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

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At least 1,333 records · Page 74
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

An Exchange-Correlation Functional Capturing Bulk Surface and Confinement Physics

Due to its balance of accuracy and computational cost, density functional theory has become the method of choice for computing the electronic structure and related properties of materials. However, present-day semilocal approximations to the exchange-correlation energy of density functional theory break down for materials containing d and f electrons. In this report we summarize our progress in addressing this issue. We describe the construction of the BSC exchange-correlation functional within the subsystem functional formalism which enables us to capture bulk, surface, and confinement physics with a single exchange-correlation functional. We report on the initial assessment of this functional within the jellium surface system and demonstrate that the BSC functional captures the confinement physics more accurately than standard semilocal exchange-correlation functionals. We conclude by outlining our future research objectives which focus on refining the functional form of the BSC functional and achieving significantly more accurate energetics of materials containing f and d electrons than existing semilocal functionals.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Efficient approach to kinetic simulation in the inner magnetically insulated transmission line on Z

This project explores the idea of performing kinetic numerical simulations in the Z inner magnetically insulated transmission line (inner MITL) by reduced physics models such as a guiding center drift kinetic approximation for particles and electrostatic and magnetostatic approximation for the fields. The basic problem explored herein is the generation, formation, and evolution of vortices by electron space charge limited (SCL) emission. The results indicate that for relevant to Z values of peak current and pulse length, these approximations are excellent, while also providing tens to hundreds of times reduction in the computational load. The benefits could be enormous: Implementation of these reduced physics models in present particle-in-cell (PIC) codes could enable them to be routinely used for experimental design while still capturing essential non-thermal (kinetic) physics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Energy-conserving physics for nonhydrostatic dynamics in mass coordinate models

Abstract. Motivated by reducing errors in the energy budget related to enthalpy fluxes within the Energy Exascale Earth System Model (E3SM), we study several physics–dynamics coupling approaches. Using idealized physics, a moist rising bubble test case, and the E3SM's nonhydrostatic dynamical core, we consider unapproximated and approximated thermodynamics applied at constant pressure or constant volume. With the standard dynamics and physics time-split implementation, we describe how the constant-pressure and constant-volume approaches use different mechanisms to transform physics tendencies into dynamical motion and show that only the constant-volume approach is consistent with the underlying equations. Using time step convergence studies, we show that the two approaches both converge but to slightly different solutions. We reproduce the large inconsistencies between the energy flux internal to the model and the energy flux of precipitation when using approximate thermodynamics, which can only be removed by considering variable latent heats, both when computing the latent heating from phase change and when applying this heating to update the temperature. Finally, we show that in the nonhydrostatic case, for physics applied at constant pressure, the general relation that enthalpy is locally conserved no longer holds. In this case, the conserved quantity is enthalpy plus an additional term proportional to the difference between hydrostatic pressure and full pressure.

58 GEOSCIENCES↗
DOE OSTI2026

Attosecond response of molecules to impulsive ionization

When matter interacts with energetic radiation it can undergo sudden, or impulsive, ionization. This process can drive chemical change and occurs widely in space and planetary atmospheres, yet its comprehensive description challenges our current theoretical and computational capabilities as it requires advanced treatment of electron correlation and nonadiabatic dynamics beyond the Born–Oppenheimer approximation. Here, in this study, we measure the response of the para-aminophenol molecule to sudden ionization. Using attosecond X-ray absorption spectroscopy, we resolve the ultrafast dynamics of the ionized molecule with atomic precision. A subfemtosecond decay corresponds to states undergoing non-radiative decay, whereas few-femtosecond oscillatory signatures are associated with electronic wavepacket motion in stable cation states that later couple to nuclear motion. We compare our measurement with state-of-the-art computational modelling, qualitatively reproducing the observed response across multiple timescales. These results provide a benchmark for computational models of sudden ionization and ultrafast charge motion in matter.

Driver, Taran [SLAC National Accelerator Laborator↗
DOE OSTI2019

Modeling the Ex-core Detector Response into a Production Option in MPACT

In the past few years, the Consortium for Advanced Simulation of Light Water Reactors (CASL) has overseen a successful activity to extend the radiation transport capability from the reactor in-core geometry to the ex-core geometry by coupling the deterministic neutronics code MPACT, with the Monte Carlo code Shift. However, transient problems such as RIAs require an efficient prediction of the ex-core detector response to determine the timeframe for a reactor trip. Therefore, in addition to the high-fidelity MPACT-Shift coupled calculation, separate efforts have been made to explore simplified methods for ex-core detector response with MPACT standalone calculation. In a previous milestone L3_RTM.MCH.P17.06, several simplified methods for ex-core detector response were developed in MPACT. In particular, the double kernel method is based on the default MPACT core geometry, so extensive modeling or transport calculation with full reflector and ex-core details are not needed in this method. Since the 1-D diffusion and neutron streaming kernels are used for extended ex-core calculations, the extra computational efforts are very small. The work implemented in the current milestone provides a fully integrated option for MPACT to approximately calculate the ex-core detector response using the double kernel method. To overcome the difficulty of obtaining the consistent diffusion coefficients (these were obtained through separate CMFD calculation and edits), the 1-D diffusion solver is replaced by a 1-D Sn transport solver to compute the neutron flux at the vessel outer surface. The new VERA inputs for ex-core detector are processed in MPACT. The detector signals are linked to the SCRAM logic as an option to trip the core during transient calculation. Two sets of 3-D quarter core problems are run with MPACT standalone and VeraShift to verify the radial and axial effects on detector response by varying the moderator density and control rod position. For the cases with moderator density changes, the detector responses from MPACT are within 2 sigma error of VeraShift. For the cases at different control rod positions, the axial offsets computed from MPACT are within 2% error of VeraShift results.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2018

Hybrid Finite Element--Spectral Method for the Fractional Laplacian: Approximation Theory and Efficient Solver

Here, a numerical scheme is presented for approximating fractional order Poisson problems in two and three dimensions. The scheme is based on reformulating the original problem posed over $\Omega$ on the extruded domain $\mathcal{C}=\Omega\times[0,\infty)$ following. The resulting degenerate elliptic integer order PDE is then approximated using a hybrid FEM-spectral scheme. Finite elements are used in the direction parallel to the problem domain $\Omega$, and an appropriate spectral method is used in the extruded direction. The spectral part of the scheme requires that we approximate the true eigenvalues of the integer order Laplacian over $\Omega$. We derive an a priori error estimate which takes account of the error arising from using an approximation in place of the true eigenvalues. We further present a strategy for choosing approximations of the eigenvalues based on Weyl's law and finite element discretizations of the eigenvalue problem. The system of linear algebraic equations arising from the hybrid FEM-spectral scheme is decomposed into blocks which can be solved effectively using standard iterative solvers such as multigrid and conjugate gradient. Numerical examples in two and three dimensions suggest that the approach is quasi-optimal in terms of complexity.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Exact Bayesian computation using H-functions

In the Bayesian Statistics, the use of conjugate prior distributions allows to obtain exact posterior quantities, avoiding the use of approximate methods. However, there are only a few conjugate structures available, which limits the use in practical problems. In this work we propose a general procedure to obtain the posterior distribution in an exact form in non-conjugate location parameter models with known (possibly, heteroskedastic) variance. The theory is based on special functions, specifically the H-function, which embraces most of the probability distributions. We express explicitly in a computable form all the Bayesian tools for posterior inferences, that is the posterior and the posterior predictive distributions and their moments, as well as the cumulative posterior distribution. As an illustration we consider a problem in astronomy of estimating the distance to the Large Magellanic Cloud, the largest galaxy now orbiting the Milky Way Galaxy.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

A low-rank power iteration scheme for neutron transport criticality problems

Computing effective eigenvalues for neutron transport often requires a fine numerical resolution. Here, the main challenge of such computations is the high memory effort of classical solvers, which limits the accuracy of chosen discretizations. In this work, we derive a method for the computation of effective eigenvalues when the underlying solution has a low-rank structure. This is accomplished by utilizing dynamical low-rank approximation (DLRA), which is an efficient strategy to derive time evolution equations for low-rank solution representations. The main idea is to interpret the iterates of the classical inverse power iteration as pseudo-time steps and apply the DLRA concepts in this framework. In our numerical experiment, we demonstrate that our method significantly reduces memory requirements while achieving the desired accuracy. Analytic investigations show that the proposed iteration scheme inherits the convergence speed of the inverse power iteration, at least for a simplified setting.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Numerical gate synthesis for quantum heuristics on bosonic quantum processors

There is a recent surge of interest and insights regarding the interplay of quantum optimal control and variational quantum algorithms. We study the framework in the context of qudits which are, for instance, definable as controllable electromagnetic modes of a superconducting cavity system coupled to a transmon. By employing recent quantum optimal control approaches described in (Petersson and Garcia, 2021), we showcase control of single-qudit operations up to eight states, and two-qutrit operations, mapped respectively onto a single mode and two modes of the resonator. We discuss the results of numerical pulse engineering on the closed system for parametrized gates useful to implement Quantum Approximate Optimization Algorithm (QAOA) for qudits. The results show that high fidelity ( > 0.99) is achievable with sufficient computational effort for most cases under study, and extensions to multiple modes and open, noisy systems are possible. The tailored pulses can be stored and used as calibrated primitives for a future compiler in circuit quantum electrodynamics (cQED) systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Exact Gaussian processes for massive datasets via non-stationary sparsity-discovering kernels

Abstract A Gaussian Process (GP) is a prominent mathematical framework for stochastic function approximation in science and engineering applications. Its success is largely attributed to the GP’s analytical tractability, robustness, and natural inclusion of uncertainty quantification. Unfortunately, the use of exact GPs is prohibitively expensive for large datasets due to their unfavorable numerical complexity of $$O(N^3)$$ O ( N 3 ) in computation and $$O(N^2)$$ O ( N 2 ) in storage. All existing methods addressing this issue utilize some form of approximation—usually considering subsets of the full dataset or finding representative pseudo-points that render the covariance matrix well-structured and sparse. These approximate methods can lead to inaccuracies in function approximations and often limit the user’s flexibility in designing expressive kernels. Instead of inducing sparsity via data-point geometry and structure, we propose to take advantage of naturally-occurring sparsity by allowing the kernel to discover—instead of induce—sparse structure. The premise of this paper is that the data sets and physical processes modeled by GPs often exhibit natural or implicit sparsities, but commonly-used kernels do not allow us to exploit such sparsity. The core concept of exact, and at the same time sparse GPs relies on kernel definitions that provide enough flexibility to learn and encode not only non-zero but also zero covariances. This principle of ultra-flexible, compactly-supported, and non-stationary kernels, combined with HPC and constrained optimization, lets us scale exact GPs well beyond 5 million data points.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Hole–hole Tamm–Dancoff-approximated density functional theory: A highly efficient electronic structure method incorporating dynamic and static correlation

The study of photochemical reaction dynamics requires accurate as well as computationally efficient electronic structure methods for the ground and excited states. While time-dependent density functional theory (TDDFT) is not able to capture static correlation, complete active space self-consistent field methods neglect much of the dynamic correlation. Hence, inexpensive methods that encompass both static and dynamic electron correlation effects are of high interest. Here, we revisit hole–hole Tamm–Dancoff approximated (hh-TDA) density functional theory for this purpose. The hh-TDA method is the hole–hole counterpart to the more established particle–particle TDA (pp-TDA) method, both of which are derived from the particle–particle random phase approximation (pp-RPA). In hh-TDA, the N-electron electronic states are obtained through double annihilations starting from a doubly anionic (N+2 electron) reference state. In this way, hh-TDA treats ground and excited states on equal footing, thus allowing for conical intersections to be correctly described. Furthermore, the treatment of dynamic correlation is introduced through the use of commonly employed density functional approximations to the exchange-correlation potential. Additionally, we show that hh-TDA is a promising candidate to efficiently treat the photochemistry of organic and biochemical systems that involve several low-lying excited states—particularly those with both low-lying ππ* and nπ* states where inclusion of dynamic correlation is essential to describe the relative energetics. In contrast to the existing literature on pp-TDA and pp-RPA, we employ a functional-dependent choice for the response kernel in pp- and hh-TDA, which closely resembles the response kernels occurring in linear response and collinear spin-flip TDDFT.

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

We Know Where We Don't Know: 3D Bayesian CNNs for Credible Geometric Uncertainty

Deep learning has been successfully applied to the segmentation of 3D Computed Tomography (CT) scans. Establishing the credibility of these segmentations requires uncertainty quantification (UQ) to identify untrustworthy predictions. Recent UQ architectures include Monte Carlo dropout networks (MCDNs), which approximate deep Gaussian processes, and Bayesian neural networks (BNNs), which learn the distribution of the weight space. BNNs are advantageous over MCDNs for UQ but are thought to be computationally infeasible in high dimension, and neither architecture has produced interpretable geometric uncertainty maps. We propose a novel 3D Bayesian convolutional neural network (BCNN), the first deep learning method which generates statistically credible geometric uncertainty maps and scales for application to 3D data. We present experimental results on CT scans of graphite electrodes and laser-welded metals and show that our BCNN outperforms an MCDN in recent uncertainty metrics. The geometric uncertainty maps generated by our BCNN capture distributions of sigmoid values that are interpretable as confidence intervals, critical for applications that rely on deep learning for high-consequence decisions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Nonnegative canonical tensor decomposition with linear constraints: nnCANDELINC

Abstract There is an emerging interest for tensor factorization applications in big‐data analytics and machine learning. To speed up the factorization of extra‐large datasets, organized in multidimensional arrays (also known as tensors), easy to compute compression‐based tensor representations, such as, Tucker and tensor train formats, are used to approximate the initial large‐tensor. Further, tensor factorization is used to extract latent features that can facilitate discoveries of new mechanisms and signatures hidden in the data, where the explainability of the latent features is of principal importance. Nonnegative tensor factorization extracts latent features that are naturally sparse and parts of the data, which makes them easily interpretable. However, to take into account available domain knowledge and subject matter expertise, often additional constraints need to be imposed, which lead us to canonical decomposition with linear constraints (CANDELINC), a canonical polyadic decomposition with rank deficient factors. In CANDELINC, Tucker compression is used as a preprocessing step, which lead to a larger residual error but to more explainable latent features. Here, we propose a nonnegative CANDELINC (nnCANDELINC) accomplished via a specific nonnegative Tucker decomposition; we refer to as minimal or canonical nonnegative Tucker. We derive several results required to understand the specificity of nnCANDELINC, focusing on the difficulties of preserving the nonnegative rank of a tensor to its Tucker core and comparing the real valued to nonnegative case. Finally, we demonstrate nnCANDELINC performance on synthetic and real‐world examples.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Polynomial chaos expansions for dependent random variables

Polynomial chaos expansions (PCE) are well-suited to quantifying uncertainty in models parameterized by independent random variables. The assumption of independence leads to simple strategies for building multivariate orthonormal bases and for sampling strategies to evaluate PCE coefficients. In contrast, the application of PCE to models of dependent variables is much more challenging. Three approaches can be used to construct PCE of models of dependent variables. The first approach uses mapping methods where measure transformations, such as the Nataf and Rosenblatt transformation, can be used to map dependent random variables to independent ones; however we show that this can significantly degrade performance since the Jacobian of the map must be approximated. A second strategy is the class of dominating support methods. In these approaches a PCE is built using independent random variables whose distributional support dominates the support of the true dependent joint density; we provide evidence that this approach appears to produce approximations with suboptimal accuracy. A third approach, the novel method proposed here, uses Gram-Schmidt orthogonalization (GSO) to numerically compute orthonormal polynomials for the dependent random variables. This approach has been used successfully when solving differential equations using the intrusive stochastic Galerkin method, and in this paper we use GSO to build PCE using a non-intrusive stochastic collocation method. The stochastic collocation method treats the model as a black box and builds approximations of the input-output map from a set of samples. Building PCE from samples can introduce ill-conditioning which does not plague stochastic Galerkin methods. To mitigate this ill-conditioning we generate weighted Leja sequences, which are nested sample sets, to build accurate polynomial interpolants. We show that our proposed approach, GSO with weighted Leja sequences, produces PCE which are orders of magnitude more accurate than PCE constructed using mapping or dominating support methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Reduced order models for thermal radiative transfer problems based on moment equations and data-driven approximations of the Eddington tensor

Here a new group of structure and asymptotic preserving reduced-order models (ROMs) for multidimensional nonlinear thermal radiative transfer (TRT) problems is presented. They are formulated by means of the nonlinear projective approach and data compression techniques. The nonlinear projection is applied to the Boltzmann transport equation (BTE) to derive a hierarchy of low-order moment equations. Approximation of the Eddington tensor that provides exact closure for the system of moment equations is found with projection-based data-driven methodologies. These include the (i) proper orthogonal decomposition (POD), (ii) dynamic mode decomposition (DMD) and (iii) a variant of the DMD. A parameterization is derived for this ROM for the temperature of radiation incoming to the problem domain (the radiation drive temperature). This parameterization is informed from results of a dimensionless study of the TRT problem. Analysis of the ROMs is performed on the classical Fleck-Cummings TRT multigroup test problem in 2D geometry with a radiation-driven Marshak wave. Numerical results are presented to demonstrate the performance of these ROMs for the simulation of evolving radiation and heat waves. Results show these models to be sufficiently accurate for practical computations with rather low-rank representations of the Eddington tensor. As the rank of the approximation is increased, the errors of solutions generated by the ROMs gradually decreases.

42 ENGINEERING↗
DOE OSTI2020

On the Convergence of Physics Informed Neural Networks for Linear Second-Order Elliptic and Parabolic Type PDEs

Physics informed neural networks (PINNs) are deep learning based techniques for solving partial differential equations (PDEs) encountered in computational science and engineering. Guided by data and physical laws, PINNs find a neural network that approximates the solution to a system of PDEs. Such a neural network is obtained by minimizing a loss function in which any prior knowledge of PDEs and data are encoded. Despite its remarkable empirical success in one, two or three dimensional problems, there is little theoretical justification for PINNs. As the number of data grows, PINNs generate a sequence of minimizers which correspond to a sequence of neural networks. We want to answer the question: Does the sequence of minimizers converge to the solution to the PDE? We consider two classes of PDEs: linear second-order elliptic and parabolic. By adapting the Schauder approach and the maximum principle, we show that the sequence of minimizers strongly converges to the PDE solution in C 0 . Furthermore, we show that if each minimizer satisfies the initial/boundary conditions, the convergence mode becomes H 1 . Computational examples are provided to illustrate our theoretical findings. To the best of our knowledge, this is the first theoretical work that shows the consistency of PINNs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Saturation and Recurrence of Quantum Complexity in Random Local Quantum Dynamics

Quantum complexity is a measure of the minimal number of elementary operations required to approximately prepare a given state or unitary channel. Recently, this concept has found applications beyond quantum computing—in studying the dynamics of quantum many-body systems and the long-time properties of anti–de Sitter black holes. In this context, Brown and Susskind [] conjectured that the complexity of a chaotic quantum system grows linearly in time up to times exponential in the system size, saturating at a maximal value, and remaining maximally complex until undergoing recurrences at doubly exponential times. In this work, we prove the saturation and recurrence of complexity in two models of chaotic time evolutions based on (i) random local quantum circuits and (ii) stochastic local Hamiltonian evolution. Our results advance an understanding of the long-time behavior of chaotic quantum systems and could shed light on the physics of black-hole interiors. From a technical perspective, our results are based on establishing new quantitative connections between the Haar measure and high-degree approximate designs, as well as the fact that random quantum circuits of sufficiently high depth converge to approximate designs. Published by the American Physical Society 2024

Oszmaniec, Michał (ORCID:0000000249466835)↗
DOE OSTI2020

VADER: A Tool for Criticality Safety Validation

The purpose of criticality safety is to prevent any inadvertent criticality from occurring during the handling or storage of fissile material. Calculations are frequently used to demonstrate that a sufficient subcritical margin exists. Validation is a key aspect of the evaluation process, establishing the suitability, accuracy, and associated uncertainty of the computational method and data to be used for the intended application. The validation process is performed by comparing the results of critical experiments with the calculated results from models of the experiments using the computational method to be validated. Laboratory critical experiments are controlled systems that achieve a k eff of approximately 1 in order to investigate the parameters at which such a critical condition is achieved. The validation parameters that are traditionally applied to safety analysis calculations are the bias and the bias uncertainty . The bias is the deviation of the average k eff of the validation suite from unity. The bias uncertainty accounts for the statistical uncertainty in the bias based on the standard deviation, sample size, and distribution of k eff values of the validation suite. The values of bias and bias uncertainty ensure that the systems predicted to be subcritical by the computational method will indeed be subcritical. The bias and bias uncertainty are often combined to determine an upper subcritical limit (USL) or computational margin that can then be applied to safety analysis calculations. Many methods have been developed by different organizations to calculate the bias and bias uncertainty for various types of criticality analyses. Each of these methods typically requires that the validity of various underpinning statistical assumptions be confirmed to demonstrate that the method is appropriate for the analysis of a given validation suite. An example of the validation decision making flow is shown in Fig.1. As shown in Fig. 1, the analyst performing the validation fits a trend line to the data and performs a test to determine if the trend was a statistically better representation of the data than if it were treated as an uncorrelated sample. If the trend line is a better representation of the data, then the analyst uses any one of a number of trending techniques to determine the bias and bias uncertainty. If a trend is not an appropriate representation of the data, then the analyst proceeds to perform a normality assessment for the data. If the normal assumption can be shown to be acceptable, then the analyst calculates the bias and bias uncertainty with the parametric technique. If the assumption of normality cannot be justified, then the nonparametric technique is used. Once the decision flow has been followed and the appropriate technique has been selected, the bias and bias uncertainty is typically combined with an administrative margin to determine a USL below which calculated values of k eff for safety analysis models can be considered subcritical. The calculations used in each decision are often performed with spreadsheets or with small programs available at various sites performing criticality analyses. Expertise in understanding and interpreting the results must be maintained to perform these calculations. This can often be an error-prone process. Oak Ridge National Laboratory (ORNL) is currently developing the Validation and Data Evaluation Resource (VADER) to simplify and automate the criticality safety validation process and to provide a software quality assurance pedigree to the calculational methods used. This paper discusses the use of the Fulcrum user interface with VADER, the anticipated initial capabilities of VADER to perform validation analyses, and the output from the code.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗