertainty Analysis and Order-by-Order Optimization of Chiral Nuclear Interactions. United States. doi:10.1103/PhysRevX.6.011019.
Carlsson, Boris, Forssen, Christian, Fahlin Strömberg, D., Jansen, Gustav R., Lilja, O., Lindby, M., and Mattsson, B. 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, Boris and Forssen, Christian and Fahlin Strömberg, D. and Jansen, Gustav R. and Lilja, O. and Lindby, M. and Mattsson, B. 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 = ,
volume = 6,
place = {United States},
year = {2016},
month = {2}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1103/PhysRevX.6.011019

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Cited by: 30 works
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Works referenced in this record:

Uncertainty Propagation in Nerve Impulses Through the Action Potential Mechanism
journal, January 2015

  • Torres Valderrama, Aldemar; Witteveen, Jeroen; Navarro, Maria
  • The Journal of Mathematical Neuroscience, Vol. 5, Issue 1
  • DOI: 10.1186/2190-8567-5-3

Quantification of modelling uncertainties in a large ensemble of climate change simulations
journal, August 2004

  • Murphy, James M.; Sexton, David M. H.; Barnett, David N.
  • Nature, Vol. 430, Issue 7001
  • DOI: 10.1038/nature02771

Bayesian uncertainty quantification and propagation in molecular dynamics simulations: A high performance computing framework
journal, October 2012

  • Angelikopoulos, Panagiotis; Papadimitriou, Costas; Koumoutsakos, Petros
  • The Journal of Chemical Physics, Vol. 137, Issue 14
  • DOI: 10.1063/1.4757266

The limits of the nuclear landscape
journal, June 2012

  • Erler, Jochen; Birge, Noah; Kortelainen, Markus
  • Nature, Vol. 486, Issue 7404
  • DOI: 10.1038/nature11188

Meaningful characterisation of perturbative theoretical uncertainties
journal, September 2011

  • Cacciari, Matteo; Houdeau, Nicolas
  • Journal of High Energy Physics, Vol. 2011, Issue 9
  • DOI: 10.1007/JHEP09(2011)039

Ab initio no core shell model
journal, March 2013

  • Barrett, Bruce R.; Navrátil, Petr; Vary, James P.
  • Progress in Particle and Nuclear Physics, Vol. 69
  • DOI: 10.1016/j.ppnp.2012.10.003

Coupled-cluster computations of atomic nuclei
journal, September 2014


Q UANTUM M ONTE C ARLO C ALCULATIONS OF L IGHT N UCLEI
journal, December 2001


Lattice simulations for few- and many-body systems
journal, July 2009


Modern ab initio approaches and applications in few-nucleon physics with
journal, January 2013


He 4 + n + n Continuum within an Ab initio Framework
journal, July 2014


Proton- 3 H scattering calculation: Elastic and charge-exchange reactions up to 30 MeV
journal, March 2015


Microscopic Calculation of the Inclusive Electron Scattering Structure Function in O 16
journal, February 2000


Lattice effective field theory for medium-mass nuclei
journal, May 2014


Ab initio Gorkov-Green's function calculations of open-shell nuclei
journal, January 2013


In-medium similarity renormalization group with chiral two- plus three-nucleon interactions
journal, March 2013


Modern theory of nuclear forces
journal, December 2009


Chiral effective field theory and nuclear forces
journal, June 2011


Effective Field Theory for Lattice Nuclei
journal, February 2015


Partial-wave analysis of all nucleon-nucleon scattering data below 350 MeV
journal, August 1993

  • Stoks, V. G. J.; Klomp, R. A. M.; Rentmeester, M. C. M.
  • Physical Review C, Vol. 48, Issue 2
  • DOI: 10.1103/PhysRevC.48.792

Updated analysis of NN elastic scattering data to 1.6 GeV
journal, December 1994

  • Arndt, Richard A.; Strakovsky, Igor I.; Workman, Ron L.
  • Physical Review C, Vol. 50, Issue 6
  • DOI: 10.1103/PhysRevC.50.2731

Construction of high-quality NN potential models
journal, June 1994

  • Stoks, V. G. J.; Klomp, R. A. M.; Terheggen, C. P. F.
  • Physical Review C, Vol. 49, Issue 6
  • DOI: 10.1103/PhysRevC.49.2950

Accurate nucleon-nucleon potential with charge-independence breaking
journal, January 1995

  • Wiringa, R. B.; Stoks, V. G. J.; Schiavilla, R.
  • Physical Review C, Vol. 51, Issue 1
  • DOI: 10.1103/PhysRevC.51.38

High-precision, charge-dependent Bonn nucleon-nucleon potential
journal, January 2001


Realistic models of pion-exchange three-nucleon interactions
journal, June 2001


Accurate charge-dependent nucleon-nucleon potential at fourth order of chiral perturbation theory
journal, October 2003


The two-nucleon system at next-to-next-to-next-to-leading order
journal, January 2005


Improved chiral nucleon-nucleon potential up to next-to-next-to-next-to-leading order
journal, May 2015


Optimized Chiral Nucleon-Nucleon Interaction at Next-to-Next-to-Leading Order
journal, May 2013


Phenomenological high precision neutron–proton delta-shell potential
journal, July 2013


Coarse-grained potential analysis of neutron-proton and proton-proton scattering below the pion production threshold
journal, December 2013


Coarse-grained NN potential with chiral two-pion exchange
journal, February 2014


Statistical error analysis for phenomenological nucleon-nucleon potentials
journal, June 2014


Low-energy chiral two-pion exchange potential with statistical uncertainties
journal, May 2015


Statistical uncertainties of a chiral interaction at next-to-next-to leading order
journal, February 2015

  • Ekström, A.; Carlsson, B. D.; Wendt, K. A.
  • Journal of Physics G: Nuclear and Particle Physics, Vol. 42, Issue 3
  • DOI: 10.1088/0954-3899/42/3/034003

Error analysis of nuclear forces and effective interactions
journal, February 2015

  • Pérez, R. Navarro; Amaro, J. E.; Arriola, E. Ruiz
  • Journal of Physics G: Nuclear and Particle Physics, Vol. 42, Issue 3
  • DOI: 10.1088/0954-3899/42/3/034013

Structure of A = 10 13 Nuclei with Two- Plus Three-Nucleon Interactions from Chiral Effective Field Theory
journal, July 2007


Colloquium : Three-body forces: From cold atoms to nuclei
journal, January 2013

  • Hammer, Hans-Werner; Nogga, Andreas; Schwenk, Achim
  • Reviews of Modern Physics, Vol. 85, Issue 1
  • DOI: 10.1103/RevModPhys.85.197

Phenomenological Lagrangians
journal, April 1979


Nuclear forces from chiral lagrangians
journal, November 1990


Peripheral nucleon-nucleon scattering at fifth order of chiral perturbation theory
journal, January 2015


Precision Nucleon-Nucleon Potential at Fifth Order in the Chiral Expansion
journal, September 2015


Three-nucleon forces from chiral effective field theory
journal, December 2002


Efficient calculation of chiral three-nucleon forces up to N 3 LO for ab initio studies
journal, April 2015


Determination of the Axial-Vector Weak Coupling Constant with Ultracold Neutrons
journal, October 2010


CODATA recommended values of the fundamental physical constants: 2010
journal, November 2012


Review of Particle Physics
journal, July 2012


Improved Coulomb Potential
journal, June 1983


Vacuum Polarization Effects in Proton-Proton Scattering
journal, December 1957


Magnetic moment interaction in nucleon-nucleon phase-shift analyses
journal, October 1990


Effective chiral lagrangians for nucleon-pion interactions and nuclear forces
journal, September 1991


Few-nucleon forces and systems in chiral effective field theory
journal, October 2006


Nucleon-nucleon potential from an effective chiral Lagrangian
journal, March 1994


Nucleon-nucleon potential and minimal relativity
journal, August 1969


Renormalization of one-pion exchange and power counting
journal, November 2005


Power Counting of Contact-Range Currents in Effective Field Theory
journal, February 2015


Formalism of nucleon-nucleon elastic scattering experiments
journal, January 1978


Scattering formalism for nonidentical spinor particles
journal, January 1980


Phase-Shift Analysis of 310-Mev Proton-Proton Scattering Experiments
journal, January 1957


Electromagnetic contributions to the nucleon-nucleon interaction
journal, October 1977


Accurate momentum-space method for scattering by nuclear and Coulomb potentials
journal, July 1974


Phase shift analysis of 0 30 MeV pp scattering data
journal, July 1988

  • Bergervoet, J. R.; van Campen, P. C.; van der Sanden, W. A.
  • Physical Review C, Vol. 38, Issue 1
  • DOI: 10.1103/PhysRevC.38.15

Momentum space calculations and helicity formalism in nuclear physics
journal, November 1971


Chiral three-nucleon force at N 4 LO: Longest-range contributions
journal, May 2012


Electromagnetic corrections to hadron-hadron scattering
journal, July 1974


Electromagnetic corrections to π N scattering
journal, February 1977


Coulomb corrections to πN elastic scattering
journal, July 1973


Theory of the Effective Range in Nuclear Scattering
journal, July 1949


Few-nucleon systems in a translationally invariant harmonic oscillator basis
journal, March 2000


Isoscalar Hamiltonians for light atomic nuclei
journal, August 1999


Proton radius, Darwin-Foldy term and radiative corrections
journal, November 2010


Table of experimental nuclear ground state charge radii: An update
journal, January 2013


Three-Nucleon Low-Energy Constants from the Consistency of Interactions and Currents in Chiral Effective Field Theory
journal, September 2009


Half-life and <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mi>f</mml:mi><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo stretchy="false">/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math> value for the bare triton
journal, March 2005


Error estimates of theoretical models: a guide
journal, May 2014

  • Dobaczewski, J.; Nazarewicz, W.; Reinhard, P-G
  • Journal of Physics G: Nuclear and Particle Physics, Vol. 41, Issue 7
  • DOI: 10.1088/0954-3899/41/7/074001

Charge symmetry, quarks and mesons
journal, October 1990


Parameterization dependence of T -matrix poles and eigenphases from a fit to π N elastic scattering data
journal, September 2012


Hydrogen-Deuterium 1 S 2 S Isotope Shift and the Structure of the Deuteron
journal, January 1998


Nuclear energy density optimization
journal, August 2010


Accurate nuclear radii and binding energies from a chiral interaction
journal, May 2015


Nuclear saturation and the smoothness of nucleon-nucleon potentials
journal, December 1970


Wigner Symmetry in the Limit of Large Scattering Lengths
journal, August 1999


Dimensional Power Counting in Nuclei
journal, December 1997


Neutron-proton effective range parameters and zero-energy shape dependence
journal, April 2006


Determination of the deuteron mean square radius
journal, August 1986


Nuclear sizes and the isotope shift
journal, December 1997


High-Precision Determination of the Pion-Nucleon σ Term from Roy-Steiner Equations
journal, August 2015


Search for Resonance Structure in the np Total Cross Section below 800 MeV
journal, July 1982


Uncertainties of predictions from parton distribution functions. I. The Lagrange multiplier method
journal, December 2001


Bayesian methods for parameter estimation in effective field theories
journal, March 2009


Cosmic calibration: Constraints from the matter power spectrum and the cosmic microwave background
journal, October 2007


Nonparametric Dark Energy Reconstruction from Supernova Data
journal, December 2010


    Works referencing / citing this record:

    Dimensional Power Counting in Nuclei
    journal, December 1997


    Charge symmetry, quarks and mesons
    journal, October 1990


    Nuclear forces from chiral lagrangians
    journal, November 1990


    Nucleon-nucleon potential and minimal relativity
    journal, August 1969


    Nuclear saturation and the smoothness of nucleon-nucleon potentials
    journal, December 1970


    Determination of the deuteron mean square radius
    journal, August 1986


    Phenomenological Lagrangians
    journal, April 1979


    Coulomb corrections to πN elastic scattering
    journal, July 1973


    Electromagnetic corrections to hadron-hadron scattering
    journal, July 1974


    Table of experimental nuclear ground state charge radii: An update
    journal, January 2013


    Bayesian methods for parameter estimation in effective field theories
    journal, March 2009


    The two-nucleon system at next-to-next-to-next-to-leading order
    journal, January 2005


    Half-life and <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mi>f</mml:mi><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo stretchy="false">/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math> value for the bare triton
    journal, March 2005


    Phenomenological high precision neutron–proton delta-shell potential
    journal, July 2013


    Lattice effective field theory for medium-mass nuclei
    journal, May 2014


    Chiral effective field theory and nuclear forces
    journal, June 2011


    Few-nucleon forces and systems in chiral effective field theory
    journal, October 2006


    Lattice simulations for few- and many-body systems
    journal, July 2009


    Modern ab initio approaches and applications in few-nucleon physics with
    journal, January 2013


    Ab initio no core shell model
    journal, March 2013

    • Barrett, Bruce R.; Navrátil, Petr; Vary, James P.
    • Progress in Particle and Nuclear Physics, Vol. 69
    • DOI: 10.1016/j.ppnp.2012.10.003

    Quantification of modelling uncertainties in a large ensemble of climate change simulations
    journal, August 2004

    • Murphy, James M.; Sexton, David M. H.; Barnett, David N.
    • Nature, Vol. 430, Issue 7001
    • DOI: 10.1038/nature02771

    The limits of the nuclear landscape
    journal, June 2012

    • Erler, Jochen; Birge, Noah; Kortelainen, Markus
    • Nature, Vol. 486, Issue 7404
    • DOI: 10.1038/nature11188

    Formalism of nucleon-nucleon elastic scattering experiments
    journal, January 1978


    Scattering formalism for nonidentical spinor particles
    journal, January 1980


    Bayesian uncertainty quantification and propagation in molecular dynamics simulations: A high performance computing framework
    journal, October 2012

    • Angelikopoulos, Panagiotis; Papadimitriou, Costas; Koumoutsakos, Petros
    • The Journal of Chemical Physics, Vol. 137, Issue 14
    • DOI: 10.1063/1.4757266

    Coupled-cluster computations of atomic nuclei
    journal, September 2014


    Error estimates of theoretical models: a guide
    journal, May 2014

    • Dobaczewski, J.; Nazarewicz, W.; Reinhard, P-G
    • Journal of Physics G: Nuclear and Particle Physics, Vol. 41, Issue 7
    • DOI: 10.1088/0954-3899/41/7/074001

    Statistical uncertainties of a chiral interaction at next-to-next-to leading order
    journal, February 2015

    • Ekström, A.; Carlsson, B. D.; Wendt, K. A.
    • Journal of Physics G: Nuclear and Particle Physics, Vol. 42, Issue 3
    • DOI: 10.1088/0954-3899/42/3/034003

    Error analysis of nuclear forces and effective interactions
    journal, February 2015

    • Pérez, R. Navarro; Amaro, J. E.; Arriola, E. Ruiz
    • Journal of Physics G: Nuclear and Particle Physics, Vol. 42, Issue 3
    • DOI: 10.1088/0954-3899/42/3/034013

    Improved chiral nucleon-nucleon potential up to next-to-next-to-next-to-leading order
    journal, May 2015


    Proton radius, Darwin-Foldy term and radiative corrections
    journal, November 2010


    Q UANTUM M ONTE C ARLO C ALCULATIONS OF L IGHT N UCLEI
    journal, December 2001


    Uncertainty Propagation in Nerve Impulses Through the Action Potential Mechanism
    journal, January 2015

    • Torres Valderrama, Aldemar; Witteveen, Jeroen; Navarro, Maria
    • The Journal of Mathematical Neuroscience, Vol. 5, Issue 1
    • DOI: 10.1186/2190-8567-5-3