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DOE OSTI2020

Quantum approximate optimization of the long-range Ising model with a trapped-ion quantum simulator

Quantum computers and simulators may offer significant advantages over their classical counterparts, providing insights into quantum many-body systems and possibly improving performance for solving exponentially hard problems, such as optimization and satisfiability. Here, we report the implementation of a low-depth Quantum Approximate Optimization Algorithm (QAOA) using an analog quantum simulator. We estimate the ground-state energy of the Transverse Field Ising Model with long-range interactions with tunable range, and we optimize the corresponding combinatorial classical problem by sampling the QAOA output with high-fidelity, single-shot, individual qubit measurements. We execute the algorithm with both an exhaustive search and closed-loop optimization of the variational parameters, approximating the ground-state energy with up to 40 trapped-ion qubits. We benchmark the experiment with bootstrapping heuristic methods scaling polynomially with the system size. We observe, in agreement with numerics, that the QAOA performance does not degrade significantly as we scale up the system size and that the runtime is approximately independent from the number of qubits. We finally give a comprehensive analysis of the errors occurring in our system, a crucial step in the path forward toward the application of the QAOA to more general problem instances.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2018

A computationally efficient ductile damage model accounting for nucleation and micro-inertia at high triaxialities

The computational formulation of a micro-mechanical material model for the dynamic failure of ductile metals is presented in this paper. The statistical nature of porosity initiation is accounted for by introducing an arbitrary probability density function which describes the pores nucleation pressures. Each micropore within the representative volume element is modeled as a thick spherical shell made of plastically incompressible material. The treatment of porosity by a distribution of thick-walled spheres also allows for the inclusion of micro-inertia effects under conditions of shock and dynamic loading. The second order ordinary differential equation governing the microscopic porosity evolution is solved with a robust implicit procedure. A new Chebyshev collocation method is employed to approximate the porosity distribution and remapping is used to optimize memory usage. The adaptive approximation of the porosity distribution leads to a reduction of computational time and memory usage of up to two orders of magnitude. Moreover, the proposed model affords consistent performance: changing the nucleation pressure probability density function and/or the applied strain rate does not reduce accuracy or computational efficiency of the material model. The numerical performance of the model and algorithms presented is tested against three problems for high density tantalum: single void, one-dimensional uniaxial strain, and two-dimensional plate impact. Here, the results using the integration and algorithmic advances suggest a significant improvement in computational efficiency and accuracy over previous treatments for dynamic loading conditions.

42 ENGINEERING↗

DOE OSTI2014

Analytical estimation of emission zone mean position and width in organic light-emitting diodes from emission pattern image-source interference fringes

We present an analytical method for evaluating the first and second moments of the effective exciton spatial distribution in organic light-emitting diodes (OLED) from measured emission patterns. Specifically, the suggested algorithm estimates the emission zone mean position and width, respectively, from two distinct features of the pattern produced by interference between the emission sources and their images (induced by the reflective cathode): the angles in which interference extrema are observed, and the prominence of interference fringes. The relations between these parameters are derived rigorously for a general OLED structure, indicating that extrema angles are related to the mean position of the radiating excitons via Bragg's condition, and the spatial broadening is related to the attenuation of the image-source interference prominence due to an averaging effect. The method is applied successfully both on simulated emission patterns and on experimental data, exhibiting a very good agreement with the results obtained by numerical techniques. We investigate the method performance in detail, showing that it is capable of producing accurate estimations for a wide range of source-cathode separation distances, provided that the measured spectral interval is large enough; guidelines for achieving reliable evaluations are deduced from these results as well. As opposed to numerical fitting tools employed to perform similar tasks to date, our approximate method explicitly utilizes physical intuition and requires far less computational effort (no fitting is involved). Hence, applications that do not require highly resolved estimations, e.g., preliminary design and production-line verification, can benefit substantially from the analytical algorithm, when applicable. This introduces a novel set of efficient tools for OLED engineering, highly important in the view of the crucial role the exciton distribution plays in determining the device performance.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2019

DCA++: A software framework to solve correlated electron problems with modern quantum cluster methods

We present the first open release of the DCA++ project, a high-performance research software framework to solve quantum many-body problems with cutting edge quantum cluster algorithms. DCA++ implements the dynamical cluster approximation (DCA) and its DCA extension with a continuous self-energy. The algorithms capture nonlocal correlations in strongly correlated electron systems, thereby giving insight into high-$T_c$ superconductivity. The code’s scalability allows efficient usage of systems at all scales, from workstations to leadership computers. With regard to the increasing heterogeneity of modern computing machines, DCA++ provides portable performance on conventional and emerging new architectures, such as hybrid CPU–GPU, sustaining multiple petaflops on ORNL’s Titan and CSCS’ Piz Daint supercomputers. Moreover, we show how sustainable and scalable development of the code base has been achieved by adopting standard techniques of the software industry. These include employing a distributed version control system, applying test-driven development and following continuous integration.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

CE TSUNAMI-3D Algorithm Improvements in SCALE 6.2

The TSUNAMI (Tools for Sensitivity and Uncertainty Analysis Methodology Implementation) capabilities within the SCALE code system make use of sensitivity coefficients for an extensive number of criticality safety applications such as quantifying the data-induced uncertainty in the eigenvalue of critical systems, assessing the neutronic similarity between different systems, quantifying computational biases, and guiding nuclear data adjustment studies. The continuous-energy (CE) TSUNAMI-3D code is a new tool included in SCALE 6.2 that allows for eigenvalue and generalized response sensitivity calculations using high-fidelity CE Monte Carlo methods. This paper describes several improvements to CE TSUNAMI-3D beyond those previously published. These improvements primarily consist of - A multi-response capability for the CE TSUNAMI generalized response sensitivity calculation mode; and - Efficiency improvements in CE TSUNAMI's Iterated Fission Probability (IFP)-based algorithms. This paper documents several improvements to the CE TSUNAMI-3D sensitivity algorithms included in the SCALE 6.2 release. These improvements have enabled the simulation of multiple GPT responses within a single CE TSUNAMI simulation, a feature that increases the memory footprint of the simulations by approximately 1-3% per response and the runtime by approximately 1-2%, per response. These algorithmic improvements have also significantly improved the computational efficiency of CE TSUNAMI IFP-based sensitivity calculations, reducing the memory footprints approximately by a factor of 3 and the simulation runtimes by 10-70%. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2012

Strategic Analysis of Complex Security Scenarios

Many advanced technical tools are available to prevent attacks on national infrastructure. Nevertheless, while traditional analyses of security problems have succeeded in producing good technical solutions, they have often ignored the human factor integral to these problems. Human attackers (who may be individuals or state-level attackers) expend substantial effort to breach security because they have the incentive for doing so. People involved in implementing security follow individual incentives, which need not align with global security concerns; consequently, desired security solutions are often implemented poorly, or not at all. This complex interplay between individual incentives and global (organizational and/or national) goals can be modeled and analyzed using game theoretic techniques. By analyzing not only what is possible, but also what is motivated, a holistic approach to security problems can be developed, informing policy and providing tools to policy makers. We study game theoretic models that unify several current incentive-based approaches to security, and develop simulation-based and mathematical optimization methods for analyzing such models that exploit the high-performance computing capabilities at Sandia. Our first model studies security in interdependent settings, offering a scalable local search heuristic to approximate optimal security decisions in general, and a linear programming approach, coupled with simulations of consequences, to optimally compute security in an important special case. Our second class of models addresses security patrolling problems when an adversary gets to observe the patrol location. We present a general framework, based on stochastic games, for computing optimal security policies in such settings, and present more scalable tools that apply in the important special cases. Our third contribution is a model of security that involves many defenders, but only models non-adaptive attackers (or natural disasters, inadvertent errors, etc). In this model, we demonstrate that the security decisions of many players result in global security configuration that is not very far from optimal, and is much more resilient to environment changes that an optimal solution. This positive effect dissipates, however, when the number of decision makers becomes too large.

Vorobeychik, Yevgeniy↗

DOE OSTI2017

A Taylor Expansion-Based Adaptive Design Strategy for Global Surrogate Modeling With Applications in Groundwater Modeling

Global sensitivity analysis (GSA) and uncertainty quantification (UQ) for groundwater modeling are challenging because of the model complexity and significant computational requirements. To reduce the massive computational cost, a cheap-to-evaluate surrogate model is usually constructed to approximate and replace the expensive groundwater models in the GSA and UQ. Constructing an accurate surrogate requires actual model simulations on a number of parameter samples. Thus, a robust experimental design strategy is desired to locate informative samples so as to reduce the computational cost in surrogate construction and consequently to improve the efficiency in the GSA and UQ. In this study, we develop a Taylor expansion-based adaptive design (TEAD) that aims to build an accurate global surrogate model with a small training sample size. TEAD defines a novel hybrid score function to search informative samples, and a robust stopping criterion to terminate the sample search that guarantees the resulted approximation errors satisfy the desired accuracy. The good performance of TEAD in building global surrogate models is demonstrated in seven analytical functions with different dimensionality and complexity in comparison to two widely used experimental design methods. The application of the TEAD-based surrogate method in two groundwater models shows that the TEAD design can effectively improve the computational efficiency of GSA and UQ for groundwater modeling.

58 GEOSCIENCES↗

DOE OSTI2023

Residual-based error correction for neural operator accelerated infinite-dimensional Bayesian inverse problems

We explore using neural operators, or neural network representations of nonlinear maps between function spaces, to accelerate infinite-dimensional Bayesian inverse problems (BIPs) with models governed by nonlinear parametric partial differential equations (PDEs). Neural operators have gained significant attention in recent years for their ability to approximate the parameter-to-solution maps defined by PDEs using as training data solutions of PDEs at a limited number of parameter samples. The computational cost of BIPs can be drastically reduced if the large number of PDE solves required for posterior characterization are replaced with evaluations of trained neural operators. However, reducing error in the resulting BIP solutions via reducing the approximation error of the neural operators in training can be challenging and unreliable. We provide an a priori error bound result that implies certain BIPs can be ill-conditioned to the approximation error of neural operators, thus leading to inaccessible accuracy requirements in training. To reliably deploy neural operators in BIPs, we consider a strategy for enhancing the performance of neural operators: correcting the prediction of a trained neural operator by solving a linear variational problem based on the PDE residual. We show that a trained neural operator with error correction can achieve a quadratic reduction of its approximation error, all while retaining substantial computational speedups of posterior sampling when models are governed by highly nonlinear PDEs. The strategy is applied to two numerical examples of BIPs based on a nonlinear reaction–diffusion problem and deformation of hyperelastic materials. We demonstrate that posterior representations of the two BIPs produced using trained neural operators are greatly and consistently enhanced by error correction.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Quantum-Based Molecular Dynamics Simulations Using Tensor Cores

Tensor cores, along with tensor processing units, represent a new form of hardware acceleration specifically designed for deep neural network calculations in artificial intelligence applications. Tensor cores provide extraordinary computational speed and energy efficiency but with the caveat that they were designed for tensor contractions (matrix–matrix multiplications) using only low-precision floating-point operations. Despite this perceived limitation, we demonstrate how tensor cores can be applied with high efficiency to the challenging and numerically sensitive problem of quantum-based Born–Oppenheimer molecular dynamics, which requires highly accurate electronic structure optimizations and conservative force evaluations. The interatomic forces are calculated on-the-fly from an electronic structure that is obtained from a generalized deep neural network, where the computational structure naturally takes advantage of the exceptional processing power of the tensor cores and allows for high performance in excess of 100 Tflops on a single Nvidia A100 GPU. Stable molecular dynamics trajectories are generated using the framework of extended Lagrangian Born–Oppenheimer molecular dynamics, which combines computational efficiency with long-term stability, even when using approximate charge relaxations and force evaluations that are limited in accuracy by the numerically noisy conditions caused by the low-precision tensor core floating-point operations. A canonical ensemble simulation scheme is also presented, where the additional numerical noise in the calculated forces is absorbed into a Langevin-like dynamics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Exploring the scaling limitations of the variational quantum eigensolver with the bond dissociation of hydride diatomic molecules

Abstract Materials simulations involving strongly correlated electrons pose fundamental challenges to state‐of‐the‐art electronic structure methods but are hypothesized to be the ideal use case for quantum computing algorithms. To date, no quantum computer has simulated a molecule of a size and complexity relevant to real‐world applications, despite the fact that the variational quantum eigensolver (VQE) algorithm can predict chemically accurate total energies. Nevertheless, because of the many applications of moderately sized, strongly correlated systems, such as molecular catalysts, the successful use of the VQE stands as an important waypoint in the advancement toward useful chemical modeling on near‐term quantum processors. In this paper, we take a significant step in this direction. We lay out the steps, write, and run parallel code for an (emulated) quantum computer to compute the bond dissociation curves of the TiH, LiH, NaH, and KH diatomic hydride molecules using the VQE. TiH was chosen as a relatively simple chemical system that incorporates d orbitals and strong electron correlation. Because current VQE implementations on existing quantum hardware are limited by qubit error rates, the number of qubits available, and the allowable gate depth, recent studies using it have focused on chemical systems involving s and p block elements. Through VQE + UCCSD calculations of TiH, we evaluate the near‐term feasibility of modeling a molecule with d‐orbitals on real quantum hardware. We demonstrate that the inclusion of d‐orbitals and the use of the UCCSD ansatz, which are both necessary to capture the correct TiH physics, dramatically increase the cost of this problem. We estimate the approximate error rates necessary to model TiH on current quantum computing hardware using VQE + UCCSD and show them to likely be prohibitive until significant improvements in hardware and error correction algorithms are available.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

tih_vqe [SWR-23-32]

This software supports the paper, "Exploring the scaling limitations of the variational quantum eigensolver with the bond dissociation of hydride diatomic molecules," published in the International Journal of Quantum Chemistry, whose abstract is as follows: Materials simulations involving strongly correlated electrons pose fundamental challenges to state-of-the-art electronic structure methods but are hypothesized to be the ideal use case for quantum computing. To date, no quantum computer has simulated a molecule of a size and complexity relevant to real-world applications, despite the fact that the variational quantum eigensolver (VQE) algorithm can predict chemically accurate total energies. Nevertheless, because of the many applications of moderately-sized, strongly correlated systems, such as molecular catalysts, the successful use of the VQE stands as an important waypoint in the advancement toward useful chemical modeling on near-term quantum processors. In this paper, we take a significant step in this direction. We lay out the steps, write, and run parallel code for an (emulated) quantum computer to compute the bond dissociation curves of the TiH, LiH, NaH, and KH diatomic hydride molecules using VQE. TiH was chosen as a relatively simple chemical system that incorporates d orbitals and strong electron correlation. Because current VQE implementations on existing quantum hardware are limited by qubit error rates, the number of qubits available, and the allowable gate depth, recent studies have focused on chemical systems involving s and p block elements. Through VQE + UCCSD calculations of TiH, we evaluate the near-term feasibility of modeling a molecule with d-orbitals on real quantum hardware. We demonstrate that the inclusion of d-orbitals and the use of the UCCSD ansatz, which are both necessary to capture the correct TiH physics, dramatically increase the cost of this problem. We estimate the approximate error rates necessary to model TiH on current quantum computing hardware using VQE+UCCSD and show them to likely be prohibitive until significant improvements in hardware and error correction algorithms are available.

Graf, Peter↗

DOE OSTI2020

2D-FFTLog: efficient computation of real-space covariance matrices for galaxy clustering and weak lensing

ABSTRACT Accurate covariance matrices for two-point functions are critical for inferring cosmological parameters in likelihood analyses of large-scale structure surveys. Among various approaches to obtaining the covariance, analytic computation is much faster and less noisy than estimation from data or simulations. However, the transform of covariances from Fourier space to real space involves integrals with two Bessel integrals, which are numerically slow and easily affected by numerical uncertainties. Inaccurate covariances may lead to significant errors in the inference of the cosmological parameters. In this paper, we introduce a 2D-FFTLog algorithm for efficient, accurate, and numerically stable computation of non-Gaussian real-space covariances for both 3D and projected statistics. The 2D-FFTLog algorithm is easily extended to perform real-space bin-averaging. We apply the algorithm to the covariances for galaxy clustering and weak lensing for a Dark Energy Survey Year 3-like and a Rubin Observatory’s Legacy Survey of Space and Time Year 1-like survey, and demonstrate that for both surveys, our algorithm can produce numerically stable angular bin-averaged covariances with the flat sky approximation, which are sufficiently accurate for inferring cosmological parameters. The code CosmoCov for computing the real-space covariances with or without the flat-sky approximation is released along with this paper.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Edge ICRF simulations in 3D geometry: From MHD equilibrium to coupling determination

We present in this work a consistent numerical scheme that allows the computation of 3D magnetic fields a nd 3D density profiles and their usage in ion cyclotron range of frequencies (ICRF) coupling simulations. We first utilize the PARVMEC code to compute the 3D free-boundary plasma equilibrium in the ideal magnetohydrodynamic (MHD) approximation. Since the PARVMEC solution is only defined within the last closed flux surface (LCFS), the magnetic field domain is extended to the scrape-off layer (SOL) via the BMW code, which computes a divergence-free magnetic field solution arising from the external conductors’ vacuum field a nd t he PARVMEC flux surface currents. This magnetic reconstruction is then used in the EMC3-EIRENE transport code in order to compute 3D density profiles. In the last step, the RAPLICASOL code is utilized to compute the ICRF antenna S-matrices resulting from the 3D density profiles. We exemplify this scheme for the ASDEX Upgrade tokamak. A new implementation of a curved model for the ASDEX Upgrade ICRF 2-strap antenna in RAPLICASOL allows simulations in realistic geometry, without any coordinate transformations.

Lopez, Graham↗

DOE OSTI2025

Reduced basis approximations of parameterized dynamical partial differential equations via neural networks

Projection-based reduced order models are effective at approximating parameter-dependent differential equations that are parametrically separable. When parametric separability is not satisfied, which occurs in both linear and nonlinear problems, projection-based methods fail to adequately reduce the computational complexity. Devising alternative reduced order models is crucial for obtaining efficient and accurate approximations to expensive high-fidelity models. In this work, we develop a timestepping procedure for dynamical parameter-dependent problems, in which a neural-network is trained to propagate the coefficients of a reduced basis expansion. This results in an online stage with a computational cost independent of the size of the underlying problem. Here, we demonstrate our method on several parabolic partial differential equations, including a problem that is not parametrically separable.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

MICROCALORIMETER SPECTROSCOPY AT HIGH PULSE RATES: A MULTI-PULSE FITTING TECHNIQUE

Transition Edge Sensor microcalorimeters can measure X-ray and gamma-ray energies with very high energy resolution and high photon-collection efficiency. For this technology to reach its full potential in future X-ray observatories, each sensor must be able to measure hundreds or even thousands of photon energies per second. Current “optimal filtering” approaches to achieve the best possible energy resolution work only for photons that are well isolated in time, a requirement which is in direct conflict with the need for high-rate measurements. We describe a new analysis procedure to allow fitting for the pulse height of all photons even in the presence of heavy pulse pile-up. In the limit of isolated pulses, the technique reduces to standard optimal filtering with long records. We employ reasonable approximations to the noise covariance function in order to render this procedure computationally viable even for very long data records. The technique is employed to analyze X-ray emission spectra at 600 eV and 6 keV at rates up to 250 counts s{sup −1} in microcalorimeters having exponential signal decay times of approximately 1.2 ms.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2012

Modeling CANDU-6 liquid zone controllers for effects of thorium-based fuels

We use the DRAGON code to model the CANDU-6 liquid zone controllers and evaluate the effects of thorium-based fuels on their incremental cross sections and reactivity worth. We optimize both the numerical quadrature and spatial discretization for 2D cell models in order to provide accurate fuel properties for 3D liquid zone controller supercell models. We propose a low computer cost parameterized pseudo-exact 3D cluster geometries modeling approach that avoids tracking issues on small external surfaces. This methodology provides consistent incremental cross sections and reactivity worths when the thickness of the buffer region is reduced. When compared with an approximate annular geometry representation of the fuel and coolant region, we observe that the cluster description of fuel bundles in the supercell models does not increase considerably the precision of the results while increasing substantially the CPU time. In addition, this comparison shows that it is imperative to finely describe the liquid zone controller geometry since it has a strong impact of the incremental cross sections. This paper also shows that liquid zone controller reactivity worth is greatly decreased in presence of thorium-based fuels compared to the reference natural uranium fuel, since the fission and the fast to thermal scattering incremental cross sections are higher for the new fuels. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2023

FastACE

SAND2024-01893O The Fast Adaptive Cosine Estimator (FastACE) algorithm modifies the well-known Adaptive Cosine Estimator for target detection in hyperspectral imagery. Specifically, FastACE modifies the computation of the background precision matrix (C_b^-1) under a Vecchia approximation. That is, each spectral band, conditioned on a local neighborhood of bands around that band, is independent of the other spectral bands. The FastACE algorithm leverages a parameterizable, auto-regressive neighborhood for the conditional independence assumption. The underlying math used for computing detection scores is equivalent to ACE, but it is implemented within FastACE. The software implements a target detection algorithm and associated utilities for target detection in hyperspectral imagery. Provided with a hyperspectral image and corresponding target signature, it produces relevant background statistics and the corresponding detection scores for the target signature in the image. The software is designed to integrate into other end-user applications or processing. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & 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.

VanderLaan, John↗

DOE OSTI2021

Ensemble Learning Based Convex Approximation of Three-Phase Power Flow

Though the convex optimization has been widely used in power systems, it still cannot guarantee to yield a tight (accurate) solution to some problems. To mitigate this issue, this paper proposes an ensemble learning based convex approximation for alternating current (AC) power flow equations that differs from the existing convex relaxations. The proposed approach is based on three-phase quadratic power flow equations in rectangular coordinates. To develop this data-driven convex approximation of power flows, the polynomial regression (PR) is first deployed as a basic learner to fit convex relationships between the independent and dependent variables. Then, ensemble learning algorithms such as gradient boosting (GB) and bagging are introduced to combine learners to boost model performance. Based on the learned convex approximation of power flow, optimal power flow (OPF) is formulated as a convex quadratic programming problem. The simulation results on IEEE standard cases of both balanced and unbalanced systems show that, in the context of solving OPF, the proposed data-driven convex approximation outperforms the conventional semi-definite programming (SDP) relaxation in both accuracy and computational efficiency, especially in the cases that the conventional SDP relaxation fails

Convex approximation↗