Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userGet on the BAND Wagon: A Bayesian Framework for Quantifying Model Uncertainties in Nuclear Dynamics
119
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We describe the Bayesian Analysis of Nuclear Dynamics (BAND) framework, a cyberinfrastructure that we are developing which will unify the treatment of nuclear models, experimental data, and associated uncertainties. We overview the statistical principles and nuclear-physics contexts underlying the BAND toolset, with an emphasis on Bayesian methodologys ability to leverage insight from multiple models. In order to facilitate understanding of these tools we provide a simple and accessible example of the BAND frameworks application. Four case studies are presented to highlight how elements of the framework will enable progress on complex, far-ranging problems in nuclear physics. By collecting notation and terminology, providing illustrative examples, and giving an overview of the associated techniques, this paper aims to open paths through which the nuclear physics and statistics communities can contribute to and build upon the BAND framework.
rate research
Read More
We make ab initio predictions for the A = 6 nuclear level scheme based on two- and three-nucleon interactions up to next-to-next-to-leading order in chiral effective field theory ($chi$EFT). We utilize eigenvector continuation and Bayesian methods to quantify uncertainties stemming from the many-body method, the $chi$EFT truncation, and the low-energy constants of the nuclear interaction. The construction and validation of emulators is made possible via the development of JupiterNCSM -- a new M-scheme no-core shell model code that uses on-the-fly Hamiltonian matrix construction for efficient, single-node computations up to $N_mathrm{max} = 10$ for ${}^{6}mathrm{Li}$. We find a slight underbinding of ${}^{6}mathrm{He}$ and ${}^{6}mathrm{Li}$, although consistent with experimental data given our theoretical error bars. As a result of incorporating a correlated $chi$EFT-truncation errors we find more precise predictions (smaller error bars) for separation energies: $S_d({}^{6}mathrm{Li}) = 0.89 pm 0.44$ MeV, $S_{2n}({}^{6}mathrm{He}) = 0.20 pm 0.60$ MeV, and for the beta decay Q-value: $Q_{beta^-}({}^{6}mathrm{He}) = 3.71 pm 0.65$ MeV. We conclude that our error bars can potentially be reduced further by extending the model space used by JupiterNCSM.
Probabilistic machine learning techniques can learn both complex relations between input features and output quantities of interest as well as take into account stochasticity or uncertainty within a data set. In this initial work, we explore the use of one such probabilistic network, the Mixture Density Network (MDN), to reproduce fission yields and their uncertainties. We study mass yields for the spontaneous fission of $^{252}$Cf, exploring the number of training samples needed for converged predictions, how different levels of uncertainty propagate from the training set to the MDN predictions, and how well physical constraints of the yields - such as normalization and symmetry - are upheld by the algorithm. Finally, we test the ability of the MDN to interpolate between and extrapolate beyond samples in the training set using energy-dependent mass yields for the neutron-induced fission on $^{235}$U. The MDN provides a reliable way to include and predict uncertainties and is a promising path forward for supplementing sparse sets of nuclear data.
The coupled-channels density-matrix technique for nuclear reaction dynamics, which is based on the Liouville-von Neumann equation with Lindblad dissipative terms, is developed with the inclusion of full angular momentum couplings. It allows a quantitative study of the role and importance of quantum decoherence in nuclear scattering. Formulae of asymptotic observables that can reveal effects of quantum decoherence are given. A method for extracting energy-resolved scattering information from the time-dependent density matrix is introduced. As an example, model calculations are carried out for the low-energy collision of the $^{16}$O projectile on the $^{154}$Sm target.
We perform statistically rigorous uncertainty quantification (UQ) for chiral effective field theory ($chi$EFT) applied to infinite nuclear matter up to twice nuclear saturation density. The equation of state (EOS) is based on high-order many-body perturbation theory calculations with nucleon-nucleon and three-nucleon interactions up to fourth order in the $chi$EFT expansion. From these calculations our newly developed Bayesian machine-learning approach extracts the size and smoothness properties of the correlated EFT truncation error. We then propose a novel extension that uses multitask machine learning to reveal correlations between the EOS at different proton fractions. The inferred in-medium $chi$EFT breakdown scale in pure neutron matter and symmetric nuclear matter is consistent with that from free-space nucleon-nucleon scattering. These significant advances allow us to provide posterior distributions for the nuclear saturation point and propagate theoretical uncertainties to derived quantities: the pressure and incompressibility of symmetric nuclear matter, the nuclear symmetry energy, and its derivative. Our results, which are validated by statistical diagnostics, demonstrate that an understanding of truncation-error correlations between different densities and different observables is crucial for reliable UQ. The methods developed here are publicly available as annotated Jupyter notebooks.
Within a Bayesian statistical framework using the standard Skyrme-Hartree-Fcok model, the maximum a posteriori (MAP) values and uncertainties of nuclear matter incompressibility and isovector interaction parameters are inferred from the experimental data of giant resonances and neutron-skin thicknesses of typical heavy nuclei. With the uncertainties of the isovector interaction parameters constrained by the data of the isovector giant dipole resonance and the neutron-skin thickness, we have obtained $K_0 = 223_{-8}^{+7}$ MeV at 68% confidence level using the data of the isoscalar giant monopole resonance in $^{208}$Pb measured at the Research Center for Nuclear Physics (RCNP), Japan, and at the Texas A&M University (TAMU), USA. Although the corresponding $^{120}$Sn data gives a MAP value for $K_0$ about 5 MeV smaller than the $^{208}$Pb data, there are significant overlaps in their posterior probability distribution functions.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
