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 methodology's 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 framework's 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.
Theoretical predictions need quantified uncertainties for a meaningful comparison to experimental results. This is an idea which presently permeates the field of theoretical nuclear physics. In light of the recent progress in estimating theoretical uncertainties in ab initio nuclear physics, we here present and compare methods for evaluating the statistical part of the uncertainties. A special focus is put on the (for the field) novel method of Lagrange multipliers (LM). Uncertainties from the fit of the nuclear interaction to experimental data are propagated to a few observables in light-mass…
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 predictio…
We present a simple method for determining the (correlated) uncertainties of the light element abundances expected from big bang nucleosynthesis, which avoids the need for lengthy Monte Carlo simulations. Our approach helps to clarify the role of the different nuclear reactions contributing to a particular elemental abundance and makes it easy to implement energy-independent changes in the measured reaction rates. As an application, we demonstrate how this method simplifies the statistical estimation of the nucleon-to-photon ratio through comparison of the standard BBN predictions with the obs…
A compressible liquid-drop model (CLDM) is used to correlate uncertainties associated with the properties of the neutron star (NS) crust with theoretical estimates of the uncertainties associated with the equation of state (EOS) of homogeneous neutron and nuclear matter. For the latter, we employ recent calculations based on Hamiltonians constructed using Chiral Effective Field theory. Fits to experimental nuclear masses are employed to constrain the CLDM further, and we find that they disfavor some of the Chiral Hamiltonians. The CLDM allows us to study the complex interplay between bulk, sur…
With the increasing sensitivity of gravitational-wave detectors, we expect to observe multiple binary neutron-star systems through gravitational waves in the near future. The combined analysis of these gravitational-wave signals offers the possibility to constrain the neutron-star radius and the equation of state of dense nuclear matter with unprecedented accuracy. However, it is crucial to ensure that uncertainties inherent in the gravitational-wave models will not lead to systematic biases when information from multiple detections are combined. To quantify waveform systematics, we perform an…
The influence of the uncertainties of the equation of state empirical parameters on the neutron stars crust-core phase transition is explored within a meta-modeling approach, in which the energy per particle is expanded as a Taylor series in density and asymmetry around the saturation point. The phase transition point is estimated from the intersection of the spinodal instability region for dynamical fluctuations with the chemical equilibrium curve. Special attention is paid to the inclusion of high-order parameters of the Taylor series and their influence on the transition point. An uncorrela…
Background: Modern ab initio theory combined with high-quality nucleon-nucleon (NN) and three-nucleon (3N) interactions from chiral effective field theory (EFT) can provide a predictive description of low-energy light-nuclei reactions relevant for astrophysics and fusion-energy applications. However, the high cost of computations has so far impeded a complete analysis of the uncertainty budget of such calculations. Purpose: Starting from NN potentials up to fifth order (N4LO) combined with leading-order 3N forces, we study how the order-by-order convergence of the chiral expansion and confiden…
\noindent{\bf Background:} Deuteron-induced nuclear reactions are an essential tool for probing the structure of nuclei as well as astrophysical information such as $(n,γ)$ cross sections. The deuteron-nucleus system is typically described within a Faddeev three-body model consisting of a neutron ($n$), a proton ($p$), and the target nucleus ($A$) interacting through pairwise phenomenological potentials. While Faddeev techniques enable the exact description of the three-body dynamics, their predictive power is limited in part by the omission of irreducible neutron-proton-nucleus three-body for…
We perform statistically rigorous uncertainty quantification (UQ) for chiral effective field theory ($χ$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 $χ$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 l…
We report the results of a study aimed at quantifying the impact on the oscillation analysis of the uncertainties associated with the description of the neutrino-nucleus cross section in the two-particle--two-hole sector. The results of our calculations, based on the kinematic method of energy reconstruction and carried out comparing two data-driven approaches, show that the existing discrepancies in the neutrino cross sections have a sizable effect on the extracted oscillation parameters, particularly in the antineutrino channel.
Uncertainty quantification has become increasingly more prominent in nuclear physics over the past several years. In few-body reaction theory, there are four main sources that contribute to the uncertainties in the calculated observables: the effective potentials, approximations made to the few-body problem, structure functions, and degrees of freedom left out of the model space. In this work, we illustrate some of the features that can be obtained when modern statistical tools are applied in the context of nuclear reactions. This work consists of a summary of the progress that has been made i…
Closed-form expressions for tree-level gluon-gluon scattering: a framework for obtaining theoretical systematic uncertainties for jet-medium Monte Carlo simulations
What is the origin of nuclear clustering and how does it emerge from the nuclear interaction? While there is ample experimental evidence for this phenomenon, its theoretical characterization directly from nucleons as degrees of freedom remains a challenge, making it difficult to improve nuclear forces using clustering observables. In this work, a simple ratio of energies based on effective scale arguments is proposed to assess the quality of nuclear forces on alpha clustering (${ {}^{4}\text{He} }$) in bound and narrow ground-state nuclei. The proposed clustering ratio is parameter-free and co…
Neutrino oscillation experiments use heavy nuclear targets to achieve sufficient interaction rates. Nuclear effects are introduced in the experimental environment by the use of these targets and need to be quantified as they add to the systematic errors. In the low energy region(around 1 GeV) multinucleon events are also present along with Quasi Elastic(QE) and Delta interactions. Therefore if these multinucleon events are not incorporated in the data set properly, we end up with an inaccurate reconstruction of neutrino energy. In our work, we have illustrated the importance of incorporation o…
We introduce a new framework for quantifying correlated uncertainties of the infinite-matter equation of state derived from chiral effective field theory ($χ$EFT). Bayesian machine learning via Gaussian processes with physics-based hyperparameters allows us to efficiently quantify and propagate theoretical uncertainties of the equation of state, such as $χ$EFT truncation errors, to derived quantities. We apply this framework to state-of-the-art many-body perturbation theory calculations with nucleon-nucleon and three-nucleon interactions up to fourth order in the $χ$EFT expansion. This produce…
There is an increasing interest in quantifying the predictive power in nuclear structure calculations. We discuss how both experimental and systematic errors at the NN-level can be used to estimate the theoretical uncertainties by rather simple means and without solving the full nuclear many body problem. We emphasize the role of effective interactions defined by coarse graining the NN potential to length scales of the order of the minimal de Broglie wavelength probed between nucleons in nuclei. We find an a priori error of \DeltaB/A \sim 0.1 - 0.4MeV for the binding energy per particle throug…
Until recently, uncertainty quantification in low energy nuclear theory was typically performed using frequentist approaches. However in the last few years, the field has shifted toward Bayesian statistics for evaluating confidence intervals. Although there are statistical arguments to prefer the Bayesian approach, no direct comparison is available. In this work, we compare, directly and systematically, the frequentist and Bayesian approaches to quantifying uncertainties in direct nuclear reactions. Starting from identical initial assumptions, we determine confidence intervals associated with …
Predictions of nuclear properties far from measured data are inherently imprecise because of uncertainties in our knowledge of nuclear forces and in our treatment of quantum many-body effects in strongly-interacting systems. While the model bias can be directly calculated when experimental data is available, only an estimate can be made in the absence of such measurements. Current approaches to compute the estimated bias quickly lose predictive power when input variables such as proton or neutron number are extrapolated, resulting in uncontrolled uncertainties in applications such as nucleosyn…
