Occupation-number-based energy functional for nuclear masses

Bertolli, Michael; Papenbrock, T.; Wild, Stefan M.

doi:10.1103/physrevc.85.014322

Cited by 5 publications

(27 citation statements)

References 51 publications

(97 reference statements)

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“…UNEDFnb [10,11,12,20,21]. Here we focus on some of the results obtained when calibrating Skyrme energy density functionals where HFBTHO [22] was the underlying simulator.…”

Section: Derivatives and Methods For Nonlinear Least Squaresmentioning

confidence: 99%

“…Or, were substantial reductions of the objective obtained right up until the final evaluations? Figure 4 illustrates the rate of convergence on a n x = 17-parameter problem involving the calibration of an occupation number-based energy functional from [20]. The different methods in this figure illustrate the benefits-in terms of convergence speed-of exploiting structural knowledge about the optimization objective.…”

Section: Derivatives Revisitedmentioning

confidence: 99%

“…Best f value found as a function of the number of f evaluations for different model-based algorithms on a 17-dimensional parameter estimation problem from[20].…”

mentioning

confidence: 99%

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Derivative-free optimization for parameter estimation in computational nuclear physics

Wild

Sarich

Schunck

2015

J. Phys. G: Nucl. Part. Phys.

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We consider optimization problems that arise when estimating a set of unknown parameters from experimental data, particularly in the context of nuclear density functional theory. We examine the cost of not having derivatives of these functionals with respect to the parameters. We show that the POUNDERS code for local derivative-free optimization obtains consistent solutions on a variety of computationally expensive energy density functional calibration problems. We also provide a primer on the operation of the POUNDERS software in the Toolkit for Advanced Optimization.

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“…UNEDFnb [10,11,12,20,21]. Here we focus on some of the results obtained when calibrating Skyrme energy density functionals where HFBTHO [22] was the underlying simulator.…”

Section: Derivatives and Methods For Nonlinear Least Squaresmentioning

confidence: 99%

Section: Derivatives Revisitedmentioning

confidence: 99%

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Derivative-free optimization for parameter estimation in computational nuclear physics

Wild

Sarich

Schunck

2015

J. Phys. G: Nucl. Part. Phys.

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“…2, the POUNDERS algorithm converges quickly compared to the traditional Nelder-Mead algorithm; most important, it gives a better solution. POUNDERS has recently been applied to other problems of interest in nuclear physics [74,75].…”

Section: Optimization Algorithmmentioning

confidence: 99%

Uncertainty quantification and propagation in nuclear density functional theory

et al. 2015

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Nuclear density functional theory (DFT) is one of the main theoretical tools used to study the properties of heavy and superheavy elements, or to describe the structure of nuclei far from stability. While on-going efforts seek to better root nuclear DFT in the theory of nuclear forces [see Duguet et al., this issue], energy functionals remain semi-phenomenological constructions that depend on a set of parameters adjusted to experimental data in finite nuclei. In this paper, we review recent efforts to quantify the related uncertainties, and propagate them to model predictions. In particular, we cover the topics of parameter estimation for inverse problems, statistical analysis of model uncertainties and Bayesian inference methods. Illustrative examples are taken from the literature. PACS. 21.60.Jz Nuclear Density Functional Theory and extensions -21.10.-k Properties of nuclei; nuclear energy levels -02.30.Zz Inverse problems -02.60.Pn Numerical optimization -02.70.Uu Applications of Monte Carlo methods arXiv:1503.05894v1 [nucl-th]

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“…(38) has a similar form to Eq. (21). We could, in principle, use this procedure starting with the full N -body local density Ψ * (R)Ψ(R) and, integrating out collective coordinates, yield a succession of generalized-density functionals, all the way down to the Hohenberg-Kohn functional of ρ( r) if we remove all of them.…”

Section: Definitions and Existence Of A Functionalmentioning

confidence: 99%

Density functional theory with spatial-symmetry breaking and configuration mixing

Lesinski

2014

Phys. Rev. C

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This article generalizes the notion of the local density of a many-body system to introduce collective coordinates as explicit degrees of freedom. It is shown that the energy of the system can be expressed as a functional of this object. The latter can in turn be factorized as the product of the square of a collective wave function and a normalized collective-coordinate-dependent density. Energy minimization translates into a set of coupled equations, i.e. a local Schrödinger equation for the collective wave function and a set of Kohn-Sham equations for optimizing the normalized density at each point in the collective space. These equations reformulate the many-body problem exactly provided one is able to determine density-and collective-wave-function-dependent terms of the collective mass and potential which play a similar role to the exchange-correlation term in electronic Kohn-Sham density functional theory.PACS numbers: 21.60. De, 21.60.Jz for integer m. The wave function minimizing the energy for this choice of f has Ψ cm ( R) = f ( R). Note that J µ , Eq. (57) is, in this case, the average momentum of the system. This quantity is zero for this state, thus J µ ( R) = 0.(75)

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Occupation-number-based energy functional for nuclear masses

Cited by 5 publications

References 51 publications

Derivative-free optimization for parameter estimation in computational nuclear physics

Derivative-free optimization for parameter estimation in computational nuclear physics

Uncertainty quantification and propagation in nuclear density functional theory

Density functional theory with spatial-symmetry breaking and configuration mixing

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