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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Neural refinement of sample weights

Monte Carlo simulations are an essential tool in particle physics data analysis. Events are typically generated alongside weights that redistribute the cross section of the simulated process across the phase space. These weights can be negative, and several post hoc methods have been developed to eliminate or mitigate the negative values. All of these methods share the common strategy of approximating the average weight as a function of phase space. We introduce an alternative approach, which, instead of reweighting to the average, refines the initial weights with a scaling transformation, utilizing a phase space-dependent factor. Since this new refinement method does not need to model the full weight distribution, it can be more accurate. High-dimensional and unbinned phase space is processed using neural networks for the refinement method. In addition to the refinement method, we introduce a new resampling protocol, which can be used in conjunction with any weight transformation to not only preserve the average weight but also the statistical uncertainties of the initial distribution. Using both realistic and synthetic examples, we show that the new neural refinement method is able to match or exceed the accuracy of similar weight transformations and that the new resampling protocol is simpler in implementation than previous methods while exhibiting equivalent statistical properties.

Artificial neural networks↗
DOE OSTI2014

A systematic way for the cost reduction of density fitting methods

We present a simple approach for the reduction of the size of auxiliary basis sets used in methods exploiting the density fitting (resolution of identity) approximation for electron repulsion integrals. Starting out of the singular value decomposition of three-center two-electron integrals, new auxiliary functions are constructed as linear combinations of the original fitting functions. The new functions, which we term natural auxiliary functions (NAFs), are analogous to the natural orbitals widely used for the cost reduction of correlation methods. The use of the NAF basis enables the systematic truncation of the fitting basis, and thereby potentially the reduction of the computational expenses of the methods, though the scaling with the system size is not altered. The performance of the new approach has been tested for several quantum chemical methods. It is demonstrated that the most pronounced gain in computational efficiency can be expected for iterative models which scale quadratically with the size of the fitting basis set, such as the direct random phase approximation. The approach also has the promise of accelerating local correlation methods, for which the processing of three-center Coulomb integrals is a bottleneck.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

Latest development of the combinatorial model of nuclear level densities

The combinatorial model of nuclear level densities has now reached a level of accuracy comparable to that of the best global analytical expressions. We have recently improved the treatment using simultaneously the single particle levels and collective properties predicted by the newly derived D1M Gogny interaction. In addition for deformed nuclei, the transition to sphericity is coherently taken into account on the basis of a temperature-dependent Hartree-Fock calculation which provides at each temperature the structure properties needed to build the level densities. This new method is described and shown to give good results with respect to available experimental data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Biased degenerate ground-state sampling of small Ising models with converged quantum approximate optimization algorithm

The quantum alternating operator ansatz, a generalization of the quantum approximate optimization algorithm (QAOA), is a quantum algorithm used for approximately solving combinatorial optimization problems. QAOA typically uses the transverse field mixer as the driving Hamiltonian. One of the interesting properties of the transverse field driving Hamiltonian is that it results in nonuniform sampling of degenerate ground states of optimization problems. In this study, we numerically examine the fair sampling properties of the transverse field mixer QAOA, and Grover mixer QAOA (GM-QAOA), which provides theoretical guarantees of fair sampling of degenerate optimal solutions, up to a large enough p such that the mean expectation value converges to an optimal approximation ratio of 1. This comparison is performed with high-quality heuristically computed, but not necessarily optimal, QAOA angles, which give strictly monotonically improving solution quality as p increases. These angles are computed using the Julia based numerical simulation software JuliQAOA. Fair sampling of degenerate ground states is quantified using the Shannon entropy of the ground-state amplitudes distribution. The fair sampling properties are reported on several quantum signature Hamiltonians from previous quantum annealing fair sampling studies. Small random fully connected spin glasses are shown, which exhibit exponential suppression of some degenerate ground states with transverse field mixer QAOA. The transverse field mixer QAOA simulations show that some problem instances clearly saturate the Shannon entropy of 0 with a maximally biased distribution that occurs when the learning converges to an approximation ratio of 1 while other problem instances never deviate from a maximum Shannon entropy (uniform distribution) at any p step. Published by the American Physical Society 2025

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Physical-chemical evaluation of hydraulic fracturing chemicals in the context of produced water treatment

Produced water is a significant waste stream that can be treated and reused; however, the removal of production chemicals—such as those added in hydraulic fracturing—must be addressed. One motivation for treating and reusing produced water is that current disposal methods—typically consisting of deep well injection and percolation in infiltration pits—are being limited. Furthermore, oil and gas production often occurs in arid regions where there is demand for new water sources. Here in this paper, hydraulic fracturing chemical additive data from California are used as a case study where physical-chemical and biodegradation data are summarized and used to screen for appropriate produced water treatment technologies. The data indicate that hydraulic fracturing chemicals are largely treatable; however, data are missing for 24 of the 193 chemical additives identified. More than one-third of organic chemicals have data indicating biodegradability, suggesting biological treatment would be effective. Adsorption-based methods and partitioning of chemicals into oil for subsequent separation is expected to be effective for approximately one-third of chemicals. Volatilization-based treatment methods (e.g. air stripping) will only be effective for approximately 10% of chemicals. Reverse osmosis is a good catch-all with over 70% of organic chemicals expected to be removed efficiently. Other technologies such as electrocoagulation and advanced oxidation are promising but lack demonstration. Chemicals of most concern due to prevalence, toxicity, and lack of data include propargyl alcohol, 2-mercaptoethyl alcohol, tetrakis hydroxymethyl-phosphonium sulfate, thioglycolic acid, 2-bromo-3-nitrilopropionamide, formaldehyde polymers, polymers of acrylic acid, quaternary ammonium compounds, and surfactants (e.g. ethoxylated alcohols). Future studies should examine the fate of hydraulic fracturing chemicals in produced water treatment trains to demonstrate removal and clarify interactions between upstream and downstream processes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Computational modeling of charge hopping dynamics along a disordered one-dimensional wire with energy gradients in quantum environments

This computational study investigates the effects of energy gradients on charge hopping dynamics along a one-dimensional chain of discrete sites coupled to quantum bath, which is modeled at the level of Pauli master equation (PME). This study also assesses the performance of different approximations for the hopping rates. Three different methods for solving the PME, a fourth order Runge–Kutta method, numerical diagonalization of the rate matrix followed by analytic propagation, and kinetic Monte Carlo simulation method, are tested and confirmed to produce virtually identical values of time dependent mean square displacement, diffusion constant, and mobility. Five different rate expressions, exact numerical evaluation of Fermi’s Golden Rule (FGR) rate, stationary phase interpolation (SPI) approximation, semiclassical approximation, classical Marcus rate, and Miller–Abrahams rate, are tested to help understand the effects of approximations in representing quantum environments in the presence of energy gradients. The results based on direct numerical evaluation of FGR rate exhibit transition from diffusive to non-diffusive behavior with the increase in the gradient and show that the charge transport in the quantum bath is more sensitive to the magnitude of the gradient and the disorder than in the classical bath. Among all the four approximations for the hopping rates, the SPI approximation is confirmed to work best overall. A comparison of two different methods to calculate the mobility identifies drift motion of the population distribution as the major source of non-diffusive behavior and provides more reliable information on the contribution of quantum bath.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2013

Heel effect adaptive flat field correction of digital x-ray detectors

Purpose: Anode heel effect renders large-scale background nonuniformities in digital radiographs. Conventional offset/gain calibration is performed at mono source-to-image distance (SID), and disregards the SID-dependent characteristic of heel effect. It results in a residual nonuniform background in the corrected radiographs when the SID settings for calibration and correction differ. In this work, the authors develop a robust and efficient computational method for digital x-ray detector gain correction adapted to SID-variant heel effect, without resorting to physical filters, phantoms, complicated heel effect models, or multiple-SID calibration and interpolation.Methods: The authors present the Duo-SID projection correction method. In our approach, conventional offset/gain calibrations are performed only twice, at the minimum and maximum SIDs of the system in typical clinical use. A fast iterative separation algorithm is devised to extract the detector gain and basis heel patterns from the min/max SID calibrations. The resultant detector gain is independent of SID, while the basis heel patterns are parameterized by the min- and max-SID. The heel pattern at any SID is obtained from the min-SID basis heel pattern via projection imaging principles. The system gain desired at a specific acquisition SID is then constructed using the projected heel pattern and detector gain map.Results: The method was evaluated for flat field and anatomical phantom image corrections. It demonstrated promising improvements over interpolation and conventional gain calibration/correction methods, lowering their correction errors by approximately 70% and 80%, respectively. The separation algorithm was able to extract the detector gain and heel patterns with less than 2% error, and the Duo-SID corrected images showed perceptually appealing uniform background across the detector.Conclusions: The Duo-SID correction method has substantially improved on conventional offset/gain corrections for digital x-ray imaging in an SID-variant environment. The technique is relatively simple, and can be easily incorporated into multiple-point gain calibration/correction techniques. It offers a potentially valuable tool for preprocessing digital x-ray images to boost image quality of mammography, chest and cardiac radiography, as well as automated computer aided diagnostic radiology.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2018

Fast Approximate Union Volume in High Dimensions with Line Samples

The classical problem of calculating the volume of the union of d-dimensional balls is known as "Union Volume." We present line-sampling approximation algorithms for Union Volume. Our methods may be extended to other Boolean operations, such as setminus; or to other shapes, such as hyper-rectangles. The deterministic, exact approaches for Union Volume do not scale well to high dimensions. However, we adapt several of these exact approaches to approximation algorithms based on sampling. We perform local sampling within each ball using lines. We have several variations, depending on how the overlapping volume is partitioned, and depending on whether radial, axis-aligned, or other line patterns are used. Our variations fall within the family of Monte Carlo sampling, and hence have about the same theoretical convergence rate, 1 /$\sqrt{M}$, where M is the number of samples. In our limited experiments, line-sampling proved more accurate per unit work than point samples, because a line sample provides more information, and the analytic equation for a sphere makes the calculation almost as fast. We performed a limited empirical study of the efficiency of these variations. We suggest a more extensive study for future work. We speculate that different ball arrangements, differentiated by the distribution of overlaps in terms of volume and degree, will benefit the most from patterns of line samples that preferentially capture those overlaps. Acknowledgement We thank Karl Bringman for explaining his BF-ApproxUnion (ApproxUnion) algorithm [3] to us. We thank Josiah Manson for pointing out that spoke darts oversample the center and we might get a better answer by uniform sampling. We thank Vijay Natarajan for suggesting random chord sampling. The authors are grateful to Brian Adams, Keith Dalbey, and Vicente Romero for useful technical discussions. This work was sponsored by the Laboratory Directed Research and Development (LDRD) Program at Sandia National Laboratories. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research (ASCR), Applied Mathematics Program. Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA0003525.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Explicit solutions of the radiative transport equation in the P{sub 3} approximation

Purpose: Explicit solutions of the monoenergetic radiative transport equation in the P{sub 3} approximation have been derived which can be evaluated with nearly the same computational effort as needed for solving the standard diffusion equation (DE). In detail, the authors considered the important case of a semi-infinite medium which is illuminated by a collimated beam of light. Methods: A combination of the classic spherical harmonics method and the recently developed method of rotated reference frames is used for solving the P{sub 3} equations in closed form. Results: The derived solutions are illustrated and compared to exact solutions of the radiative transport equation obtained via the Monte Carlo (MC) method as well as with other approximated analytical solutions. It is shown that for the considered cases which are relevant for biomedical optics applications, the P{sub 3} approximation is close to the exact solution of the radiative transport equation. Conclusions: The authors derived exact analytical solutions of the P{sub 3} equations under consideration of boundary conditions for defining a semi-infinite medium. The good agreement to Monte Carlo simulations in the investigated domains, for example, in the steady-state and time domains, as well as the short evaluation time needed suggests that the derived equations can replace the often applied solutions of the diffusion equation for the homogeneous semi-infinite medium.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Systematic investigation on topological properties of layered GaS and GaSe under strain

The topological properties of layered β-GaS and ε-GaSe under strain are systematically investigated by ab initio calculations with the electronic exchange-correlation interactions treated beyond the generalized gradient approximation (GGA). Based on the GW method and the Tran-Blaha modified Becke-Johnson potential approach, we find that while ε-GaSe can be strain-engineered to become a topological insulator, β-GaS remains a trivial one even under strong strain, which is different from the prediction based on GGA. The reliability of the fixed volume assumption rooted in nearly all the previous calculations is discussed. By comparing to strain calculations with optimized inter-layer distance, we find that the fixed volume assumption is qualitatively valid for β-GaS and ε-GaSe, but there are quantitative differences between the results from the fixed volume treatment and those from more realistic treatments. This work indicates that it is risky to use theoretical approaches like GGA that suffer from the band gap problem to address physical properties, including, in particular, the topological nature of band structures, for which the band gap plays a crucial role. In the latter case, careful calibration against more reliable methods like the GW approach is strongly recommended.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2014

TH-E-BRE-02: A Forward Scattering Approximation to Dose Calculation Using the Linear Boltzmann Transport Equation

Purpose: To investigate the use of the linear Boltzmann transport equation as a dose calculation tool which can account for interface effects, while still having faster computation times than Monte Carlo methods. In particular, we introduce a forward scattering approximation, in hopes of improving calculation time without a significant hindrance to accuracy. Methods: Two coupled Boltzmann transport equations were constructed, one representing the fluence of photons within the medium, and the other, the fluence of electrons. We neglect the scattering term within the electron transport equation, resulting in an extreme forward scattering approximation to reduce computational complexity. These equations were then solved using a numerical technique for solving partial differential equations, known as a finite difference scheme, where the fluence at each discrete point in space is calculated based on the fluence at the previous point in the particle's path. Using this scheme, it is possible to develop a solution to the Boltzmann transport equations by beginning with boundary conditions and iterating across the entire medium. The fluence of electrons can then be used to find the dose at any point within the medium. Results: Comparisons with Monte Carlo simulations indicate that even simplistic techniques for solving the linear Boltzmann transport equation yield expected interface effects, which many popular dose calculation algorithms are not capable of predicting. Implementation of a forward scattering approximation does not appear to drastically reduce the accuracy of this algorithm. Conclusion: Optimized implementations of this algorithm have been shown to be very accurate when compared with Monte Carlo simulations, even in build up regions where many models fail. Use of a forward scattering approximation could potentially give a reasonably accurate dose distribution in a shorter amount of time for situations where a completely accurate dose distribution is not required, such as in certain optimization algorithms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

The impact of different neutrino transport methods on multidimensional core-collapse supernova simulations

Neutrinos play a crucial role in the core-collapse supernova (CCSN) explosion mechanism. The requirement of accurately calculating the transport of neutrinos makes simulations of the CCSN mechanism extremely challenging and computationally expensive. Historically, this stiff challenge has been met by making approximations to the full transport equation. In this work, we compare CCSN simulations in one- and two-dimensions with three approximate neutrino transport schemes, each implemented in the FLASH simulation framework. We compare a two-moment M1 scheme with an analytic closure (M1), the isotropic diffusion source approximation (IDSA), and the advanced spectral leakage method. We identify and discuss the advantages and disadvantages of each scheme. For each approximate transport scheme, we use identical grid setups, hydrodynamics, and gravity solvers to investigate the transport effects on supernova shock dynamics and neutrino quantities. We find that the transport scheme has a small effect on the evolution of protoneutron star (PNS) radius, PNS mass, and the mass accretion rate. The neutrino luminosities, mean energies, and shock radii have a ~10%–20% quantitative difference but the overall qualitative trends are fairly consistent between all three approximations. We find larger differences in the gain region properties, including the gain region mass and the net heating rate in the gain region, as well as the strength of PNS convection in the core. We investigate the progenitor, nuclear equation of state, and stochastic perturbation dependence of our simulations and find similar magnitudes of impact on key quantities. We also compare the computational expense of the various approximations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2015

Technical Note: On the proton range and nuclear interactions in compounds and mixtures

Purpose: Range and probability of nonelastic nuclear interactions (NNIs) for protons can be found only for a limited number of compounds and mixtures in nuclear data tables, and the proton-related analytical studies are therefore restricted to those materials for which the data are provided in these documents. In this paper, the authors present general solutions for calculating the proton range and probability of NNIs for desired compounds and mixtures. Methods: Benefiting from the Bragg–Kleeman approximation of mass stopping power, the authors derive a concise formula for calculating the proton range in materials with arbitrary number of constituent elements. Additionally, the authors propose another relation for obtaining the probability of undergoing NNIs which is suggested to be additive. Results: The examination of the formula presented shows that the authors’ method can be considered as general solutions for analytical evaluation of the range in compounds and mixtures. The formula proposed for probability of NNIs is valid for almost every compound except for those materials containing H. It is shown that this formula can be modified so that it covers these materials. Conclusions: The authors present a general analytical method for calculating the range and probability of NNIs for protons which are mathematically easy to handle and valid for desired compounds or mixtures composed of an arbitrary number of constituent elements, including materials of interest for proton radiotherapy purposes.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2016

The packing problem of uncertain multicasts

Summary Multicast performs better than unicast in delivering the same content from a fixed single source to a set of destinations. Many efforts have been made to optimize such kind of deterministic multicast, such as minimizing the transmission cost of each multicast session. In practice, it is not necessary that the source of each multicast session has to be in a specific location, as long as certain constraints are satisfied. Accordingly, applications usually meet a novel multicast with uncertain sources, ie, uncertain multicast. That is, multiple nodes have the responsibility to act as the root node of a multicast session. Prior proposals have addressed an uncertain multicast by constructing the minimum cost forest. However, it is still unknown how to efficiently share the network resources, when a set of uncertain multicast occupies the network simultaneously. To tackle such a challenging issue, we present the packing problem of uncertain multicasts (MPU) to minimize the total transmission cost, under the constraint of link capacity. We prove that the MPU problem is NP‐hard. An intrinsic solution is constructing the minimum cost forest for each uncertain multicast individually. This method, however, is inefficient and may be infeasible because of the constraint of link capacity. Thus, we design 2 dedicated greedy methods, named priority‐based and adjusting congested link, to approximate the optimal solution. The comprehensive results indicate that both of our 2 methods can find a feasible solution for the MPU problem. Moreover, given a set of uncertain multicasts, the adjusting congested link method can generate a desired transmission structure for each uncertain multicast and achieve the least total cost when packing them.

Ren, Bangbang↗
DOE OSTI2023

Influence of near-surface oxide layers on TiFe hydrogenation: mechanistic insights and implications for hydrogen storage applications

The inevitable formation of passivating oxide films on the surface of the TiFe intermetallic compound limits its performance as a stationary hydrogen storage material. Extensive experimental efforts have been dedicated to the activation of TiFe, i.e. oxide layer removal prior to utilization for hydrogen storage. However, development of an efficient activation protocol necessitates a fundamental understanding of the composition and structure of the air-exposed surface and its interaction with hydrogen, which is currently absent. Therefore, in this study we explored the growth and nature of oxide films on the most exposed TiFe surface (110) in depth using static and dynamic first-principles methods. We identified the lowest energy structures for six oxygen coverages up to approximately 1.12 nm of thickness with a global optimization method and studied the temperature effects and structural evolution of the oxide phases in detail via ab initio molecular dynamics (AIMD). Based on structural similarity and coordination analysis, motifs for TiO 2 and TiFeO 3 as well as Ti(FeO 2 ) x (x = 2, 3 or 5) phases were identified. On evaluating the interaction of the oxidized surface with hydrogen, a minimal energy barrier of 0.172 eV was predicted for H 2 dissociation while H migration from the top of the oxidized surface to the bulk TiFe was limited by several high-lying energy barriers above 1.4 eV. Our mechanistic insights will prove themselves valuable for informed designs towards new activation methods of TiFe and related systems as hydrogen storage materials.

08 HYDROGEN↗
DOE OSTI2022

Fast and noise-tolerant determination of the center of rotation in tomography

High-quality tomographic reconstruction is not possible without the accurate localization of the center of rotation. Poor localization leads to artifacts in the data and can even cause reconstructions to fail. There are many approaches to solving this problem, some of which involve the collection of full sinograms, or even provisional tomographic reconstructions, in order to determine the center of rotation. Here, a simple method based on the expected symmetry of the Fourier transform of summed projections approximately 180° apart is presented; unlike cross-correlation methods, it requires only a single Fourier transform to compute, and uses mainly low spatial frequency information which is less susceptible to noise. This approach is shown to be fast, and robust against poor signal-to-noise as well as to projection images acquired at angles that are not exactly 180° apart. This rapid method can be useful as a first step in the processing of tomographic data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2012

Precise calculations of observables of polarized moller scattering: From JLAB to ILC energies

One-loop electroweak corrections to observables of the reaction e{sup -}e{sup -} {yields} e{sup -}e{sup -}({gamma}) were calculated over a broad range of energies: from conditions of the MOLLER experiment at the Thomas Jefferson Laboratory (JLab) to those of planned experiments at the International Linear Collider (ILC). The dependence of various contributions to the observable polarization asymmetry on various renormalization conditions was studied within the scheme of on-shell renormalization. The results were obtained by two methods: precisely, by applying the FeynArts, FormCalc, LoopTools, and Form computer codes, and approximately, with the aid of the asymptotic-estimation methods. The resulting compact formulas are absolutely free from nonphysical parameters and are convenient for deducing numerical estimates. It is shown that the total one-loop correction is independent of renormalization conditions and takes an identical value within different computational schemes.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Approximate inverse-based block preconditioners in poroelasticity

We focus on the fully implicit solution of the linear systems arising from a three-field mixed finite element approximation of Biot’s poroleasticity equations. The objective is to develop algebraic block preconditioners for the efficient solution of such systems by Krylov subspace methods. In this work, we investigate the use of approximate inverse-based techniques to decouple the native system of equations and obtain explicit sparse approximations of the Schur complements related to the physics-based partitioning of the unknowns by field type. Here, the proposed methods are tested in various numerical experiments including real-world applications dealing with petroleum and geotechnical engineering.

54 ENVIRONMENTAL SCIENCES↗