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At least 757 records · Page 42
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Galaxy bispectrum in the spherical Fourier-Bessel basis

The bispectrum, the three-point correlation in Fourier space, is a crucial statistic for studying many effects targeted by the next-generation galaxy surveys, such as primordial non-Gaussianity (PNG) and general relativistic (GR) effects on large scales. In this work we develop a formalism for the bispectrum in the spherical Fourier-Bessel (SFB) basis—a natural basis for computing correlation functions on the curved sky, as it diagonalizes the Laplacian operator in spherical coordinates. Working in the SFB basis allows for line-of-sight effects such as redshift space distortions and GR to be accounted for exactly, i.e., without having to resort to perturbative expansions to go beyond the plane-parallel approximation. Only analytic results for the SFB bispectrum exist in the literature given the intensive computations needed. We numerically calculate the SFB bispectrum for the first time, enabled by a few techniques: We implement a template decomposition of the redshift-space kernel Z 2 into Legendre polynomials, and separately treat the PNG and velocity-divergence terms. We derive an identity to integrate a product of three spherical harmonics connected by a Dirac delta function as a simple sum and use it to investigate the limit of a homogeneous and isotropic Universe. Furthermore, we present a formalism for convolving the signal with separable window functions and use a toy spherically symmetric window to demonstrate the computation and give insights into the properties of the observed bispectrum signal. While our implementation remains computationally challenging, it is a step toward a feasible full extraction of information on large scales via a SFB bispectrum analysis.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Parallel Algorithms for Efficient Computation of High-Order Line Graphs of Hypergraphs

This paper considers structures of systems beyond dyadic (pairwise) interactions and investigates mathematical modeling of multi-way interactions and connections as hypergraphs, where captured relationships among system entities are set-valued. To date, in most situations, entities in a hypergraph are considered connected as long as there is at least one common ``neighbor''. However, minimal commonality sometimes discards the ``strength'' of connections and interactions among groups. To this end, considering the ``width'' of a connection, referred to as the \emph{$s$-overlap} of neighbors, provides more meaningful insights into how closely the communities or entities interact with each other. In addition, $s$-overlap computation is the fundamental kernel to construct the line graph of a hypergraph, a low-order approximation of the hypergraph which can carry significant information about the original hypergraph. Subsequent stages of a data analytics pipeline then can apply highly-tuned graph algorithms on the line graph to reveal important features. Given a hypergraph, computing the $s$-overlaps by exhaustively considering all pairwise entities can be computationally prohibitive. To tackle this challenge, we develop efficient algorithms to compute $s$-overlaps and the corresponding line graph of a hypergraph. We propose several heuristics to avoid execution of redundant work and improve performance of the $s$-overlap computation. Our parallel algorithm, combined with these heuristics, is orders of magnitude (more than $10\times$) faster than the naive algorithm in all cases and the SpGEMM algorithm with filtration in most cases (especially with large $s$ value).

hypergraph algorithms, graph algorithms, parallel ↗
DOE OSTI2024

Density scaling approximation for Monte-Carlo simulations of radioactive plumes

The release of radioactive gas into the atmosphere can diffuse into large volumes of air downwind from the point of release. The extent of radioactivity can cover thousands of cubic meters of air. For such large volumes, the weather models used to predict the down-wind distribution of the plume and the radiation transport models used to predict the radiation reaching ground-level from the plume can take tens of hours of computer time on multi-node institutional High-Performance Computing facilities. In this paper we focus on the radiation transport aspect of plume modeling. Here, we describe a phenomenological method for approximating the amounts of radiation that reach ground level from large volumes of a static radioactive plume that can be calculated on a stand-alone personal computer in much shorter computation times than those usually needed for such large volume evaluations. We refer to this method as the Density Scaling Approximation (DSA). Its ability to approximate ground-level count rates of large plumes comes from using a small-plume volume with a scaled-up value of air density to simulate the same number of scatterings that occur during transport in larger plume volumes at normal air density. We demonstrate the DSA by using a 100 m-diameter air-filled hemispherical dome geometry with a uniform volumetric activity of 135 Xe gas throughout the air-filled volume. The DSA for a larger dome diameter is obtained by evaluating the 100 m dome with an air density scaled up by the linear ratio of the larger diameter to the 100 m diameter. We find that this approximation works well for dome diameters up to 1200 m – the largest diameter studied and a size more than sufficient for accounting for all the radiation from 135 Xe. Moreover, most of our DSA results can be calculated over 500 times faster than corresponding full-sized geometry with normal air density. To help evaluate the accuracy of the DSA and gain insight into how well it can reproduce different regions of the spectra, we use three, easily understood regions of interest to compare the DSA results to the full-sized geometry at normal air density results. These regions are the full-energy peak, the region of single-Compton scattering, and the region of multiple-Compton scattering. We show how the dominance of the Compton scattering mechanism determines this division and thus provides insight into how Compton scattering is manifested in spectra from photon scattering through air in general, and how well the DSA approximation works.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2023

Fourier-informed knot placement schemes for B-spline approximation

Fitting B-splines to scientific data is especially challenging when the given data contain noise, jumps, or corners. Here, we describe how periodic data sets with these features can be efficiently approximated with B-splines by analyzing the Fourier spectrum of the data. Our method uses a collection of spectral filters to compute high-order derivatives, smoothed versions of noisy data, and the locations of jump discontinuities. Further, these quantities are then combined to choose knots that capture the qualitative features of the data, leading to accurate B-spline approximations with few knots. The method we introduce is direct and does not require any intermediate B-spline fitting before choosing the final knot distribution. Aside from fast Fourier transforms to transfer to and from Fourier space, the method runs in linear time with very little communication. We assess performance on several test cases in one and two dimensions, including data sets with jump discontinuities and noise. These tests show the method fits discontinuous data without spurious oscillations and remains effective in the presence of noise.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

What do physics-informed DeepONets learn? Understanding and improving training for scientific computing applications

Physics-informed deep operator networks (DeepONets) have emerged as a promising approach toward numerically approximating the solution of partial differential equations (PDEs). In this work, we aim to develop further understanding of what is being learned by physics-informed DeepONets by assessing the universality of the extracted basis functions and demonstrating their potential toward model reduction with spectral methods. Results provide clarity about measuring the performance of a physics-informed DeepONet through the decays of singular values and expansion coefficients. In addition, we propose a transfer learning approach for improving training for physics-informed DeepONets between parameters of the same PDE as well as across different, but related, PDEs where these models struggle to train well. This approach results in significant error reduction and learned basis functions that are more effective in representing the solution of a PDE.

Deep operator networks↗
DOE OSTI2022

Fock-Space Schrieffer–Wolff Transformation: Classically-Assisted Rank-Reduced Quantum Phase Estimation Algorithm

We present an extension of many-body downfolding methods to reduce the resources required in the quantum phase estimation (QPE) algorithm. In this paper, we focus on the Schrieffer–Wolff (SW) transformation of the electronic Hamiltonians for molecular systems that provides significant simplifications of quantum circuits for simulations of quantum dynamics. We demonstrate that by employing Fock-space variants of the SW transformation (or rank-reducing similarity transformations (RRST)) one can significantly increase the locality of the qubit-mapped similarity-transformed Hamiltonians. The practical utilization of the SW-RRST formalism is associated with a series of approximations discussed in the manuscript. In particular, amplitudes that define RRST can be evaluated using conventional computers and then encoded on quantum computers. The SW-RRST QPE quantum algorithms can also be viewed as an extension of the standard state-specific coupled-cluster downfolding methods to provide a robust alternative to the traditional QPE algorithms to identify the ground and excited states for systems with various numbers of electrons using the same Fock-space representations of the downfolded Hamiltonian. The RRST formalism serves as a design principle for developing new classes of approximate schemes that reduce the complexity of quantum circuits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

A comparison of Gaussian processes and neural networks for computer model emulation and calibration

The Department of Energy relies on complex physics simulations for prediction in domains like cosmology, nuclear theory, and materials science. These simulations are often extremely computationally intensive, with some requiring days or weeks for a single simulation. In order to assure their accuracy, these models are calibrated against observational data in order to estimate inputs and systematic biases. Because of their great computational complexity, this process typically requires the construction of an emulator, a fast approximation to the simulation. In this paper, two emulator approaches are compared: Gaussian process regression and neural networks. Their emulation accuracy and calibration performance on three real problems of Department of Energy interest is considered. On these problems, the Gaussian process emulator tends to be more accurate with narrower, but still well-calibrated uncertainty estimates. The neural network emulator is accurate, but tends to have large uncertainty on its predictions. Finally, as a result, calibration with the Gaussian process emulator produces more constrained posteriors that still perform well in prediction.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

NLO QCD corrections to full off-shell production of $t\overline{t}Z$ including leptonic decays

Motivated by ongoing new physics searches in the top-quark sector at the Large Hadron Collider we report on the calculation of NLO QCD corrections to the Standard Model $pp$→$t\overline{t}Z + X$ process in the tetra-lepton decay channel. This calculation is based on the matrix elements for the $e^+v_eμ^-\bar v_μb\bar bτ^+τ^-$ final state and includes all resonant and non-resonant Feynman diagrams, interferences and off-shell effects of the top quark as well as the W and Z gauge bosons. Also incorporated are photon-induced contributions. As it is customary for such studies, we show theoretical predictions for both fixed and dynamical factorisation and renormalisation scale choices and different PDF sets. Furthermore, we study the main theoretical uncertainties that are associated with neglected higher-order terms in the perturbative expansion and with the parameterisation of the PDF sets. In order to investigate the size of off-shell effects and higher-order corrections in top-quark decays, we perform a second computation for this process, which is based on the narrow-width-approximation where the top quarks, W and Z gauge bosons are kept on-shell. Results are given for the integrated and differential fiducial cross sections for the LHC Run II center-of-mass energy of 13 TeV.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Efficient discontinuous Galerkin implementations and preconditioners for implicit unsteady compressible flow simulations

This work presents and compares efficient implementations of high-order discontinuous Galerkin methods: a modal matrix-free discontinuous Galerkin (DG) method, a hybridizable discontinuous Galerkin (HDG) method, and a primal formulation of HDG, applied to the implicit solution of unsteady compressible flows. The matrix-free implementation allows for a reduction of the memory footprint of the solver when dealing with implicit time-accurate discretizations. HDG reduces the number of globally-coupled degrees of freedom relative to DG, at high order, by statically condensing element-interior degrees of freedom from the system in favor of face unknowns. The primal formulation further reduces the element-interior degrees of freedom by eliminating the gradient as a separate unknown. This paper introduces a p-multigrid preconditioner implementation for these discretizations and presents results for various flow problems. Benefits of the p-multigrid strategy relative to simpler, less expensive, preconditioners are observed for stiff systems, such as those arising from low-Mach number flows at high-order approximation. The p-multigrid preconditioner also shows excellent scalability for parallel computations. Finally, additional savings in both speed and memory occur with a matrix-free/reduced version of the preconditioner.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Verification and validation of the open-source plasma fluid code: Zapdos

Zapdos is an open-source finite element plasma fluid solver based on the MOOSE multiphysics framework. This paper outlines Zapdos verification, benchmarking, and validation efforts for 1D and 2D RF capacitively coupled plasma discharge models for mid-range pressures (0.1 - 1 Torr). The verification process involved using the method of manufactured solutions to assess Zapdos spatial and temporal error convergence. L2 errors ranged from 10 -2 to 10 -4 , while the convergence’s slope were in agreement with the predicted slopes for the tested variable and time integration orders. The benchmarking process involved comparisons to previously results from the validated finite element code, LSODI. These works included 1D and 2D simulations for a range of plasma parameters (densities, temperatures, voltage, etc.). For the 1D cases, Zapdos and LSODI results were in very good agreement. In the 2D cases, variable behaviors matched, with slight discrepancies in peak values. The validation process involved comparisons to experimental works including electron density measurements by microwave interferometry and metastable density measurements by planar laser-induced fluorescence imaging. Results shown reasonable agreement at higher pressure, with results starting to diverge at low pressures. Furthermore, probable causes for this diverges are the limitation of the fluid assumption for plasmas at low pressure, or the need for more robust boundary conditions. Overall, Zapdos shown reasonable results for the verification, benchmarking, and validation efforts, and Zapdos can be downloaded at https://github.com/shannon-lab/zapdos.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Implicit shock tracking for unsteady flows by the method of lines

Here, a recently developed high-order implicit shock tracking (HOIST) framework for resolving discontinuous solutions of inviscid, steady conservation laws is extended to the unsteady case. Central to the framework is an optimization problem which simultaneously computes a discontinuity-aligned mesh and the corresponding high-order approximation to the flow, which provides nonlinear stabilization and a high-order approximation to the solution. This work extends the implicit shock tracking framework to the case of unsteady conservation laws using a method of lines discretization via a diagonally implicit Runge-Kutta method by “solving a steady problem at each timestep”. We formulate and solve an optimization problem that produces a feature-aligned mesh and solution at each Runge-Kutta stage of each timestep, and advance this solution in time by standard Runge-Kutta update formulas. A Rankine-Hugoniot based prediction of the shock location together with a high-order, untangling mesh smoothing procedure provides a high-quality initial guess for the optimization problem at each time, which results in rapid convergence of the sequential quadratic programing (SQP) optimization solver. This method is shown to deliver highly accurate solutions on coarse, high-order discretizations without nonlinear stabilization and recover the design accuracy of the Runge-Kutta scheme. We demonstrate this framework on a series of inviscid, unsteady conservation laws in both one- and two- dimensions. We also verify that our method is able to recover the design order of accuracy of our time integrator in the presence of a strong discontinuity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

SCF Framework, HF Stability, and RPA Correlation for Jordan–Wigner-Transformed Spin Hamiltonians on Arbitrary Coupling Topologies

Mapping spins to fermions via the Jordan–Wigner (JW) transformation can render mean-field (Hartree–Fock, HF) descriptions effective for strongly correlated spin systems. As established in recent work, the application of such approaches is not limited by the nonlocal structure of JW strings or by site ordering because string operators can be absorbed into Thouless rotations of a Slater determinant, and the variational optimization of a unitary Lie-algebraic similarity transformation removes any ordering dependence. Leveraging these ideas, we develop a self-consistent field (SCF) scheme that expresses the mean-field energy as a functional of the single-particle density matrix, providing an alternative to gradient-based optimization of Thouless parameters. We derive the analytical orbital Hessian to diagnose HF stability and compute the ground-state correlation energy through the random-phase approximation (RPA). Benchmark results for the XXZ and J 1 –J 2 model on one- and two-dimensional lattices demonstrate that RPA significantly improves mean-field accuracy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Computational Discovery of Intermolecular Singlet Fission Materials Using Many-Body Perturbation Theory

Intermolecular singlet fission (SF) is the conversion of a photogenerated singlet exciton into two triplet excitons residing on different molecules. SF has the potential to enhance the conversion efficiency of solar cells by harvesting two charge carriers from one high-energy photon, whose surplus energy would otherwise be lost to heat. The development of commercial SF-augmented modules is hindered by the limited selection of molecular crystals that exhibit intermolecular SF in the solid state. Computational exploration may accelerate the discovery of new SF materials. The GW approximation and Bethe–Salpeter equation (GW+BSE) within the framework of many-body perturbation theory is the current state-of-the-art method for calculating the excited-state properties of molecular crystals with periodic boundary conditions. In this Review, we discuss the usage of GW+BSE to assess candidate SF materials as well as its combination with low-cost physical or machine learned models in materials discovery workflows. We demonstrate three successful strategies for the discovery of new SF materials: (i) functionalization of known materials to tune their properties, (ii) finding potential polymorphs with improved crystal packing, and (iii) exploring new classes of materials. In addition, three new candidate SF materials are proposed here, which have not been published previously.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Optimal Design of Sustainable Ammonia-Based Food–Energy–Water Systems with Nitrogen Management

As the basis for virtually any form of nitrogen fertilizers, ammonia plays a vital role in agriculture; in addition, there has been an increased interest in its use as a carbon-free energy carrier. However, ammonia is also associated with two major environmental concerns: CO 2 emissions from the conventional production process and nitrogen pollution from the excessive use of ammonia-based fertilizers. To mitigate these environmental impacts, we develop an optimization framework for the design of a sustainable ammonia-based agricultural system that synergistically integrates the production of ammonia from renewable resources and effective measures for nitrogen management. The proposed model captures the effect of intermittency by incorporating both design and detailed operational decisions. Here, by applying a multiscale time representation that reduces the problem size and a tailored surrogate model that accurately approximates model nonlinearity, we are able to achieve optimal solutions within reasonable computation times. A computational case study is conducted using real-world data from a local farm in Morris, Minnesota, and the results indicate the trade-off between cost and nitrogen loss. Importantly, we show that practicing effective nitrogen management can significantly reduce the nitrogen loss with only a small increase in net present cost.

10 SYNTHETIC FUELS↗
DOE OSTI2022

Scaling quantum approximate optimization on near-term hardware

The quantum approximate optimization algorithm (QAOA) is an approach for near-term quantum computers to potentially demonstrate computational advantage in solving combinatorial optimization problems. However, the viability of the QAOA depends on how its performance and resource requirements scale with problem size and complexity for realistic hardware implementations. Here, we quantify scaling of the expected resource requirements by synthesizing optimized circuits for hardware architectures with varying levels of connectivity. Assuming noisy gate operations, we estimate the number of measurements needed to sample the output of the idealized QAOA circuit with high probability. We show the number of measurements, and hence total time to solution, grows exponentially in problem size and problem graph degree as well as depth of the QAOA ansatz, gate infidelities, and inverse hardware graph degree. These problems may be alleviated by increasing hardware connectivity or by recently proposed modifications to the QAOA that achieve higher performance with fewer circuit layers.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Photoionization of the I 4d and valence orbitals of methyl iodide

Here, the photoabsorption and photoionization dynamics of the I 4d and valence orbitals in methyl iodide have been studied both experimentally and theoretically. Synchrotron radiation has been employed to measure the total ion yield in the vicinity of the I 4d ionization thresholds. The observed structure, due to excitations into Rydberg or valence states, has been assigned using transition energies and relative intensities computed with time-dependent density functional theory within the Tamm–Dancoff approximation. Photoelectron spectra, recorded with plane polarized radiation in two polarization geometries, have allowed the effect of autoionization on the valence electron angular distributions to be investigated. The spectra obtained at photon energies of 50.62 and 52.34 eV, coinciding respectively with the I 4d 5/2 → σ* and 4d 3/2 → σ* transitions, reveal, in addition to valence shell photoelectron bands, features not associated with simple photoionization of the parent molecule. High resolution photoelectron spectra of the I 4d main-lines display structure resulting from spin–orbit coupling and molecular field splitting. The binding energies of the five states contributing to the (I 4d) -1 ionization have been determined. The iodine (in CH 3 I) N 45 VV Auger spectrum has been measured and the observed structure has been assigned using the core hole binding energies derived in the present work together with established ionization energies of the doubly charged ion. The experimentally determined Auger electron angular distributions have been discussed in relation to the theoretical angular distribution parameter characterizing the spatial alignment of molecular axes in the (I 4d) -1 state.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

Seismic waves in medium with poroelastic/elastic interfaces: a two-dimensional P-SV finite-difference modelling

SUMMARY We present a new methodology of the finite-difference (FD) modelling of seismic wave propagation in a strongly heterogeneous medium composed of poroelastic (P) and (strictly) elastic (E) parts. The medium can include P/P, P/E and E/E material interfaces of arbitrary shapes. The poroelastic part can be with (i) zero resistive friction, (ii) non-zero constant resistive friction or (iii) JKD model of the frequency-dependent permeability and resistive friction. Our FD scheme is capable of subcell resolution: a material interface can have an arbitrary position in the spatial grid. The scheme keeps computational efficiency of the scheme for a smoothly and weakly heterogeneous medium (medium without material interfaces). Numerical tests against independent analytical, semi-analytical and spectral-element methods prove the efficiency and accuracy of our FD modelling. In numerical examples, we indicate effect of the P/E interfaces for the poroelastic medium with a constant resistive friction and medium with the JKD model of the frequency-dependent permeability and resistive friction. We address the 2-D P-SV problem. The approach can be readily extended to the 3-D problem.

58 GEOSCIENCES↗
DOE OSTI2023

Exploring the dependence of gas cooling and heating functions on the incident radiation field with machine learning

ABSTRACT Gas cooling and heating functions play a crucial role in galaxy formation. But, it is computationally expensive to exactly compute these functions in the presence of an incident radiation field. These computations can be greatly sped up by using interpolation tables of pre-computed values, at the expense of making significant and sometimes even unjustified approximations. Here, we explore the capacity of machine learning to approximate cooling and heating functions with a generalized radiation field. Specifically, we use the machine learning algorithm XGBoost to predict cooling and heating functions calculated with the photoionization code cloudy at fixed metallicity, using different combinations of photoionization rates as features. We perform a constrained quadratic fit in metallicity to enable a fair comparison with traditional interpolation methods at arbitrary metallicity. We consider the relative importance of various photoionization rates through both a principal component analysis (PCA) and calculation of SHapley Additive exPlanation (shap) values for our XGBoost models. We use feature importance information to select different subsets of rates to use in model training. Our XGBoost models outperform a traditional interpolation approach at each fixed metallicity, regardless of feature selection. At arbitrary metallicity, we are able to reduce the frequency of the largest cooling and heating function errors compared to an interpolation table. We find that the primary bottleneck to increasing accuracy lies in accurately capturing the metallicity dependence. This study demonstrates the potential of machine learning methods such as XGBoost to capture the non-linear behaviour of cooling and heating functions.

79 ASTRONOMY AND ASTROPHYSICS↗