Sensitivity analysis of random two-body interactions

Johnson, Calvin W.; Krastev, Plamen G.

doi:10.1103/physrevc.81.054303

Cited by 5 publications

(2 citation statements)

References 25 publications

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“…In the fit they found that about five or six linear combinations of parameters were the most important. (Interesting, a similar result was found for random values of the matrix elements [19]).…”

Section: Introductionsupporting

confidence: 76%

Uncertainty quantification of an empirical shell-model interaction using principal component analysis

Fox,

Johnson,

Perez

2019

Preprint

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Recent investigations have emphasized the importance of uncertainty quantification (UQ) to describe errors in nuclear theory. We carry out UQ for configuration-interaction shell model calculations in the 1s-0d valence space, investigating the sensitivity of observables to perturbations in the 66 parameters (matrix elements) of a high-quality empirical interaction. The large parameter space makes computing the corresponding Hessian numerically costly, so we construct a cost-effective approximation using the Feynman-Hellmann theorem. Diagonalizing the approximated Hessian yields the principal components: linear combinations of parameters ordered by sensitivity. This approximately decoupled distribution of parameters facilitates theoretical error propagation onto structure observables: electromagnetic transitions, Gamow-Teller decays, and dark-matter interaction matrix elements.

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Section: Introductionsupporting

confidence: 76%

Uncertainty quantification of an empirical shell-model interaction using principal component analysis

Fox,

Johnson,

Perez

2019

Preprint

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“…[34][35][36][37]), in nuclear physics we are just starting to explore such ideas in many-body calculations. However, there have been a variety of attempts to employ factorization techniques in fitting procedures or as diagnostic tools [38][39][40][41].…”

Section: Introductionmentioning

confidence: 99%

Least-square approach for singular value decompositions of scattering problems

Tichai,

Arthuis,

Hebeler

et al. 2022

Preprint

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It was recently observed that chiral two-body interactions can be efficiently represented using matrix factorization techniques such as the singular value decomposition. However, the exploitation of these low-rank structures in a few-or many-body framework is nontrivial and requires reformulations that explicitly utilize the decomposition format. In this work, we present a general least-square approach that is applicable to different few-and many-body frameworks and allows for an efficient reduction to a low number of singular values in the least-square iteration. We verify the feasibility of the least-square approach by solving the Lippmann-Schwinger equation in factorized form. The resulting low-rank approximations of the T matrix are found to fully capture scattering observables. Potential applications of the least-square approach to other frameworks with the goal of employing tensor factorization techniques are discussed.

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Regular Structures with Random Interactions: A New Paradigm

Kota

2014

Embedded Random Matrix Ensembles in Quantum Physics

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Sensitivity analysis of random two-body interactions

Cited by 5 publications

References 25 publications

Uncertainty quantification of an empirical shell-model interaction using principal component analysis

Uncertainty quantification of an empirical shell-model interaction using principal component analysis

Least-square approach for singular value decompositions of scattering problems

Regular Structures with Random Interactions: A New Paradigm

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