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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Variational Monte Carlo Calculations of A ≤ 4 Nuclei with an Artificial Neural-Network Correlator Ansatz

Here, the complexity of many-body quantum wave functions is a central aspect of several fields of physics and chemistry where nonperturbative interactions are prominent. Artificial neural networks (ANNs) have proven to be a flexible tool to approximate quantum many-body states in condensed matter and chemistry problems. In this work we introduce a neural-network quantum state ansatz to model the ground-state wave function of light nuclei, and approximately solve the nuclear many-body Schrodinger equation. Using efficient stochastic sampling and optimization schemes, our approach extends pioneering applications of ANNs in the field, which present exponentially scaling algorithmic complexity. We compute the binding energies and point-nucleon densities of A ≤ 4 nuclei as emerging from a leading-order pionless effective field theory Hamiltonian. We successfully benchmark the ANN wave function against more conventional parametrizations based on two- and three-body Jastrow functions, and virtually exact Green's function Monte Carlo results.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Electromagnetic radii of light nuclei from variational Monte Carlo calculations

We present variational Monte Carlo calculations of charge and magnetic radii in 𝐴 ≤ 10 nuclei. The calculations are based on the Norfolk two- and three-nucleon interactions, and associated one- and two-nucleon electromagnetic charge and current operators derived up to next-to-next-to-next-to-leading order in the chiral expansion. The charge and magnetic radii are extracted from the respective form factors. We find that the charge radii are within 5% of the experimental values for the nuclei considered. For the magnetic radii, a comparison is available only with 3 H and 3 ⁢He electron scattering data that are affected by large error bars. We hope that our predictions foster an interest in precisely measuring magnetic radii of heavier systems.

lepton induced nuclear reactions↗
DOE OSTI2025

Reducing the Cost of Energy Differences in Variational Monte Carlo with Spotlight Sampling

Here, we investigate an approximate sampling scheme that can significantly reduce the cost scaling of variational Monte Carlo when it is employed to predict the energy differences associated with local chemical changes. Inspired by side-chaining and embedding methods, this spotlight sampling approach adopts an approximate fragmented Hamiltonian and correlated sampling to reduce cost scaling to the point that it is essentially linear with system size, with the potential to go sublinear if certain conditions are met. In tests on bond stretching energies in alcohols, hydrogen dimer chains, and molecules with various degrees of π-system delocalization, we observe the anticipated linear scaling and an explicit cost crossover with standard variational Monte Carlo.

Bumann, Sonja [University of California, Berkeley,↗
DOE OSTI2024

Convergence of variational Monte Carlo simulation and scale-invariant pre-training

We provide theoretical convergence bounds for the variational Monte Carlo (VMC) method as applied to optimize neural network wave functions for the electronic structure problem. Here, we study both the energy minimization phase and the supervised pre-training phase that is commonly used prior to energy minimization. For the energy minimization phase, the standard algorithm is scale-invariant by design, and we provide a proof of convergence for this algorithm without modifications. The pre-training stage typically does not feature such scale-invariance. We propose using a scale-invariant loss for the pretraining phase and demonstrate empirically that it leads to faster pre-training.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Optimization Stability in Excited-State-Specific Variational Monte Carlo

Here, we investigate the issue of optimization stability in variance-based state-specific variational Monte Carlo, discussing the roles of the objective function, the complexity of wave function ansatz, the amount of sampling effort, and the choice of minimization algorithm. Using a small cyanine dye molecule as a test case, we systematically perform minimizations using variants of the linear method as both a standalone algorithm and in a hybrid combination with accelerated descent. We demonstrate that adaptive step control is crucial for maintaining the linear method's stability when optimizing complicated wave functions and that the hybrid method enjoys both greater stability and minimization performance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Improved energies and local energies with weighted variational Monte Carlo

Neural network parametrizations have increasingly been used to represent the ground and excited states in variational Monte Carlo (VMC) with promising results. However, traditional VMC methods only optimize the wave function in regions of peak probability. The wave function is uncontrolled in the tails of the probability distribution, which can limit the accuracy of the trained wave function. To improve the approximation accuracy in the probability tails, this paper interprets VMC as a gradient flow in the space of wave functions, followed by a projection step. From this perspective, arbitrary probability distributions can be used in the projection step, allowing the user to prioritize accuracy in different regions of state space. Motivated by this theoretical perspective, the paper tests a weighted VMC method on the antiferromagnetic Heisenberg model for a periodic spin chain. Compared to traditional VMC, weighted VMC reduces the error in the ground state energy by a factor of 2, and it reduces the errors in the local energies away from the mode by large factors of 10 2 –10 4 .

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

A random-sampling method as an efficient alternative to variational Monte Carlo for solving Gutzwiller wavefunctions

Abstract We present a random-sampling (RS) method for evaluating expectation values of physical quantities using the variational approach. We demonstrate that the RS method is computationally more efficient than the variational Monte Carlo method using the Gutzwiller wavefunctions applied on single-band Hubbard models as an example. Non-local constraints can also been easily implemented in the current scheme that capture the essential physics in the limit of strong on-site repulsion. In addition, we extend the RS method to study the antiferromagnetic states with multiple variational parameters for 1D and 2D Hubbard models.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Variational Monte Carlo calculations of n + H 3 scattering

A paramount goal in nuclear physics is to unify ab initio treatments of bound and unbound states. The position-space quantum Monte Carlo (QMC) methods have a long history of successful bound-state calculations in light systems but have seen minimal implementation in unbound systems. Here, we introduce a numerical method to improve the efficiency and accuracy of unbound-state calculations in QMC. As an initial application, we compute scattering observables for the smallest system available to probe three-body forces, the neutron-triton system, using variational Monte Carlo (VMC) wave functions. The method involves inferring long-range amplitudes in the wave function from integrals over the short-range region where all the particles interact. This approach using integral relations is well established in the literature; here, we develop it for the QMC framework. We validate our approach with a consistency check between short-range spectroscopic overlap functions computed from direct evaluation and from the integral relations; scattering amplitudes are long-range asymptotics of those overlaps. Comparison against published benchmark calculations using the same potential demonstrates that when applied to the current VMC wave functions, the integral method produces more accurate scattering observables than direct evaluation from the same variational wave function. However, it still differs noticeably from the exact results. Using additional interactions, we then present phase shifts and mixing parameters for the n + 3 H system. In particular, we present one of the first applications of the Norfolk family of local coordinate-space chiral potentials in unbound systems of A > 2. The Norfolk results accurately describe s-wave scattering but predict p-wave cross sections too large. Compared with previous QMC scattering calculations, the integral method avoids difficulties associated with the precise computation of energy differences and with convergence outside the interaction region, which is particularly severe in the variational calculation. Application of the integral method here paves the way for its use in Green's function Monte Carlo (GFMC) calculations. In GFMC, the wave functions are more accurate, but the high-precision convergence of their tails is slow, and there are additional difficulties in reading out amplitudes. Here, the integral methods will address both of those remaining problems.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Glauber-theory analysis of nuclear reactions on a 12 C target with variational Monte Carlo wave functions

The application of Glauber theory has been playing an increasingly important role with the study of unstable or exotic nuclei. Its adaptation to medium and high-energy nucleus-nucleus collisions is severely limited because one has to evaluate the matrix elements of multiple-scattering operators. The extraction of physical observables has been done using ‘approximate’ Glauber theory whose validity is hard to evaluate. Here, we perform a full calculation of the matrix elements using Monte Carlo integration and analyze the elastic differential cross sections and the total reaction cross sections for p+¹²C, ⁴,⁶He+¹²C, and ¹²C+¹²C collisions. We use the variational Monte Carlo wave functions for ⁴,⁶He and ¹²C obtained by using realistic two- and three-nucleon potentials. We demonstrate the performance of the Glauber-theory calculations by comparing with available experimental data. We further discuss the accuracy of the conventional approximate methods in the light of the cumulant expansion for Glauber’s phase-shift function.

Horiuchi, W. [Osaka Metropolitan University (Japan↗
DOE OSTI2026

Glauber-Theory Calculations of High-Energy Nuclear Scattering Observables Using Variational Monte Carlo Wave Functions

Experiments using intermediate- to high-energy radioactive nuclear beams present numerous findings. Extracting important properties of physical observables relies on a firm theoretical analysis. Though Glauber theory is believed to work well, no convincing calculation has so far been done. Here, we perform ab initio Glauber theory calculations of both elastic differential cross sections and total reaction cross sections for p+ 12 C, 12 C+ 12 C, and 6 He+ 12 C systems. The wave functions of both 6 He and 12 C are generated by variational Monte Carlo calculations with spatial and spin-isospin correlations induced by realistic two- and three-nucleon potentials. Glauber’s phase-shift function is computed by Monte Carlo integration up to all orders of nucleon-nucleon multiple scatterings. We show an excellent performance of the Glauber description to the selected data on the above systems. We also find that the cumulant expansion of the phase-shift function converges rapidly up to the second order for the above systems. This finding will open up interesting applications for the analysis of high-energy nuclear experiments.

Horiuchi, W. [Osaka Metropolitan University (Japan↗
DOE OSTI2022

Explicitly antisymmetrized neural network layers for variational Monte Carlo simulation

The combination of neural networks and quantum Monte Carlo methods has arisen as a promising path forward for highly accurate electronic structure calculations. Previous proposals have combined equivariant neural network layers with a final antisymmetric layer in order to satisfy the antisymmetry requirements of the electronic wavefunction. However, to date it is unclear if one can represent antisymmetric functions of physical interest, and it is difficult to precisely measure the expressiveness of the antisymmetric layer. Here, this work attempts to address this problem by introducing explicitly antisymmetrized universal neural network layers. This approach has a computational cost which increases factorially with respect to the system size, but we are nonetheless able to apply it to small systems to better understand how the structure of the antisymmetric layer affects its performance. We first introduce a generic antisymmetric (GA) neural network layer, which we use to replace the entire antisymmetric layer of the highly accurate ansatz known as the FermiNet. We demonstrate that the resulting FermiNet-GA architecture can yield effectively the exact ground state energy for small atoms and molecules. We then consider a factorized antisymmetric (FA) layer which more directly generalizes the FermiNet by replacing the products of determinants with products of antisymmetrized neural networks. We find, interestingly, that the resulting FermiNet-FA architecture does not significantly outperform the FermiNet. This strongly suggests that the sum of products of antisymmetries is a key limiting aspect of the FermiNet architecture. To explore this further, we investigate a slight modification of the FermiNet, called the full determinant mode, which replaces each product of determinants with a single combined determinant. We find that the full single-determinant FermiNet closes a large part of the gap between the standard single-determinant FermiNet and FermiNet-GA on small atomic and molecular problems. Surprisingly, on the nitrogen molecule at a dissociating bond length of 4.0 Bohr, the full single-determinant FermiNet can outperform the largest standard FermiNet calculation with 64 determinants.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Uncertainties in the production of iron-group nuclides in core-collapse supernovae from Monte Carlo variations of reaction rates

Core-collapse supernovae, occurring at the end of massive star evolution, produce heavy elements, including those in the iron peak. Although the explosion mechanism is not yet fully understood, theoretical models can reproduce optical observations and observed elemental abundances. However, many nuclear reaction rates involved in explosive nucleosynthesis have large uncertainties, impacting the reliability of abundance predictions. To address this, we have previously developed a Monte Carlo-based nucleosynthesis code that accounts for reaction rate uncertainties and has been applied to nucleosynthesis processes beyond iron. Our framework is also well suited for studying explosive nucleosynthesis in supernovae. In this paper, we investigate 1D explosion models using the ‘PUSH method’ , focusing on progenitors with varying metallicities and initial masses around $M_{\rm ZAMS} = 16\, {\rm M}_{\odot }$. Detailed post-process nucleosynthesis calculations and Monte Carlo analyses are used to explore the effects of reaction rate uncertainties and to identify key reaction rates in explosive nucleosynthesis. We find that many reactions have little impact on the production of iron-group nuclei, as these elements are primarily synthesized in the nuclear statistical equilibrium. However, we identify a few ‘key reactions’ that significantly influence the production of radioactive nuclei, which may affect astrophysical observables. In particular, for the production of ${}^{44}{\rm Ti}$, we confirm that several traditionally studied nuclear reactions have a strong impact. However, determining a single reaction rate is insufficient to draw a definitive conclusion.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Investigating the crust of neutron stars with neural-network quantum states

An accurate description of low-density nuclear matter is crucial for explaining the physics of neutron star crusts. In the density range between approximately 0.01 fm −3 and 0.1 fm −3 , matter transitions from neutron-rich nuclei to various higher-density pasta shapes, before ultimately reaching a uniform liquid. In this work, we introduce a variational Monte Carlo method based on a neural Pfaffian-Jastrow quantum state, which allows us to model the transition from the liquid phase to neutron-rich nuclei microscopically. At low densities, nuclear clusters dynamically emerge from the microscopic interactions among protons and neutrons, which we model based on pionless effective field theory. Our variational Monte Carlo approach represents a significant improvement over the state-of-the-art auxiliary-field diffusion Monte Carlo method, which is severely hindered by the fermion-sign problem in this low-density regime and cannot capture the onset of clusters. In addition to computing the energy per particle of symmetric nuclear matter and pure neutron matter, we analyze an intermediate isospin-asymmetry configuration to elucidate the formation of nuclear clusters. We also provide evidence that the presence of such nuclear clusters influences the amount of protons in the crust compared to protons in beta-equilibrated, neutrino-transparent matter.

Nuclear astrophysics↗