Estimating Parameter Uncertainty in Binding-Energy Models by the Frequency-Domain Bootstrap

Bertsch, G. F.; Bingham, Derek

doi:10.1103/physrevlett.119.252501

Cited by 31 publications

(49 citation statements)

References 16 publications

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“…Accordingly, we can use, as a performance criterion, the improvement on rms error on testing datasets outside the training domain [29]. This is a different strategy than testing samples of interior points randomly taken out of the training sample -which has been done in the previous papers [27,28,[30][31][32]. In search of universality, we model the residuals globally on the large domain of even-even nuclei.…”

Section: Objective and Evaluationmentioning

confidence: 99%

“…Here, a powerful strategy is to estimate residuals by developing an emulator for δ(Z, N ) using a training set of known masses. An emulator δ em (Z, N ) can, for instance, be constructed by employing Bayesian approaches, such as Gaussian processes, neural networks, and frequency-domain bootstrap [23][24][25][26][27][28][29][30][31][32]. The unknown separation energies can then be estimated from Eq.…”

Section: Introductionmentioning

confidence: 99%

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Bayesian approach to model-based extrapolation of nuclear observables

et al. 2018

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Background: The mass, or binding energy, is the basis property of the atomic nucleus. It determines its stability, and reaction and decay rates. Quantifying the nuclear binding is important for understanding the origin of elements in the universe. The astrophysical processes responsible for the nucleosynthesis in stars often take place far from the valley of stability, where experimental masses are not known. In such cases, missing nuclear information must be provided by theoretical predictions using extreme extrapolations. In order to take full advantage of the information contained in mass model residuals, i.e., deviations between experimental and calculated masses, one can utilize Bayesian machine learning techniques to improve predictions.Purpose: In order to improve the quality of model-based predictions of nuclear properties of rare isotopes far from stability, we consider the information contained in the residuals in the regions where the experimental information exist. As a case in point, we discuss two-neutron separation energies S2n of even-even nuclei. Through this observable, we assess the predictive power of global mass models towards more unstable neutron-rich nuclei and provide uncertainty quantification of predictions.Methods: We consider 10 global models based on nuclear Density Functional Theory with realistic energy density functionals as well as two more phenomenological mass models. The emulators of S2n residuals and credibility intervals (Bayesian confidence intervals) defining theoretical error bars are constructed using Bayesian Gaussian processes and Bayesian neural networks. We consider a large training dataset pertaining to nuclei whose masses were measured before 2003. For the testing datasets, we considered those exotic nuclei whose masses have been determined after 2003. By establishing statistical methodology and parameters, we carried out extrapolations towards the 2n dripline.Results: While both Gaussian processes and Bayesian neural networks reduce the rms deviation from experiment significantly, GP offers a better and much more stable performance. The increase in the predictive power of microscopic models aided by the statistical treatment is quite astonishing: the resulting rms deviations from experiment on the testing dataset are similar to those of more phenomenological models. We found that Bayesian neural networks results are prone to instabilities caused by the large number of parameters in this method. Moreover, since the classical sigmoid activation function used in this approach has linear tails that do not vanish, it is poorly suited for a bounded extrapolation. The empirical coverage probability curves we obtain match very well the reference values, in a slightly conservative way in most cases, which is highly desirable to ensure honesty of uncertainty quantification. The estimated credibility intervals on predictions make it possible to evaluate predictive power of individual models, and also make quantified predictions using groups of models. Conclusions:The propose...

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Section: Objective and Evaluationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Bayesian approach to model-based extrapolation of nuclear observables

et al. 2018

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“…In the regions where experimental mass data are absent, nuclear models must be deployed to provide the missing information about the topography of the mass surface. In this context, the quality of theoretical mass predictions can be significantly improved when aided by the current experimental information through machine learning techniques [29][30][31][32][33][34][35][36][37][38][39]. Recently, we developed the statistical framework of Bayesian Gaussian process techniques to quantify patterns of systematic deviations between theory and experiment by providing statistical corrections to average prediction values, and develop full uncertainty quantification on predictions through credibility intervals [40].…”

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confidence: 99%

Beyond the proton drip line: Bayesian analysis of proton-emitting nuclei

et al. 2020

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Background: The limits of the nuclear landscape are determined by nuclear binding energies. Beyond the proton drip lines, where the separation energy becomes negative, there is not enough binding energy to prevent protons from escaping the nucleus. Predicting properties of unstable nuclear states in the vast territory of proton emitters poses an appreciable challenge for nuclear theory as it often involves far extrapolations. In addition, significant discrepancies between nuclear models in the proton-rich territory call for quantified predictions.Purpose: With the help of Bayesian methodology, we mix a family of nuclear mass models corrected with statistical emulators trained on the experimental mass measurements, in the proton-rich region of the nuclear chart.Methods: Separation energies were computed within nuclear density functional theory using several Skyrme and Gogny energy density functionals. We also considered mass predictions based on two models used in astrophysical studies. Quantified predictions were obtained for each model using Bayesian Gaussian processes trained on separation-energy residuals and combined via Bayesian model averaging. Results:We obtained a good agreement between averaged predictions of statistically corrected models and experiment. In particular, we quantified model results for one-and two-proton separation energies and derived probabilities of proton emission. This information enabled us to produce a quantified landscape of proton-rich nuclei. The most promising candidates for two-proton decay studies have been identified. Conclusions:The methodology used in this work has broad applications to model-based extrapolations of various nuclear observables. It also provides a reliable uncertainty quantification of theoretical predictions.

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“…This has been successfully implemented in statistical models like Canonical Thermodynamical Model(CTM) [10], the Statistical Multifragmentation Model (SMM) [3] and others in order to throw light on the nuclear multifragmentation process. Excellent fits of experimental masses with high level of accuracy for ground state masses at normal density are available [13][14][15]. The process of nuclear multifragmentation however occurs at sub saturation density and at higher excitation energies.…”

Section: Introductionmentioning

confidence: 93%

Effect of liquid drop model parameters on nuclear liquid-gas phase transition

Chaudhuri

Mallik

2019

Phys. Rev. C

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The phenomenon of liquid-gas phase transition occurring in heavy ion collisions at intermediate energies is a subject of contemporary interest. In statistical models of fragmentation, the liquid drop model is generally used to calculate the ground state binding energies of the fragments. It is well known that the surface and symmetry energy of the hot fragments at the low density freeze out can be considerably modified. In addition to this, the level density parameter also has a wide variation. The effect of variation of these parameters is studied on fragmentation observables which are related to the nuclear liquid gas phase transition. The canonical thermodynamical model which has been very successful in describing the phenomenon of fragmentation is used for the study. The shift in transition temperature owing to the variation in liquid drop model parameters has been examined.

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Estimating Parameter Uncertainty in Binding-Energy Models by the Frequency-Domain Bootstrap

Cited by 31 publications

References 16 publications

Bayesian approach to model-based extrapolation of nuclear observables

Bayesian approach to model-based extrapolation of nuclear observables

Beyond the proton drip line: Bayesian analysis of proton-emitting nuclei

Effect of liquid drop model parameters on nuclear liquid-gas phase transition

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