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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 865 records · Page 48
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Autoregressive Neural Network for Simulating Open Quantum Systems via a Probabilistic Formulation

The theory of open quantum systems lays the foundation for a substantial part of modern research in quantum science and engineering. Rooted in the dimensionality of their extended Hilbert spaces, the high computational complexity of simulating open quantum systems calls for the development of strategies to approximate their dynamics. In this Letter, we present an approach for tackling open quantum system dynamics. Using an exact probabilistic formulation of quantum physics based on positive operator-valued measure, we compactly represent quantum states with autoregressive neural networks; such networks bring significant algorithmic flexibility due to efficient exact sampling and tractable density. We further introduce the concept of string states to partially restore the symmetry of the autoregressive neural network and improve the description of local correlations. Efficient algorithms have been developed to simulate the dynamics of the Liouvillian superoperator using a forward-backward trapezoid method and find the steady state via a variational formulation. Our approach is benchmarked on prototypical one-dimensional and two-dimensional systems, finding results which closely track the exact solution and achieve higher accuracy than alternative approaches based on using Markov chain Monte Carlo method to sample restricted Boltzmann machines. Our Letter provides general methods for understanding quantum dynamics in various contexts, as well as techniques for solving high-dimensional probabilistic differential equations in classical setups.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Clustering at Massive Scale

ClaMS provides hierarchical clustering technology for use on massive, high-dimensional datasets that require distributed memory for processing. The algorithm employed is inspired by the popular HDBSCAN algorithm but makes use of computational kernels better suited for distributed computing. ClaMS is built on scalable nearest neighbor graph construction, metric forest completion, and approximate minimum spanning tree techniques.

Stanley, ThomasA [Lawrence Livermore National Labo↗
DOE OSTI2021

Exactly unitary discrete representations of the metaplectic transform for linear-time algorithms

The metaplectic transform (MT), a generalization of the Fourier transform sometimes called the linear canonical transform, is a tool used ubiquitously in modern optics, for example, when calculating the transformations of light beams in paraxial optical systems. The MT is also an essential ingredient of the geometrical-optics modeling of caustics that we recently proposed. In particular, this application relies on the near-identity MT (NIMT); however, the NIMT approximation used so far is not exactly unitary and leads to numerical instability. Here, we develop a discrete MT that is exactly unitary, and approximate it to obtain a discrete NIMT that is also unitary and can be computed in linear time. We prove that the discrete NIMT converges to the discrete MT when iterated, thereby allowing the NIMT to compute MTs that are not necessarily near-identity. Finally, we then demonstrate the new algorithms with a series of examples.

47 OTHER INSTRUMENTATION↗
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 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 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↗
DOE OSTI2025

Modeling cross-beam energy transfer with sector ray tracing

Ray-based cross-beam energy transfer (CBET) models are an essential feature of the radiation-hydrodynamic codes used to simulate inertial confinement fusion implosions, but full 3D ray-based CBET calculations can have a prohibitively high computational cost. Sector ray tracing can be used to reduce the cost by orders of magnitude in cases where the coronal plasma and laser drive can be approximated as spherically symmetric. An extension of sector ray tracing (section ray tracing) can be used to relax the assumption of a spherically symmetric drive while still retaining most of the computational savings of a sector ray trace. We discuss the foundations of sector and section ray tracing and compare them to full ray tracing.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Spectral Element Applications in Complex Nuclear Reactor Geometries: Tet-to-Hex Meshing

The spectral element code Nek5000 is an open-source, higher-order computational fluid dynamics code developed at Argonne National Laboratory. It is designed to solve incompressible Navier-Stokes equations, but it also has a low-Mach-number approximation feature available. Large eddy simulation is approached by explicit filtering of the velocity field (and other fields) to mimic the effect of dissipation due to the unresolved scale. The computational domain is decomposed into second-order hexahedral elements that conform to the boundaries. However, generating a high-quality pure-hexahedral mesh can be challenging for some problems. For simple geometries, traditional blocking methods can be used to decompose the domain into smaller blocks to generate a so-called structural mesh. A structural mesh can maintain good orthogonality but can have a highly skewed mesh to conform to the geometry, as well as unnecessary refinement in the far field. Moreover, for geometries with relative complexity, blocking the geometry becomes impossible. To address these issues, we adopted a let-to-hex strategy to generate a pure hexahedral mesh for Nek5000. First, we generate a pure tetrahedral mesh for the geometry; then we divide one tetrahedral element into four hexahedral elements. A pure tetrahedral mesh could be easily generated for complex geometries by using many current meshing codes. In this paper, we use the commercial codes ANSYS meshing and ANSYSICEM to generate the pure tetrahedral mesh and then convert it to a pure hexahedral mesh. Boundary layers are extruded in ANSYSICEM to maintain near-wall resolution.

ANSYS ICEM↗