Publications


2023

  • Emulators and their applications in low-energy nuclear physics*
    Alberto J. Garcia, Doctoral dissertation (2023).

    Nuclear physics is the study of phenomena involving the strong interaction, through its fundamental theory of quantum chromodynamics (QCD) or through effective theories with composite degrees of freedom. It seeks to understand the origin and evolution of visible matter; the organizational principles and emergent phenomena of nuclei; how the fundamental interactions can be understood using the nucleus as a laboratory; and how nuclear physics research can benefit society. To make progress, experimental facilities, such as the Facility of Rare Isotope Beams (FRIB) and ATLAS, are continuously collecting data to further our understanding of atomic nuclei and astrophysical processes. At the same time, theoretical approaches are tasked with providing accurate models whose theoretical errors are well-known. By working together, theoretical results can help guide experimentalists in understanding which regions and measurements provide the most return. The results presented in this thesis contribute to this effort by describing the construction of surrogate models (i.e., emulators) that produce fast, but accurate predictions for bound and scattering systems with various interactions. Emulators provide the means necessary for obtaining well-defined errors of a theoretical model by accurately reproduce their high-fidelity counterpart in a fraction of the time it takes to solve the underlying physics equations. These emulators can make feasible the use of Bayesian parameter estimation in low-energy nuclear physics by using the emulators to make predictions with many different parameter sets, allowing one to properly and efficiently propagate the theoretical uncertainties to nucleon-nucleon (NN) observables. When used in conjunction with Bayesian experimental design, it allows one to establish the optimal experimental design needed to produce quality measurements in a much faster way compared to traditional calculations. The emulators described in this thesis fall into two categories: model-driven and data-driven. The data-driven approach relies only on the output of high-fidelity calculations in order to train the model, thus acting like a black box problem in regards to the physics. These are machine learning approaches such as neural networks and Gaussian processes. On the other hand, the model-driven approach relies on deriving a set of reduced-order equations that incorporate all the important underlying physics needed to make accurate predictions by projecting the high-dimensional space into a low-dimension manifold. The process of obtaining the reduced-order equations can be further described through the use of variational and Galerkin projection methods, which allow us a way of producing an efficient basis. This thesis demonstrates these points by describing the construction of different emulators from variational and Galerkin projection methods, emphasizing the benefits of offline-online decompositions, and showing how these concepts lead to fast & accurate emulators for bound and scattering systems. We then apply these emulators to various interactions with many different model parameter sets and compare the results with their respective high-fidelity model and each other in order to determine the efficiency of the different emulators in making predictions. We also explore the use of neural networks and their effectiveness in extrapolating the ground-state observables of different nuclei, and use them to examine the infrared (IR) and ultraviolet (UV) dependence of the no-core shell model (NCSM) model space to detect correlations between observables of different nuclei. Furthermore, we point to future extensions and applications of these emulators in nuclear physics.

  • Wave function-based emulation for nucleon-nucleon scattering in momentum space*
    A.J. Garcia, C. Drischler, R.J. Furnstahl, J.A. Melendez, and Xilin Zhang, Phys.Rev.C 107 (2023), arXiv:2301.05093.

    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.

2022

  • BUQEYE Guide to Projection-Based Emulators in Nuclear Physics*
    C. Drischler, J.A. Melendez, R.J. Furnstahl, A.J. Garcia, and Xilin Zhang, Front. Phys. 10 (2023), arXiv:2212.04912.

    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.

  • Model reduction methods for nuclear emulators*
    J.A. Melendez, C. Drischler, R.J. Furnstahl, A.J. Garcia, and Xilin Zhang, J. Phys. G: Nucl. Part. Phys. 49 102001 (2022), arXiv:2203.05528.

    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.

2021

  • Fast & accurate emulation of two-body scattering observables without wave functions*
    J.A. Melendez, C. Drischler, A.J. Garcia, R.J. Furnstahl, and Xilin Zhang, Phys. Lett. B 821, 136608 (2021), arXiv:2106.15608.

    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.

2020

  • Efficient emulators for scattering using eigenvector continuation*
    R.J. Furnstahl, A.J. Garcia, P.J. Millican, and Xilin Zhang, Phys. Lett. B 809, 135719 (2020), arXiv:2007.03635.

    Eigenvector continuation (EC) has been shown to accurately and efficiently reproduce ground states for targeted sets of Hamiltonian parameters. It uses as variational basis vectors the corresponding ground-state eigensolutions from selected other sets of parameters. Here we extend the EC approach to scattering using the Kohn variational principle. We first test it using a model for S-wave nucleon-nucleon scattering and then demonstrate that it also works to give accurate predictions for non-local potentials, charged-particle scattering, complex optical potentials, and higher partial waves. These proofs-of-principle validate EC as an effective emulator for applying Bayesian inference to parameter estimation constrained by scattering observables.

2018

  • Parameter Dependence of Pair Correlations in Clean Superconducting-Magnetic Proximity Systems**
    Alberto J. Garcia, Master's thesis (2018).

    Cooper pairs are known to tunnel through a barrier between superconductors in a Josephson junction. The spin states of the pairs can be a mixture of singlet and triplet states when the barrier is an inhomogeneous magnetic material. The purpose of this thesis is to better understand the behavior of pair correlations in the ballistic regime for different magnetic configurations and varying physical parameters. We use a tight-binding Hamiltonian to describe the system and consider singlet-pair conventional superconductors. Using the Bogoliubov-Valatin transformation, we derive the Bogoliubov-de Gennes equations and numerically solve the associated eigenvalue problem. Pair correlations in the magnetic Josephson junction are obtained from the Green's function formalism for a superconductor. This formalism is applied to Josephson junctions composed of discrete and continuous magnetic materials. The differences between representing pair correlations in the time and frequency domain are discussed, as well as the advantages of describing the Gor'kov functions on a log scale rather than the commonly used linear scale, and in a rotating basis as opposed to a static basis. Furthermore, the effects of parameters such as ferromagnetic width, magnetization strength, and band filling will be investigated. Lastly, we compare results in the clean limit with known results in the diffusive regime.


* Supported in part by the US Department of Energy, the National Science Foundation, and the SciDAC NUCLEI-2 project.
** Supported in part by the National Science Foundation.