arXiv subjects

Pablo Giuliani

Publications and source records attributed to Pablo Giuliani.

17 recordsLinked to original sources

arXiv2026

Bayesian Inference for Extracting Barrier Distributions from Fusion Excitation Functions

Barrier distributions encode rich information about the structure and dynamics of fusing nuclei, but extracting them from experimental fusion cross sections requires an estimate of the fusion excitation function's second derivative. In this work we approach the task of extracting barrier distributions with uncertainty estimates from sparse experimental measurements as a Bayesian inference problem. We introduce a method based on AutoBNN, an interpretable Bayesian machine learning framework, to provide a robust statistical approach for analyzing fusion excitation functions. Benchmarking against Gaussian process regression on simulated excitation functions that span a wide range of realistic experimental conditions, we find that AutoBNN more faithfully recovers the underlying barrier distribution and reports well-calibrated uncertainties. We then apply the AutoBNN method to four experimentally measured heavy-ion fusion reactions where it mitigates spurious above-barrier structure and constrains existing predictions. Alongside these results, we have developed a user-friendly software implementation of our method, facilitating its application to future heavy and light-ion fusion experiments.

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arXiv2026

Emulating Density Functional Theory Calculations via Empirical Interpolation

Nuclear density functional theory (DFT) is a suitable tool for predicting nuclear ground-state and fission properties. Statistical uncertainty quantification is desirable to make those predictions reliable, especially for nuclei far from stability. However, the computational cost associated with describing deformed nuclei in DFT makes such uncertainty quantification a challenge. In many solvers, the main computational bottleneck is the transformation of the wavefunction-dependent operators from coordinate to configuration space. We explore the use of the empirical interpolation method (EIM) to speed up the coordinate-configuration transformations, effectively constructing DFT emulators for ground-state and fission properties. To train and test the emulator we vary the model parameters across their realistic posterior distribution. We consider both a simplified one-dimensional model, and realistic axially-deformed nuclei at the Hartree-Fock-Boguliubov (HFB) level. For realistic calculations, we consider sample nuclei from across the chart, from $A=60$ up to $A=254$, as well as a highly-deformed fission isomer. We construct one emulator for each case, and study the binding energy, quadrupole deformation, and excitation energy of the fission isomer. In all nuclei, for all observables considered, the EIM emulator agrees with the DFT value to the precision of the original DFT calculations, using as few as 100 HFB calculations to build the emulator. For a given nuclear ground state or isomer, the emulator is able to predict all observables simultaneously. The emulator provides an order-of-magnitude speedup over the original solver, making EIM a suitable emulation scheme for DFT, especially when high precision is desired as in model calibration and fission. Thus, the EIM helps make statistical uncertainty feasible, improving the reliability of future predictions.

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arXiv2025

Wavefunction-Based Emulation of Coupled-Channels Scattering with Non-Affinely Parametrized Interactions

Physics based emulators offer a fast and reliable replacement for an exact solution of the scattering problem in nuclear physics. Previous work developed a reduced-basis emulator for single-channel elastic scattering using an optical potential. Since many reactions of interest can be cast as a coupled-channel problem, the purpose of this work is to extend the RBM to a coupled-channel framework (CC-RBM). Although the framework derived is general, in this work we apply it to reactions where the Hamiltonian coupling term comes from assuming a rotational structure model for the target. From a set of training coupled-channel wavefunctions, we perform a singular value decomposition to obtain a reduced set of basis wavefunctions, and then solve the extended (Petrov-)Galerkin equations. In addition, the empirical interpolation method is used to expand the potentials. We apply the CC-RBM method to elastic and inelastic scattering of neutrons on 48Ca including a quadrupole coupling to populate the first 2+ state, and neutrons on 208Pb, including an octupole coupling to populate its first 3- state. We demonstrate that the CC-RBM calculated cross sections match those obtained using traditional finite-difference methods. We show that the CC-RBM results can reliably reproduce the nuclear scattering cross sections at different energy regimes. The computational accuracy versus time plots demonstrate that the CC-RBM method efficiently increases precision with increasing basis size. Most importantly, for the precisions required in reaction calculations (a percent on the cross section), we find the CC-RBM method offers roughly one and a half orders of magnitude gain in computational speed compared to the traditional coupled-channels solver. However, we also discuss how this scaling becomes less favorable, the larger the number of channels included in the coupled-channel set.

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arXiv2025

Nuclear Beavers

Nuclear physics is a very abstract field with little accessibility for wider audiences, and yet it is a field of physics with far reaching implications for everyday life. The Nuclear Beavers demonstration is a hands-on experience that offers an intuitive lens into nuclear structure and decay. We aim to provide a more accessible entry point for students and educators by substituting complex nuclear structures and interactions with tactile building blocks following well-defined rules, thereby opening nuclear physics concepts to the general public.

physics.ed-ph↗

arXiv2025

Emulators for Scarce and Noisy Data: Application to Auxiliary-Field Diffusion Monte Carlo for Neutron Matter

Understanding the equation of state (EOS) of pure neutron matter is necessary for interpreting multimessenger observations of neutron stars. Reliable data analyses of these observations require well-quantified uncertainties for the EOS input, ideally propagating uncertainties from nuclear interactions directly to the EOS. This, however, requires calculations of the EOS for a prohibitively large number of nuclear Hamiltonians, solving the nuclear many-body problem for each one. Quantum Monte Carlo methods, such as auxiliary-field diffusion Monte Carlo (AFDMC), provide precise and accurate results for the neutron matter EOS, but they are very computationally expensive, making them unsuitable for the fast evaluations necessary for uncertainty propagation. Here, we employ parametric matrix models to develop fast emulators for AFDMC calculations of neutron matter and use them to directly propagate uncertainties of coupling constants in the Hamiltonian to the EOS. As these uncertainties include estimates of the effective field theory truncation uncertainty, this approach provides robust uncertainty estimates for use in astrophysical data analyses. This Letter will enable novel applications such as using astrophysical observations to put constraints on coupling constants for nuclear interactions.

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arXiv2024

Motivations for Early High-Profile FRIB Experiments

This white paper is the result of a collaboration by those that attended a workshop at the Facility for Rare Isotope Beams (FRIB), organized by the FRIB Theory Alliance (FRIB-TA), on Theoretical Justifications and Motivations for Early High-Profile FRIB Experiments. It covers a wide range of topics related to the science that will be explored at FRIB. After a brief introduction, the sections address: (II) Overview of theoretical methods, (III) Experimental capabilities, (IV) Structure, (V) Near-threshold Physics, (VI) Reaction mechanisms, (VII) Nuclear equations of state, (VIII) Nuclear astrophysics, (IX) Fundamental symmetries, and (X) Experimental design and uncertainty quantification.

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arXiv2024

Genetic Programming for the Nuclear Many-Body Problem: a Guide

Genetic Programming is an evolutionary algorithm that generates computer programs, or mathematical expressions, to solve complex problems. In this Guide, we demonstrate how to use Genetic Programming to develop surrogate models to mitigate the computational costs of modeling atomic nuclei with ever increasing complexity. The computational burden escalates when uncertainty quantification is pursued, or when observables must be globally computed for thousands of nuclei. By studying three models in which the mean field depends on the total particle density self-consistently, we show that by constructing reduced order models supported by Genetic Programming one can speed up many-body computations by several orders of magnitude with a negligible loss in accuracy

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arXiv2024

Towards accelerated nuclear-physics parameter estimation from binary neutron star mergers: Emulators for the Tolman-Oppenheimer-Volkoff equations

Gravitational-wave observations of binary neutron-star (BNS) mergers have the potential to revolutionize our understanding of the nuclear equation of state (EOS) and the fundamental interactions that determine its properties. However, Bayesian parameter estimation frameworks do not typically sample over microscopic nuclear-physics parameters that determine the EOS. One of the major hurdles in doing so is the computational cost involved in solving the neutron-star structure equations, known as the Tolman-Oppenheimer-Volkoff (TOV) equations. In this paper, we explore approaches to emulating solutions for the TOV equations: Multilayer Perceptrons (MLP), Gaussian Processes (GP), and a data-driven variant of the reduced basis method (RBM). We implement these emulators for three different parameterizations of the nuclear EOS, each with a different degree of complexity represented by the number of model parameters. We find that our MLP-based emulators are generally more accurate than the other two algorithms whereas the RBM results in the largest speedup with respect to the full, high-fidelity TOV solver. We employ these emulators for a simple parameter inference using a potentially loud BNS observation, and show that the posteriors predicted by our emulators are in excellent agreement with those obtained from the full TOV solver.

astro-ph.HE↗

arXiv2024

Model orthogonalization and Bayesian forecast mixing via Principal Component Analysis

One can improve predictability in the unknown domain by combining forecasts of imperfect complex computational models using a Bayesian statistical machine learning framework. In many cases, however, the models used in the mixing process are similar. In addition to contaminating the model space, the existence of such similar, or even redundant, models during the multimodeling process can result in misinterpretation of results and deterioration of predictive performance. In this work we describe a method based on the Principal Component Analysis that eliminates model redundancy. We show that by adding model orthogonalization to the proposed Bayesian Model Combination framework, one can arrive at better prediction accuracy and reach excellent uncertainty quantification performance.

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arXiv2024

Emulators for scarce and noisy data: application to auxiliary field diffusion Monte Carlo for the deuteron

The validation, verification, and uncertainty quantification of computationally expensive theoretical models of quantum many-body systems require the construction of fast and accurate emulators. In this work, we develop emulators for auxiliary field diffusion Monte Carlo (AFDMC), a powerful many-body method for nuclear systems. We introduce a reduced-basis method (RBM) emulator for AFDMC and study it in the simple case of the deuteron. Furthermore, we compare our RBM emulator with the recently proposed parametric matrix model (PMM) that combines elements of RBMs with machine learning. We contrast these two approaches with a traditional Gaussian Process emulator. All three emulators constructed here are based on a very limited set of 5 training points, as expected for realistic AFDMC calculations, but validated against $\mathcal{O}(10^3)$ exact solutions. We find that the PMM, with emulator errors of only $\approx 0.1 \%$ and speed-up factors of $\approx 10^7$, outperforms our implementation of the other two emulators when applied to AFDMC.

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arXiv2023

ROSE: A reduced-order scattering emulator for optical models

A new generation of phenomenological optical potentials requires robust calibration and uncertainty quantification, motivating the use of Bayesian statistical methods. These Bayesian methods usually require calculating observables for thousands or even millions of parameter sets, making fast and accurate emulators highly desirable or even essential. Emulating scattering across different energies or with interactions such as optical potentials is challenging because of the non-affine parameter dependence, meaning the parameters do not all factorize from individual operators. Here we introduce and demonstrate the Reduced Order Scattering Emulator (ROSE) framework, a reduced basis emulator that can handle non-affine problems. ROSE is fully extensible and works within the publicly available BAND Framework software suite for calibration, model mixing, and experimental design. As a demonstration problem, we use ROSE to calibrate a realistic nucleon-target scattering model through the calculation of elastic cross sections. This problem shows the practical value of the ROSE framework for Bayesian uncertainty quantification with controlled trade-offs between emulator speed and accuracy as compared to high-fidelity solvers. Planned extensions of ROSE are discussed.

physics.comp-ph↗

arXiv2023

Normalizing Flows for Bayesian Posteriors: Reproducibility and Deployment

We present a computational framework for efficient learning, sampling, and distribution of general Bayesian posterior distributions. The framework leverages a machine learning approach for the construction of normalizing flows for the general probability distributions typically encountered in Bayesian uncertainty quantification studies. This normalizing flow can map a trivial distribution to a more complicated one and can be stored more efficiently than the empirical distribution samples themselves. Once the normalized flow is trained, it further enables parallelized and uncorrelated sampling of the learned distribution. We demonstrate our framework with three test distributions with strong non-linear correlations, multi-modality, and heavy tails, as well as with a realistic posterior distribution obtained from a Bayesian calibration of a nuclear relativistic mean-field model. The performance of the framework, as well as its relatively simple implementation, positions it as one fundamental cornerstone in the development and deployment of continuous calibration pipelines of physical models and as a key component of future reproducible science workflows.

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arXiv2022

Deconstructing experimental decay energy spectra: the $^{26}$O case

In nuclear reaction experiments, the measured decay energy spectra can give insights into the shell structure of decaying systems. However, extracting the underlying physics from the measurements is challenging due to detector resolution and acceptance effects. The Richardson-Lucy (RL) algorithm, a deblurring method that is commonly used in optics and has proven to be a successful technique for restoring images, was applied to our experimental nuclear physics data. The only inputs to the method are the observed energy spectrum and the detector's response matrix also known as the transfer matrix. We demonstrate that the technique can help access information about the shell structure of particle-unbound systems from the measured decay energy spectrum that isn't immediately accessible via traditional approaches such as chi-square fitting. For a similar purpose, we developed a machine learning model that uses a deep neural network (DNN) classifier to identify resonance states from the measured decay energy spectrum. We tested the performance of both methods on simulated data and experimental measurements. Then, we applied both algorithms to the decay energy spectrum of $^{26}\mathrm{O} \rightarrow ^{24}\mathrm{O}$ + n + n measured via invariant mass spectroscopy. The resonance states restored using the RL algorithm to deblur the measured decay energy spectrum agree with those found by the DNN classifier. Both deblurring and DNN approaches suggest that the raw decay energy spectrum of $^{26}\mathrm{O}$ exhibits three peaks at approximately 0.15~MeV, 1.50~MeV, and 5.00~MeV, with half-widths of 0.29~MeV, 0.80~MeV, and 1.85~MeV, respectively.

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arXiv2022

Bayes goes fast: Uncertainty Quantification for a Covariant Energy Density Functional emulated by the Reduced Basis Method

A covariant energy density functional is calibrated using a principled Bayesian statistical framework informed by experimental binding energies and charge radii of several magic and semi-magic nuclei. The Bayesian sampling required for the calibration is enabled by the emulation of the high-fidelity model through the implementation of a reduced basis method (RBM) - a set of dimensionality reduction techniques that can speed up demanding calculations involving partial differential equations by several orders of magnitude. The RBM emulator we build - using only 100 evaluations of the high-fidelity model - is able to accurately reproduce the model calculations in tens of milliseconds on a personal computer, an increase in speed of nearly a factor of 3,300 when compared to the original solver. Besides the analysis of the posterior distribution of parameters, we present predictions with properly estimated uncertainties for observables not included in the fit, specifically the neutron skin thickness of 208Pb and 48Ca, as reported by PREX and CREX collaborations. The straightforward implementation and outstanding performance of the RBM makes it an ideal tool for assisting the nuclear theory community in providing reliable estimates with properly quantified uncertainties of physical observables. Such uncertainty quantification tools will become essential given the expected abundance of data from the recently inaugurated and future experimental and observational facilities.

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arXiv2022

Training and Projecting: A Reduced Basis Method Emulator for Many-Body Physics

We present the reduced basis method as a tool for developing emulators for equations with tunable parameters within the context of the nuclear many-body problem. The method uses a basis expansion informed by a set of solutions for a few values of the model parameters and then projects the equations over a well-chosen low-dimensional subspace. We connect some of the results in the eigenvector continuation literature to the formalism of reduced basis methods and show how these methods can be applied to a broad set of problems. As we illustrate, the possible success of the formalism on such problems can be diagnosed beforehand by a principal component analysis. We apply the reduced basis method to the one-dimensional Gross-Pitaevskii equation with a harmonic trapping potential and to nuclear density functional theory for $^{48}$Ca, achieving speed-ups of more than x150 in both cases when compared to traditional solvers. The outstanding performance of the approach, together with its straightforward implementation, show promise for its application to the emulation of computationally demanding calculations, including uncertainty quantification.

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arXiv2022

Nudged elastic band approach to nuclear fission pathways

The nuclear fission process is a dramatic example of the large-amplitude collective motion in which the nucleus undergoes a series of shape changes before splitting into distinct fragments. This motion can be represented by a pathway in the many-dimensional space of collective coordinates. The collective action along the fission pathway determines the spontaneous fission half-lives as well as mass and charge distributions of fission fragments. We study the performance and precision of various methods to determine the minimum action and minimum-energy fission trajectories in the collective space. We apply the nudged elastic band method (NEB), grid-based methods, and Euler Lagrange approach to the collective action minimization in two and three dimensional collective spaces. The performance of various approaches to the fission pathway problem is assessed by studying the collective motion along both analytic energy surfaces and realistic potential energy surfaces obtained with the Hartree-Fock-Bogoliubov theory. The uniqueness and stability of the solutions is studied. The NEB method is capable of efficient determination of the exit points on the outer turning surface that characterize the most probable fission pathway and constitute the key input for fission studies. This method can also be used to accurately compute the critical points (i.e., local minima and saddle points) on the potential energy surface of the fissioning nucleus that determine the static fission path. The NEB method is the tool of choice for finding the least-action and minimum energy fission trajectories. It will be particularly useful in large-scale fission calculation of superheavy nuclei and neutron-rich fissioning nuclei contributing to the astrophysical r-process recycling.

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arXiv2019

Bias-Variance Trade-off and Model Selection for Proton Radius Extractions

Intuitively, a scientist might assume that a more complex regression model will necessarily yield a better predictive model of experimental data. Herein, we disprove this notion in the context of extracting the proton charge radius from charge form factor data. Using a Monte Carlo study, we show that a simpler regression model can in certain cases be the better predictive model. This is especially true with noisy data where the complex model will fit the noise instead of the physical signal. Thus, in order to select the appropriate regression model to employ, a clear technique should be used such as the Akaike information criterion or Bayesian information criterion, and ideally selected previous to seeing the results. Also, to ensure a reasonable fit, the scientist should also make regression quality plots, such as residual plots, and not just rely on a single criterion such as reduced chi2. When we apply these techniques to low four-momentum transfer cross section data, we find a proton radius that is consistent with the muonic Lamb shift results. While presented for the case of proton radius extraction, these concepts are applicable in general and can be used to illustrate the necessity of balancing bias and variance when building a regression model and validating results, ideas that are at the heart of modern machine learning algorithms.

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