arXiv subjects

J. A. Melendez

Publications and source records attributed to J. A. Melendez.

17 recordsLinked to original sources

arXiv2025

Assessing Convergence Patterns Across Modern Nucleon-Nucleon Potentials

The BUQEYE model for correlated effective field theory (EFT) truncation errors assumes a regular pattern of dimensionless coefficients extracted from order-by-order observable calculations. This enables results from lower orders to inform statistical predictions for error estimates of omitted higher orders. We test the model for multiple chiral EFT ($χ$EFT) nucleon-nucleon (NN) potentials using a suite of six common NN scattering observables represented as functions of relative momentum and scattering angle. First, we flag irregularity in the convergence patterns of potentials with so-called "soft" regulator scales, namely that the sizes of the coefficients in the observables' expansions are mismatched between the even and odd orders. Second, we test the BUQEYE model's assumption of Gaussian process (GP) stationarity against the data and find that the GP's correlation structure as encoded in its length scale is nonstationary: The GP length scale in the angular dimension $\ell_θ$ is approximately inversely proportional to the relative momentum of the scattering process. After we remediate this issue by allowing $\ell_θ$ to vary with momentum, diagnostics show significant improvement, validating the application of the BUQEYE model after this modification. Third, we find that good performance of the BUQEYE model relies on properly choosing the $χ$EFT breakdown scale $Λ_{b}$. With $m_{\text{eff}}$ held fixed at the physical pion mass we find $Λ_{b}=600$--$750$ MeV for various N$^{3}$LO interactions. Statistically consistent distributions for $Λ_{b}$ across orders are only found for the SMS potential at a regulator scale of 450 or 500 MeV. All our results can be reproduced using a publicly available Jupyter notebook, which can be straightforwardly modified to analyze other $χ$EFT NN potentials.

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arXiv2025

From chiral EFT to perturbative QCD: a Bayesian model mixing approach to symmetric nuclear matter

Constraining the equation of state (EOS) of strongly interacting, dense matter is the focus of intense experimental, observational, and theoretical effort. Chiral effective field theory ($χ$EFT) can describe the EOS between the typical densities of nuclei and those in the outer cores of neutron stars while perturbative QCD (pQCD) can be applied to properties of deconfined quark matter, both with quantified theoretical uncertainties. However, describing the full range of densities in between with a single EOS that has well-quantified uncertainties is a challenging problem. Bayesian multi-model inference from $χ$EFT and pQCD can help bridge the gap between the two theories. In this work, we introduce a correlated Bayesian model mixing framework that uses a Gaussian Process (GP) to assimilate different information into a single QCD EOS for symmetric nuclear matter. The present implementation uses a stationary GP to infer this mixed EOS solely from the EOSs of $χ$EFT and pQCD while accounting for the truncation errors of each theory. The GP is trained on the pressure as a function of number density in the low- and high-density regions where $χ$EFT and pQCD are, respectively, valid. We impose priors on the GP kernel hyperparameters to suppress unphysical correlations between these regimes. This, together with the assumption of stationarity, results in smooth $χ$EFT-to-pQCD curves for both the pressure and the speed of sound. We show that using uncorrelated mixing requires uncontrolled extrapolation of at least one of $χ$EFT or pQCD into regions where the perturbative series breaks down and leads to an acausal EOS. We also discuss extensions of this framework to non-stationary and less differentiable GP kernels, its future application to neutron-star matter, and the incorporation of additional constraints from nuclear theory, experiment, and multi-messenger astronomy.

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arXiv2024

Assessing Correlated Truncation Errors in Modern Nucleon-Nucleon Potentials

We test the BUQEYE model of correlated effective field theory (EFT) truncation errors on Reinert, Krebs, and Epelbaum's semi-local momentum-space implementation of the chiral EFT ($χ$EFT) expansion of the nucleon-nucleon (NN) potential. This Bayesian model hypothesizes that dimensionless coefficient functions extracted from the order-by-order corrections to NN observables can be treated as draws from a Gaussian process (GP). We combine a variety of graphical and statistical diagnostics to assess when predicted observables have a $χ$EFT convergence pattern consistent with the hypothesized GP statistical model. Our conclusions are: First, the BUQEYE model is generally applicable to the potential investigated here, which enables statistically principled estimates of the impact of higher EFT orders on observables. Second, parameters defining the extracted coefficients such as the expansion parameter $Q$ must be well chosen for the coefficients to exhibit a regular convergence pattern -- a property we exploit to obtain posterior distributions for such quantities. Third, the assumption of GP stationarity across lab energy and scattering angle is not generally met; this necessitates adjustments in future work. We provide a workflow and interpretive guide for our analysis framework, and show what can be inferred about probability distributions for $Q$, the EFT breakdown scale $Λ_b$, the scale associated with soft physics in the $χ$EFT potential $m_{\rm eff}$, and the GP hyperparameters. All our results can be reproduced using a publicly available Jupyter notebook, which can be straightforwardly modified to analyze other $χ$EFT NN potentials.

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arXiv2023

Wave-function-based emulation for nucleon-nucleon scattering in momentum space

Emulators for low-energy nuclear physics can provide fast & accurate predictions of bound-state and scattering observables for applications that require repeated calculations with different parameters, such as Bayesian uncertainty quantification. In this paper, we extend a scattering emulator based on the Kohn variational principle (KVP) to momentum space (including coupled channels) with arbitrary boundary conditions, which enable the mitigation of spurious singularities known as Kohn anomalies. We test it on a modern chiral nucleon-nucleon (NN) interaction, including emulation of the coupled channels. We provide comparisons between a Lippmann-Schwinger equation emulator and our KVP momentum-space emulator for a representative set of neutron-proton (np) scattering observables, and also introduce a quasi-spline-based approach for the KVP-based emulator. Our findings show that while there are some trade-offs between accuracy and speed, all three emulators perform well. Self-contained Jupyter notebooks that generate the results and figures in this paper are publicly available.

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arXiv2022

BUQEYE Guide to Projection-Based Emulators in Nuclear Physics

The BUQEYE collaboration (Bayesian Uncertainty Quantification: Errors in Your EFT) presents a pedagogical introduction to projection-based, reduced-order emulators for applications in low-energy nuclear physics. The term emulator refers here to a fast surrogate model capable of reliably approximating high-fidelity models. As the general tools employed by these emulators are not yet well-known in the nuclear physics community, we discuss variational and Galerkin projection methods, emphasize the benefits of offline-online decompositions, and explore how these concepts lead to emulators for bound and scattering systems that enable fast & accurate calculations using many different model parameter sets. We also point to future extensions and applications of these emulators for nuclear physics, guided by the mature field of model (order) reduction. All examples discussed here and more are available as interactive, open-source Python code so that practitioners can readily adapt projection-based emulators for their own work.

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arXiv2022

Nuclear properties with semilocal momentum-space regularized chiral interactions beyond N2LO

We present a comprehensive investigation of few-nucleon systems as well as light and medium-mass nuclei up to $A=48$ using the current Low Energy Nuclear Physics International Collaboration two-nucleon interactions in combination with the third-order (N$^2$LO) three-nucleon forces. To address the systematic overbinding of nuclei starting from $A \sim 10$ found in our earlier study utilizing the N$^2$LO two- and three-nucleon forces, we take into account higher-order corrections to the two-nucleon potentials up through fifth order in chiral effective field theory. The resulting Hamiltonian can be completely determined using the $A=3$ binding energies and selected nucleon-deuteron cross sections as input. It is then shown to predict other nucleon-deuteron scattering observables and spectra of light $p$-shell nuclei, for which a detailed correlated truncation error analysis is performed, in agreement with experimental data. Moreover, the predicted ground state energies of nuclei in the oxygen isotopic chain from $^{14}$O to $^{26}$O as well as $^{40}$Ca and $^{48}$Ca show a remarkably good agreement with experimental values, given that the Hamiltonian is fixed completely from the $A \leq 3$ data, once the fourth-order (N$^3$LO) corrections to the two-nucleon interactions are taken into account. On the other hand, the charge radii are found to be underpredicted by $\sim 10\%$ for the oxygen isotopes and by almost $20\%$ for $^{40}$Ca and $^{48}$Ca.

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arXiv2022

Model reduction methods for nuclear emulators

The field of model order reduction (MOR) is growing in importance due to its ability to extract the key insights from complex simulations while discarding computationally burdensome and superfluous information. We provide an overview of MOR methods for the creation of fast & accurate emulators of memory- and compute-intensive nuclear systems. As an example, we describe how "eigenvector continuation" is a special case of a much more general and well-studied MOR formalism for parameterized systems. We continue with an introduction to the Ritz and Galerkin projection methods that underpin many such emulators, while pointing to the relevant MOR theory and its successful applications along the way. We believe that this will open the door to broader applications in nuclear physics and facilitate communication with practitioners in other fields.

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arXiv2022

Rigorous constraints on three-nucleon forces in chiral effective field theory from fast and accurate calculations of few-body observables

We explore the constraints on the three-nucleon force (3NF) of chiral effective field theory ($χ$EFT) that are provided by bound-state observables in the $A=3$ and $A=4$ sectors. Our statistically rigorous analysis incorporates experimental error, computational method uncertainty, and the uncertainty due to truncation of the $χ$EFT expansion at next-to-next-to-leading order. A consistent solution for the ${}^3$H binding energy, the ${}^4$He binding energy and radius, and the ${}^3$H $β$-decay rate can only be obtained if $χ$EFT truncation errors are included in the analysis. All of these except the $β$-decay rate give essentially degenerate constraints on the 3NF low-energy constants, so it is crucial for estimating these parameters. We use eigenvector continuation for fast and accurate emulation of No-Core Shell Model calculations of the considered few-nucleon observables. This facilitates sampling of the posterior probability distribution, allowing us to also determine the distributions of the hyperparameters that quantify the truncation error. We find a $χ$EFT expansion parameter of $Q=0.33 \pm 0.06$ for these observables.

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arXiv2021

Fast & accurate emulation of two-body scattering observables without wave functions

We combine Newton's variational method with ideas from eigenvector continuation to construct a fast & accurate emulator for two-body scattering observables. The emulator will facilitate the application of rigorous statistical methods for interactions that depend smoothly on a set of free parameters. Our approach begins with a trial $K$ or $T$ matrix constructed from a small number of exact solutions to the Lippmann--Schwinger equation. Subsequent emulation only requires operations on small matrices. We provide several applications to short-range potentials with and without the Coulomb interaction and partial-wave coupling. It is shown that the emulator can accurately extrapolate far from the support of the training data. When used to emulate the neutron-proton cross section with a modern chiral interaction as a function of 26 free parameters, it reproduces the exact calculation with negligible error and provides an over 300x improvement in CPU time.

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arXiv2021

Designing Optimal Experiments: An Application to Proton Compton Scattering

Interpreting measurements requires a physical theory, but the theory's accuracy may vary across the experimental domain. To optimize experimental design, and so to ensure that the substantial resources necessary for modern experiments are focused on acquiring the most valuable data, both the theory uncertainty and the expected pattern of experimental errors must be considered. We develop a Bayesian approach to this problem, and apply it to the example of proton Compton scattering. Chiral Effective Field Theory ($χ$EFT) predicts the functional form of the scattering amplitude for this reaction, so that the electromagnetic polarizabilities of the nucleon can be inferred from data. With increasing photon energy, both experimental rates and sensitivities to polarizabilities increase, but the accuracy of $χ$EFT decreases. Our physics-based model of $χ$EFT truncation errors is combined with present knowledge of the polarizabilities and reasonable assumptions about experimental capabilities at HI$γ$S and MAMI to assess the information gain from measuring specific observables at specific kinematics, \emph{i.e.}, to determine the relative amount by which new data are apt to shrink uncertainties. The strongest gains would likely come from new data on the spin observables $Σ_{2x}$ and $Σ_{2x^\prime}$ at $ω\simeq140$ to $200$ MeV and $40^\circ$ to $120^\circ$. These would tightly constrain $γ_{E1E1}-γ_{E1M2}$. New data on the differential cross section between $100$ and $200$\,MeV and over a wide angle range will substantially improve constraints on $α_{E1}-β_{M1}$, $γ_π$ and $γ_{M1M1}-γ_{M1E2}$. Good signals also exist around $160$ MeV for $Σ_3$ and $Σ_{2z^\prime}$. Such data will be pivotal in the continuing quest to pin down the scalar polarizabilities and refine understanding of the spin polarizabilities.

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arXiv2021

Quantifying uncertainties and correlations in the nuclear-matter equation of state

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 learning to reveal correlations between the EOS at different proton fractions. The inferred in-medium $χ$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.

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arXiv2021

How well do we know the neutron-matter equation of state at the densities inside neutron stars? A Bayesian approach with correlated uncertainties

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 produces the first statistically robust uncertainty estimates for key quantities of neutron stars. We give results up to twice nuclear saturation density for the energy per particle, pressure, and speed of sound of neutron matter, as well as for the nuclear symmetry energy and its derivative. At nuclear saturation density the predicted symmetry energy and its slope are consistent with experimental constraints.

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arXiv2020

Light nuclei with semilocal momentum-space regularized chiral interactions up to third order

We present a systematic investigation of few-nucleon systems and light nuclei using the current LENPIC interactions comprising semilocal momentum-space regularized two- and three-nucleon forces up to third chiral order (N$^2$LO). Following our earlier study utilizing the coordinate-space regularized interactions, the two low-energy constants entering the three-body force are determined from the triton binding energy and the differential cross section minimum in elastic nucleon-deuteron scattering. Predictions are made for selected observables in elastic nucleon-deuteron scattering and in the deuteron breakup reactions, for properties of the $A=3$ and $A=4$ nuclei, and for spectra of $p$-shell nuclei up to $A = 16$. A comprehensive error analysis is performed including an estimation of correlated truncation uncertainties for nuclear spectra. The obtained predictions are generally found to agree with experimental data within errors. Similar to the coordinate-space regularized chiral interactions at the same order, a systematic overbinding of heavier nuclei is observed, which sets in for $A \sim 10$ and increases with $A$.

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arXiv2020

Ab initio calculations of low-energy nuclear scattering using confining potential traps

A recently modified method to enable low-energy nuclear scattering results to be extracted from the discrete energy levels of the target-projectile clusters confined by harmonic potential traps is tested. We report encouraging results for neutron--$α$ and neutron--$^{24}\mathrm{O}$ elastic scattering from analyzing the trapped levels computed using two different ab initio nuclear structure methods. The $n$--$α$ results have also been checked against a direct ab initio reaction calculation. The $n$--$^{24}\mathrm{O}$ results demonstrate the approach's applicability for a large range of systems provided their spectra in traps can be computed by ab initio methods. A key ingredient is a rigorous understanding of the errors in the calculated energy levels caused by inevitable Hilbert-space truncations in the ab initio methods.

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arXiv2019

Quantifying Correlated Truncation Errors in Effective Field Theory

Effective field theories (EFTs) organize the description of complex systems into an infinite sequence of decreasing importance. Predictions are made with a finite number of terms, which induces a truncation error that is often left unquantified. We formalize the notion of EFT convergence and propose a Bayesian truncation error model for predictions that are correlated across the independent variables, e.g., energy or scattering angle. Central to our approach are Gaussian processes that encode both the naturalness and correlation structure of EFT coefficients. Our use of Gaussian processes permits efficient and accurate assessment of credible intervals, allows EFT fits to easily include correlated theory errors, and provides analytic posteriors for physical EFT-related quantities such as the expansion parameter. We demonstrate that model-checking diagnostics---applied to the case of multiple curves---are powerful tools for EFT validation. As an example, we assess a set of nucleon-nucleon scattering observables in chiral EFT. In an effort to be self contained, appendices include thorough derivations of our statistical results. Our methods are packaged in Python code, called gsum, that is available for download on GitHub.

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arXiv2018

Exploring Bayesian parameter estimation for chiral effective field theory using nucleon-nucleon phase shifts

We recently developed a Bayesian framework for parameter estimation in general effective field theories. Here we present selected results from using that framework to estimate parameters with a nucleon-nucleon (NN) potential derived using chiral effective field theory ($χ$EFT): the semi-local NN potential of Epelbaum, Krebs, and Meißner (EKM). There are many NN scattering data, up to high energies, and with rather small errors, so imposing a penalty for unnatural low-energy constants (LECs) usually has a small effect on the fits. In contrast, we have found that including an estimate of higher orders in $χ$EFT plays an important role in robust parameter estimation.We present two case studies where our Bayesian machinery illuminates physics issues. The first involves the EKM potential at fourth order in the $χ$EFT expansion: the two-dimensional posterior probability density function (pdf) for the fourth-order $s$-wave LECs obtained from the Nijmegen PWA93 phase shifts indicates these parameters in the NN potential are degenerate. We trace this feature of the pdf to the presence of an operator in the fourth-order NN potential that vanishes on-shell. The second case study examines the stability of LEC extractions as more data at higher energies are included in the fit. We show that as long as $χ$EFT truncation errors are properly accounted for in the parameter estimation, the LEC values extracted using our Bayesian approach are not sensitive to the maximum energy chosen for the fit.Uncorrelated and fully correlated models for the truncation errors are compared, pointing the way to the use of Gaussian processes to more generally model the correlation structure.

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arXiv2017

Bayesian truncation errors in chiral effective field theory: nucleon-nucleon observables

Chiral effective field theory (EFT) predictions are necessarily truncated at some order in the EFT expansion, which induces an error that must be quantified for robust statistical comparisons to experiment. In previous work, a Bayesian model for truncation errors of perturbative expansions was adapted to EFTs. The model yields posterior probability distribution functions (pdfs) for these errors based on expectations of naturalness encoded in Bayesian priors and the observed order-by-order convergence pattern of the EFT. A first application was made to chiral EFT for neutron-proton scattering using the semi-local potentials of Epelbaum, Krebs, and Meißner (EKM). Here we extend this application to consider a larger set of regulator parameters, energies, and observables as a general example of a statistical approach to truncation errors. The Bayesian approach allows for statistical validations of the assumptions and enables the calculation of posterior pdfs for the EFT breakdown scale. The statistical model is validated for EKM potentials whose convergence behavior is not distorted by regulator artifacts. For these cases, the posterior for the breakdown scale is consistent with EKM assumptions.

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