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At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Modifying the Asynchronous Jacobi Method for Data Corruption Resilience

Moving scientific computation from high-performance computing (HPC) and cloud computing (CC) environments to devices on the edge, i.e., physically near instruments of interest, has received tremendous interest in recent years. Such edge computing environments can operate on data in situ, offering enticing benefits over data aggregation to HPC and CC facilities that include avoiding costs of transmission, increased data privacy, and real-time data analysis. Because of the inherent unreliability of edge computing environments, new fault-tolerant approaches must be developed before the benefits of edge computing can be realized. Motivated by algorithm-based fault tolerance, a variant of the asynchronous Jacobi (ASJ) method is developed that achieves resilience to data corruption by rejecting solution approximations from neighbor devices according to a bound derived from convergence theory. Numerical results on a two-dimensional Poisson problem show that the new rejection criterion, along with a novel approximation to the shortest path length on which the criterion depends, restores convergence for the ASJ variant in the presence of certain types data corruption. Numerical results are obtained for when the singular values in the analytic bound are approximated. Additional linear systems are also explored, one with a more dense sparsity pattern and one that includes advection. All results indicate that successful resilience to data corruption depends on whether the bound tightens fast enough to reject corrupted data before the iteration evolution deviates significantly from that predicted by the convergence theory defining the bound. This observation generalizes to future work on algorithm-based fault tolerance for other asynchronous algorithms, including upcoming approaches that leverage Krylov subspaces.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Tensor Network Path Integral Study of Dynamics in B850 LH2 Ring with Atomistically Derived Vibrations

The recently introduced multisite tensor network path integral (MS-TNPI) allows simulation of extended quantum systems coupled to dissipative media. We use MS-TNPI to simulate the exciton transport and the absorption spectrum of a B850 bacteriochlorophyll (BChl) ring. The MS-TNPI network is extended to account for the ring topology of the B850 system. Accurate molecular-dynamics-based description of the molecular vibrations and the protein scaffold is incorporated through the framework of Feynman–Vernon influence functional. To relate the present work with the excitonic picture, an exploration of the absorption spectrum is done by simulating it using approximate and topologically consistent transition dipole moment vectors. Comparison of these numerically exact MS-TNPI absorption spectra are shown with second-order cumulant approximations. Finally, the effect of temperature on both the exact and the approximate spectra is also explored.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Taylor approximation variance reduction for approximation errors in PDE-constrained Bayesian inverse problems

In numerous applications, surrogate models are used as a replacement for accurate parameter-to-observable mappings when solving large-scale inverse problems governed by partial differential equations (PDEs). The surrogate model may be a computationally cheaper alternative to the accurate parameter-to-observable mappings and/or may ignore additional unknowns or sources of uncertainty. The Bayesian approximation error (BAE) approach provides a means to account for the induced uncertainties and approximation errors, i.e. the errors between the accurate parameter-to-observable mapping and the surrogate. The statistics of these errors are, however, in general unknown a priori, and are thus calculated using Monte Carlo sampling. Although the sampling is typically carried out offline, i.e. before considering the data, the process can still represent a computational bottleneck. In this work, we develop a scalable computational approach for reducing the costs associated with the sampling stage of the BAE approach. Specifically, we consider the Taylor expansion of the accurate and surrogate forward models with respect to the uncertain parameter fields either as a control variate for variance reduction or as a means to directly and efficiently approximate the mean and covariance of the approximation errors. We propose efficient methods for evaluating the expressions for the mean and covariance of the Taylor approximations based on linear(-ized) PDE solves. Furthermore, the proposed approach is independent of the dimension of the uncertain parameter, depending instead on the intrinsic dimension of the data, ensuring scalability to high-dimensional problems. The potential benefits of the proposed approach are demonstrated for two high-dimensional inverse problems governed by PDE examples, namely for the estimation of a distributed Robin boundary coefficient in a linear diffusion problem, and for a coefficient estimation problem governed by a nonlinear diffusion problem.

Bayesian approximation error↗
DOE OSTI2025

A charged particle transport approximation for thick and thin plasmas

In this work, we will construct a simple method to be utilized in the interpretation of the properties of a thin plasma from a study of the transport of charged particles through it. We do so by first demonstrating how charged particle fluxes encode local plasma information in their spectra for sufficiently thick plasmas and then propose how to extend that analysis to the thin plasma limit where the extensive geometry cannot be neglected through arguments from scale separation. We provide a numerical treatment of the transport problem and demonstrate that it is in good agreement with the approximation we present. Finally, we utilize both the numerical solution and our novel approximation to study the impact of the extensive scale of the plasma on the yield and flux normalized high-energy neutron spectra resulting from the upscattering of charged fuel ions. Using this analysis, we show that (after controlling for fusion yield) for the same uniform densities and temperatures, larger plasmas have higher magnitude but softer reaction-in-flight (RIF) neutron spectra relative to smaller plasmas. This is because larger plasmas retain more knocked-on suprathermal ions within their bulk and can downscatter them to lower average energies, while smaller plasmas allow a larger fraction of high energy particles to “range out” of the system prior to substantial downscattering or inducing an RIF reaction.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Generalized moving least squares vs. radial basis function finite difference methods for approximating surface derivatives

Approximating differential operators defined on two-dimensional surfaces is an important problem that arises in many areas of science and engineering. Over the past ten years, localized meshfree methods based on generalized moving least squares (GMLS) and radial basis function finite differences (RBF-FD) have been shown to be effective for this task as they can give high orders of accuracy at low computational cost, and they can be applied to surfaces defined only by point clouds. However, there have yet to be any studies that perform a direct comparison of these methods for approximating surface differential operators (SDOs). The first purpose of this work is to fill that gap. For this comparison, we focus on an RBF-FD method based on polyharmonic spline kernels and polynomials (PHS+Poly) since they are most closely related to the GMLS method. Additionally, we use a relatively new technique for approximating SDOs with RBF-FD called the tangent plane method since it is simpler than previous techniques and natural to use with PHS+Poly RBF-FD. Further, the second purpose of this work is to relate the tangent plane formulation of SDOs to the local coordinate formulation used in GMLS and to show that they are equivalent when the tangent space to the surface is known exactly. The final purpose is to use ideas from the GMLS SDO formulation to derive a new RBF-FD method for approximating the tangent space for a point cloud surface when it is unknown. For the numerical comparisons of the methods, we examine their convergence rates for approximating the surface gradient, divergence, and Laplacian as the point clouds are refined for various parameter choices. We also compare their efficiency in terms of accuracy per computational cost, both when including and excluding setup costs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Iterative quantum optimization of spin glass problems with rapidly oscillating transverse fields

In this work, we introduce a new iterative quantum algorithm, called Iterative Symphonic Tunneling for Satisfiability problems (IST-SAT), which solves quantum spin glass optimization problems using high-frequency oscillating transverse fields. IST-SAT operates as a sequence of iterations, in which bitstrings returned from one iteration are used to set spin-dependent phases in oscillating transverse fields in the next iteration. Over several iterations, the novel mechanism of the algorithm steers the system toward the problem ground state. We benchmark IST-SAT on sets of hard MAX-3-XORSAT problem instances with exact state vector simulation, and report polynomial speedups over Trotterized adiabatic quantum computation and the best known semi-greedy classical algorithm. When IST-SAT is seeded with a sufficiently good initial approximation, the algorithm converges to exact solution(s) in a polynomial number of iterations. Our numerical results identify a critical Hamming radius, or quality of initial approximation, where the time-to-solution crosses from exponential to polynomial scaling in problem size. This work proposes IST-SAT a new quantum algorithm, which improves upon solutions obtained from initial classical or quantum optimization algorithms. The steering mechanism we introduce through IST-SAT presents a new path toward achieving quantum advantage in optimization.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

A Probabilistic Scheme for Semilinear Nonlocal Diffusion Equations with Volume Constraints

This work presents a probabilistic scheme for solving semilinear nonlocal diffusion equations with volume constraints and integrable kernels. The nonlocal model of interest is defined by a time-dependent semilinear partial integro-differential equation (PIDE), in which the integro-differential operator consists of both local convection-diffusion and nonlocal diffusion operators. Here, our numerical scheme is based on the direct approximation of the nonlinear Feynman–Kac formula that establishes a link between nonlinear PIDEs and stochastic differential equations. The exploitation of the Feynman–Kac representation avoids solving dense linear systems arising from nonlocal operators. Compared with existing stochastic approaches, our method can achieve first-order convergence after balancing the temporal and spatial discretization errors, which is a significant improvement of existing probabilistic/stochastic methods for nonlocal diffusion problems. Error analysis of our numerical scheme is established. The effectiveness of our approach is shown in two numerical examples. The first example considers a three-dimensional nonlocal diffusion equation to numerically verify the error analysis results. The second example presents a physics problem motivated by the study of heat transport in magnetically confined fusion plasmas.

97 MATHEMATICS AND COMPUTING↗
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 OSTI2023

Efficient, direct compilation of SU(N) operations into SNAP & Displacement gates

We present a function which connects the parameter of a previously published short sequence of selective number-dependent arbitrary phase (SNAP) and displacement gates acting on a qudit encoded into the Fock states of a superconducting cavity, $V_k(\alpha)=D(\alpha)R_\pi(k)D(-2\alpha)R_\pi(k)D(\alpha)$ to the angle of the Givens rotation $G(\theta)$ on levels $|k\rangle,|k+1\rangle$ that sequence approximates, namely $\alpha=\Phi(\theta) = \frac{\theta}{4\sqrt{k+1}}$. Previous publications left the determination of an appropriate $\alpha$ to numerical optimization at compile time. The map $\Phi$ gives us the ability to compile directly any $d$-dimensional unitary into a sequence of SNAP and displacement gates in $O(d^3)$ complex floating point operations with low constant prefactor, avoiding the need for numerical optimization. Numerical studies demonstrate that the infidelity of the generated gate sequence $V_k$ per Givens rotation $G$ scales as approximately $O(\theta^6)$. We find numerically that the error on compiled circuits can be made arbitrarily small by breaking each rotation into $m$$\theta/m$ rotations, with the full $d\times d$ unitary infidelity scaling as approximately $O(m^{-4})$. This represents a significant reduction in the computational effort to compile qudit unitaries either to SNAP and displacement gates or to generate them via direct low-level pulse optimization via optimal control.

Job, Joshua↗
DOE OSTI2021

Analyzing Mechanical integrity of Microwave resonant Cavity flowmeter

The microwave resonant cavity flow sensor has been proposed to address the difficulties of measuring high-temperature molten salt flow in reactor vessels. The flow sensor consists of a metallic cylindrical cavity coupled to a microwave waveguide. The cylindrical cavity has one of the flat surfaces thin enough to undergo microscopic deflection due to dynamic pressure of the exerted by the flowing fluid. Deflection of the membrane causes a shift in the microwave resonant frequency. Fluid velocity can be estimated from the calibration curve. The objective of this report is to investigate mechanical integrity of the flowmeter’s membrane. The membrane is a thin stainless-steel circular plate with a clamped edge, subjected to uniform load. By calculating the stress on the plate due to deflection and, comparing the stress to the material ultimate tensile strength and yield strength, it can be estimated if the plate will fail. If the maximum stress is greater than the yield strength, the plate will undergo plastic deformation, and the sensor will be disabled. A stress greater than the ultimate tensile strength will cause the plate to fracture. The stress on the plate was calculated with an analytic closed form solution model, and with COMSOL Structural Mechanics Module which does not involve any approximations. Stresses in both the analytic model and COMSOL numerical model were calculated for stainless steel 316 thin circular plates under room temperature conditions, where the fluid is water. The diameter of the circular plate is approximately one inch, and thickness is 10mil. Fluid flow velocity is in the range from 0.5m/s to 1m/s. The results from the two models are similar. Both the analytic model and COMSOL model showed that maximum stresses on the plate, which are at the radial boundary of the plate, are three orders of magnitude smaller than the yield strength and ultimate tensile strength. This indicates that the sensor is at a low risk of mechanical failure.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Analytic and numerical vibronic spectra from quasi-classical trajectory ensembles

The truncated Wigner approximation to quantum dynamics in phase space is explored in the context of computing vibronic line shapes for monomer linear optical spectra. We consider multiple model potential forms including a shifted harmonic oscillator with both equal and unequal frequencies on the ground and excited state potentials as well as a shifted Morse potential model. For the equal-frequency shifted harmonic oscillator model, we derive an analytic expression for the exact vibronic line shape that emphasizes the importance of using a quantum mechanical distribution of phase space initial conditions. For the unequal-frequency shifted harmonic oscillator model, we are no longer able to obtain an exact expression for the vibronic line shape in terms of independent deterministic classical trajectories. We show how one can rigorously account for corrections to the truncated Wigner approximation through nonlinear responses of the line shape function to momentum fluctuations along a classical trajectory and demonstrate the qualitative improvement in the resulting spectrum when the leading-order quantum correction is included. Finally, we numerically simulate absorption spectra of a highly anharmonic shifted Morse potential model. We find that, while finite quantization and the dissociation limit are captured with reasonable accuracy, there is a qualitative breakdown of the quasi-classical trajectory ensemble’s ability to describe the vibronic line shape when the relative shift in Morse potentials becomes large. The work presented here provides clarity on the origin of unphysical negative features known to contaminate absorption spectra computed with quasi-classical trajectory ensembles.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

A Decision-Making Machine Learning Approach in Hermite Spectral Approximations of Partial Differential Equations

The accuracy and effectiveness of Hermite spectral methods for the numerical discretization of partial differential equations on unbounded domains are strongly affected by the amplitude of the Gaussian weight function employed to describe the approximation space. This is particularly true if the problem is under-resolved, i.e., there are no enough degrees of freedom. The issue becomes even more crucial when the equation under study is time-dependent, forcing in this way the choice of Hermite functions where the corresponding weight depends on time. In order to adapt dynamically the approximation space, it is here proposed an automatic decision-making process that relies on machine learning techniques, such as deep neural networks and support vector machines. The algorithm is numerically tested with success on a simple 1D problem, but the main goal is its exportability in the context of more serious applications. Here we also show at the end an application in the framework of plasma physics.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

A Relaxed PV Bus Model in Linear Power Flow

The emerging multimodal active energy resource units make it necessary to introduce constant voltage amplitude buses (PV bus) in the operation of modern distribution systems. To enable the analysis of PV bus using linear power flow models, this letter proposes a relaxed PV bus model for solving power flow related problems using an indirect modeling approach. The developed PV bus model can be applied to linear power flow models in both rectangular and polar coordinates. Besides, the approximation error of the relaxed PV bus model can also be controlled and quantified. Lastly, the proposed relaxed PV bus model is validated using different test systems. According to the numerical studies, the maximum error on the PV bus approximation in all case studies is only 0.61%, and the maximum error of the supporting power at the PV buses is 6.5%.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Tensor network representation of non-abelian gauge theory coupled to reduced staggered fermions

We show how to construct a tensor network representation of the path integral for reduced staggered fermions coupled to a non-abelian gauge field in two dimensions. The resulting formulation is both memory and computation efficient because reduced staggered fermions can be represented in terms of a minimal number of tensor indices while the gauge sector can be approximated using Gaussian quadrature with a truncation. Numerical results obtained using the Grassmann TRG algorithm are shown for the case of SU(2) lattice gauge theory and compared to Monte Carlo results.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Microstrata

Abstract Microstrata are the non-extremal analogues of superstrata: they are smooth, non-extremal (non-BPS) solitonic solutions to IIB supergravity whose deep-throat limits approximate black holes. Using perturbation theory and numerical methods, we construct families of solutions using a consistent truncation to three-dimensional supergravity. The most general families presented here involve two continuous parameters, or amplitudes, and four quantized parameters that set the angular momenta and energy levels. Our solutions are asymptotic to the vacuum of the D1-D5 system: AdS 3 ×S 3 × 𝕋 4 . Using holography, we show that the they are dual to multi-particle states in the D1-D5 CFT involving a large number of mutually non-BPS supergravitons and we determine the anomalous dimensions of these states from the binding energies in supergravity. These binding energies are uniformly negative and depend non-linearly on the amplitudes of the states. In one family of solutions, smoothness restricts some of the fields to lie on a special locus of the parameter space. Using precision holography we show that this special locus can be identified with the multi-particle states constructed via the standard OPE of the single-particle constituents. Our numerical analysis shows that microstrata are robust at large amplitudes and the solutions can be obtained to very high precision.

Physics↗
DOE OSTI2020

The LPM effect in sequential bremsstrahlung: nearly complete results for QCD

The splitting processes of bremsstrahlung and pair production in a medium are coherent over large distances in the very high energy limit, which leads to a suppression known as the Landau-Pomeranchuk-Migdal (LPM) effect. We continue study of the case when the coherence lengths of two consecutive splitting processes overlap (which is important for understanding corrections to standard treatments of the LPM effect in QCD), avoiding soft-emission approximations. Previous work has computed overlap effects for double splitting g → gg → ggg. To make use of those results, one also needs calculations of related virtual loop corrections to single splitting g → gg in order to cancel severe (power-law) infrared (IR) divergences. This paper provides calculations of nearly all such processes involving gluons and discusses how to organize the results to demonstrate the cancellation. In the soft emission limit, our results reproduce the known double-log behavior of earlier authors who worked in leading-log approximation. We also present a first (albeit numerical and not yet analytic) investigation of sub-leading, single IR logarithms. Ultraviolet divergences appearing in our calculations correctly renormalize the coupling αs in the usual LPM result for leading-order g → gg.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Empirical validation and comparison of methodologies to simulate micro and macro-encapsulated PCMs in the building envelope

Thermal Energy Storage (TES) has the potential to shift peak electricity demand. Passive TES is usually implemented in building envelope as micro and macro encapsulated phase change materials (PCM) to shift electric energy demand and therefore requires careful heat transfer analysis. Whole building energy modelling with simplified heat transfer analysis has become extremely important for designers, architects, engineers, and researchers to predict energy performance of buildings. It is important to validate PCM modelling algorithms used in building energy programs to quantify their error and prove their capacity to model different PCM encapsulation types. This study uses data from a microencapsulated PCM and two macroencapsulated PCMs (Bio based PCM and hydrate salts) tested in full-scale using the Advanced Multiscale Building Energy Research (AMBER) Lab located at the Colorado School of Mines and is used to validate a numerical algorithm written in MATLAB language. To approximate the heat transfer through a wall assembly with macroencapsulated PCM pouches, several modelling techniques that can reduce 3D heat transfer characteristics to 1D are explored in this research. A parallel path heat transfer modelling approach is found to give the closest agreement with the experimental data for the pouched PCMs in building envelope applications.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗