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At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Asymptotic-preserving dynamical low-rank method for the stiff nonlinear Boltzmann equation

In kinetic theory, numerically solving the full Boltzmann equation is extremely expensive. This is because the Boltzmann collision operator involves a high-dimensional, nonlinear integral that must be evaluated at each spatial grid point and every time step. The challenge becomes even more pronounced in the fluid (strong collisionality) regime, where the collision operator exhibits strong stiffness, causing explicit time integrators to impose severe stability restrictions. In this paper, we propose addressing this problem through a dynamical low-rank (DLR) approximation. The resulting algorithm requires evaluating the Boltzmann collision operator only r 2 times, where r, the rank of the approximation, is much smaller than the number of spatial grid points. We propose a novel DLR integrator, called the XL integrator, which reduces the number of steps compared to the available alternatives (such as the projector splitting or basis update & Galerkin (BUG) integrator). For a class of problems including the Boltzmann collision operator which enjoys a separation property between physical and velocity space, we further propose a specialized version of the XL integrator, called the sXL integrator. This version requires solving only one differential equation to update the low-rank factors. Furthermore, the proposed low-rank schemes are asymptotic-preserving, meaning they can capture the asymptotic fluid limit in the case of strong collisionality. Our numerical experiments demonstrate the efficiency and accuracy of the proposed methods across a wide range of regimes, from non-stiff (kinetic) to stiff (fluid).

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1986

On substructuring algorithms and solution techniques for the numerical approximation of partial differential equations

Substructuring methods are in common use in mechanics problems where typically the associated linear systems of algebraic equations are positive definite. Here these methods are extended to problems which lead to nonpositive definite, nonsymmetric matrices. The extension is based on an algorithm which carries out the block Gauss elimination procedure without the need for interchanges even when a pivot matrix is singular. Examples are provided wherein the method is used in connection with finite element solutions of the stationary Stokes equations and the Helmholtz equation, and dual methods for second-order elliptic equations.

Gunzburger, M. D.↗
NASA NTRS1987

A Taylor weak-statement algorithm for hyperbolic conservation laws

Finite element analysis, applied to computational fluid dynamics (CFD) problem classes, presents a formal procedure for establishing the ingredients of a discrete approximation numerical solution algorithm. A classical Galerkin weak-statement formulation, formed on a Taylor series extension of the conservation law system, is developed herein that embeds a set of parameters eligible for constraint according to specification of suitable norms. The derived family of Taylor weak statements is shown to contain, as special cases, over one dozen independently derived CFD algorithms published over the past several decades for the high speed flow problem class. A theoretical analysis is completed that facilitates direct qualitative comparisons. Numerical results for definitive linear and nonlinear test problems permit direct quantitative performance comparisons.

Baker, A. J.↗
NASA NTRS2004

Adaptive DFT-based Interferometer Fringe Tracking

An automatic interferometer fringe tracking system has been developed, implemented, and tested at the Infrared Optical Telescope Array (IOTA) observatory at Mt. Hopkins, Arizona. The system can minimize the optical path differences (OPDs) for all three baselines of the Michelson stellar interferometer at IOTA. Based on sliding window discrete Fourier transform (DFT) calculations that were optimized for computational efficiency and robustness to atmospheric disturbances, the algorithm has also been tested extensively on off-line data. Implemented in ANSI C on the 266 MHz PowerPC processor running the VxWorks real-time operating system, the algorithm runs in approximately 2.0 milliseconds per scan (including all three interferograms), using the science camera and piezo scanners to measure and correct the OPDs. The adaptive DFT-based tracking algorithm should be applicable to other systems where there is a need to detect or track a signal with an approximately constant-frequency carrier pulse.

Wilson, Edward↗
DOE OSTI2025

Synthesis of single-qutrit circuits from Clifford+𝑅 gates

Here, we present two deterministic compilation algorithms for single-qutrit unitaries with O ( log 1 / ɛ ) gate depth. Each algorithm selects a nearby approximation to the target unitary and then exactly synthesizes the approximation over the Clifford + R basis. The first algorithm exhaustively searches over the group; while the second algorithm searches only for Householder reflections. The exhaustive search algorithm yields an average R count of 2.193 ( 11 ) + 8.621 ( 7 ) log 10 ( 1 / ɛ ) , albeit with a time complexity of O ( ɛ − 4.4 ) . The Householder search algorithm results in a larger average R count of 3.20 ( 13 ) + 10.77 ( 3 ) log 10 ( 1 / ɛ ) at a reduced time complexity of O ( ɛ − 0.42 ) , greatly extending the reach in ɛ . These costs correspond asymptotically to 35% and 69% more non-Clifford gates compared with synthesizing the same unitary with two qubits. Such initial results are encouraging for using the R gate as the nontransversal gate for qutrit-based computation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2004

Fast Query-Optimized Kernel-Machine Classification

A recently developed algorithm performs kernel-machine classification via incremental approximate nearest support vectors. The algorithm implements support-vector machines (SVMs) at speeds 10 to 100 times those attainable by use of conventional SVM algorithms. The algorithm offers potential benefits for classification of images, recognition of speech, recognition of handwriting, and diverse other applications in which there are requirements to discern patterns in large sets of data. SVMs constitute a subset of kernel machines (KMs), which have become popular as models for machine learning and, more specifically, for automated classification of input data on the basis of labeled training data. While similar in many ways to k-nearest-neighbors (k-NN) models and artificial neural networks (ANNs), SVMs tend to be more accurate. Using representations that scale only linearly in the numbers of training examples, while exploring nonlinear (kernelized) feature spaces that are exponentially larger than the original input dimensionality, KMs elegantly and practically overcome the classic curse of dimensionality. However, the price that one must pay for the power of KMs is that query-time complexity scales linearly with the number of training examples, making KMs often orders of magnitude more computationally expensive than are ANNs, decision trees, and other popular machine learning alternatives. The present algorithm treats an SVM classifier as a special form of a k-NN. The algorithm is based partly on an empirical observation that one can often achieve the same classification as that of an exact KM by using only small fraction of the nearest support vectors (SVs) of a query. The exact KM output is a weighted sum over the kernel values between the query and the SVs. In this algorithm, the KM output is approximated with a k-NN classifier, the output of which is a weighted sum only over the kernel values involving k selected SVs. Before query time, there are gathered statistics about how misleading the output of the k-NN model can be, relative to the outputs of the exact KM for a representative set of examples, for each possible k from 1 to the total number of SVs. From these statistics, there are derived upper and lower thresholds for each step k. These thresholds identify output levels for which the particular variant of the k-NN model already leans so strongly positively or negatively that a reversal in sign is unlikely, given the weaker SV neighbors still remaining. At query time, the partial output of each query is incrementally updated, stopping as soon as it exceeds the predetermined statistical thresholds of the current step. For an easy query, stopping can occur as early as step k = 1. For more difficult queries, stopping might not occur until nearly all SVs are touched. A key empirical observation is that this approach can tolerate very approximate nearest-neighbor orderings. In experiments, SVs and queries were projected to a subspace comprising the top few principal- component dimensions and neighbor orderings were computed in that subspace. This approach ensured that the overhead of the nearest-neighbor computations was insignificant, relative to that of the exact KM computation.

Mazzoni, Dominic↗
NASA NTRS1991

An Explicit Upwind Algorithm for Solving the Parabolized Navier-Stokes Equations

An explicit, upwind algorithm was developed for the direct (noniterative) integration of the 3-D Parabolized Navier-Stokes (PNS) equations in a generalized coordinate system. The new algorithm uses upwind approximations of the numerical fluxes for the pressure and convection terms obtained by combining flux difference splittings (FDS) formed from the solution of an approximate Riemann (RP). The approximate RP is solved using an extension of the method developed by Roe for steady supersonic flow of an ideal gas. Roe's method is extended for use with the 3-D PNS equations expressed in generalized coordinates and to include Vigneron's technique of splitting the streamwise pressure gradient. The difficulty associated with applying Roe's scheme in the subsonic region is overcome. The second-order upwind differencing of the flux derivatives are obtained by adding FDS to either an original forward or backward differencing of the flux derivative. This approach is used to modify an explicit MacCormack differencing scheme into an upwind differencing scheme. The second order upwind flux approximations, applied with flux limiters, provide a method for numerically capturing shocks without the need for additional artificial damping terms which require adjustment by the user. In addition, a cubic equation is derived for determining Vegneron's pressure splitting coefficient using the updated streamwise flux vector. Decoding the streamwise flux vector with the updated value of Vigneron's pressure splitting improves the stability of the scheme. The new algorithm is applied to 2-D and 3-D supersonic and hypersonic laminar flow test cases. Results are presented for the experimental studies of Holden and of Tracy. In addition, a flow field solution is presented for a generic hypersonic aircraft at a Mach number of 24.5 and angle of attack of 1 degree. The computed results compare well to both experimental data and numerical results from other algorithms. Computational times required for the upwind PNS code are approximately equal to an explicit PNS MacCormack's code and existing implicit PNS solvers.

Korte, John J.↗
NASA NTRS1987

Improved Heat-Transfer Calculations for Hypersonic Flow

Lewis number corrected for extremely high airspeeds. Algorithm calculates improved, variable value of Lewis number, factor in equation for heat-transfer coefficient at stagnation point of body in hypersonic flow mach numbers of approximately 25. New algorithm improves accuracy of calculations of heat generated by hot air acting on moving body.

Greenschlag, S. N.↗
DOE OSTI2024

Geometry-aware training of factorized layers in tensor Tucker format

Reducing parameter redundancies in neural network architectures is crucial for achieving feasible computational and memory requirements during train and inference of large networks. Given its easy implementation and flexibility, one promising approach is layer factorization, which reshapes weight tensors into a matrix format and parameterizes it as the product of two rank-r matrices. However, this family of approaches often requires an initial full-model warm-up phase, prior knowledge of a feasible rank, and it is sensitive to parameter initialization.In this work, we introduce a novel approach to train the factors of a Tucker decomposition of the weight tensors. Our training proposal proves to be optimal in locally approximating the original unfactorized dynamics and stable for the initialization. Furthermore, the rank of each mode is dynamically updated during training.We provide a theoretical analysis of the algorithm, showing convergence, approximation and local descent guarantees. The method's performance is further illustrated through a variety of experiments, showing remarkable training compression rates and comparable or even better performance than the full baseline and alternative layer factorization strategies.

Zangrando, Emanuele [Gran Sasso Science Institute ↗
DOE OSTI2024

Continued performance improvement and integration of MOOSE's thermal-hydraulics capabilities (M3 Milestone Report)

This work introduces performance, robustness and workflow improvements to Multiphysics Object-Oriented Simulation Environment (MOOSE)-based thermal-hydraulics solvers. It presents work related to the acceleration of segregated fluid dynamics algorithms, which show approximately a factor of 10 speedup compared to the preceding implementation. Additionally, we discuss approaches to use advanced, Schurr complement-based, field split preconditioners for monolithic solution algorithms relying on the finite volume method. The presence of the Rhie-Chow interpolation makes the utilization of this preconditioner challenging, but the results indicate that for a moderately large problem a factor of 3.4 speedup can be achieved in conjunction with a factor of 3.5 reduction in memory usage. Furthermore, we introduce several pseudo-time stepping approaches to MOOSE for the robust convergence to steady-state solutions when steady-state solves don't converge due to the initial guesses being too far from the solution in Newton's method. Every MOOSE-based application has access this algorithm and can benefit from its use. Moreover, several new avenues have been presented for importing meshes from commercial software which make meshing easier. Lastly, the Component system within the Thermal-Hydraulics Module (THM) of MOOSE is abstracted by separating geometry- and physics-related properties.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2004

Adaptive DIT-Based Fringe Tracking and Prediction at IOTA

An automatic fringe tracking system has been developed and implemented at the Infrared Optical Telescope Array (IOTA). In testing during May 2002, the system successfully minimized the optical path differences (OPDs) for all three baselines at IOTA. Based on sliding window discrete Fourier transform (DFT) calculations that were optimized for computational efficiency and robustness to atmospheric disturbances, the algorithm has also been tested extensively on off-line data. Implemented in ANSI C on the 266 MHZ PowerPC processor running the VxWorks real-time operating system, the algorithm runs in approximately 2.0 milliseconds per scan (including all three interferograms), using the science camera and piezo scanners to measure and correct the OPDs. Preliminary analysis on an extension of this algorithm indicates a potential for predictive tracking, although at present, real-time implementation of this extension would require significantly more computational capacity.

Wilson, Edward↗
DOE OSTI2023

A Prototype Thick-Target Bremsstrahlung Model with Angularly-Dependent Emission in the MCNP6 ® Code

This document summarizes the current thick-target bremsstrahlung (TTB) model in MCNP and provides test results for an alternative implementation to improve the accuracy with reduced cost compared to full electron transport. It has been observed that the current TTB model produces inaccurate results in problems where the medium is thick with respect to electrons, but the photon distribution in the problem has a strong directionality. An example of such a simulation is detectors surrounding a metal target irradiated with a radiographic beam of high energy photons. The primary cause of this discrepancy is the current TTB method emits all bremsstrahlung photons in the same direction as the primary electron produced from each (γ, e ± ) interaction, leading to artificially forward peaked photon distributions for intermediate to high-energy incident photons. To improve the TTB model, we have implemented an angularly-dependent TTB model in a developer version of the MCNP6 ® code; for developers, this was done on the branch prototype/angular_ttb in the mcnp6 repo on bitbucket. The angularly-dependent TTB model accounts for the energy and scattering of electrons as they slow down in the current material, but does not sample the computationally expensive energy straggling, secondary electron events, and tracking electrons; this approach is significantly less computationally expensive than full electron transport and can be comparable to the original TTB method for problems with sufficiently complex materials and geometry. To evaluate the method, we have modeled a simple problem of a beam of 5 MeV photons incident on a sphere of plutonium surrounded by detectors at different deflection angles. For this problem, the angularly-dependent TTB produces a photon flux within 8.0% for a 90 degree deflection angle and 0.8% along the beam axis, as compared to the electron transport solution. This is an improvement compared to a 43% and 81% discrepancy with the original TTB method, respectively. The rest of this work includes the following: the first section details the current TTB treatment in MCNP, which has not been well documented elsewhere. Then, the modified TTB algorithm is detailed and the approximations compared to the condensed history algorithm are compared. Results are given comparing the two TTB methods to the condensed history transport algorithm. The appendix includes details for code developers on relevant electron transport implementation details and potential code improvements for future work.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2025

Identifying Vehicle Signals in Continuous Seismic Data Using Unsupervised Machine-Learning Techniques

Seismic sensors deployed near roadways effectively capture ground vibrations generated by passing vehicles. Although both traditional and machine‐learning algorithms have been utilized for analyzing such signals, independent validation of detected vehicle events remains limited. We applied two unsupervised machine‐learning algorithms, uniform manifold approximation and projection for dimension reduction, and hierarchical density‐based spatial clustering of applications with noise, to continuous seismic data collected along a road on the main campus of Oak Ridge National Laboratory. The algorithms identified seven distinct cluster labels across the entire dataset. By comparing these cluster labels with precipitation records from a nearby weather station and image‐derived labels from a local camera system, we identified one cluster associated with rainfall and another with vehicle activity. Our algorithms identified a greater number of vehicle‐related labels compared to the camera‐derived labels because seismic data are unaffected by poor lighting conditions. The arrival times of the newly detected vehicle signals corresponded well with the road’s speed limit, supporting our findings. Our algorithm outperformed the short‐term average/long‐term average method and k‐means clustering. Our results suggest that seismic data, when analyzed with machine‐learning algorithms, can complement existing vehicle monitoring systems, particularly under challenging environmental conditions.

Chai, Chengping [Oak Ridge National Laboratory (OR↗
DOE OSTI2022

Quantum Local Search with the Quantum Alternating Operator Ansatz

We present a new hybrid, local search algorithm for quantum approximate optimization of constrained combinatorial optimization problems. We focus on the Maximum Independent Set problem and demonstrate the ability of quantum local search to solve large problem instances on quantum devices with few qubits. This hybrid algorithm iteratively finds independent sets over carefully constructed neighborhoods and combines these solutions to obtain a global solution. We study the performance of this algorithm on 3-regular, Community, and Erdős-Rényi graphs with up to 100 nodes.

Tomesh, Teague↗
DOE OSTI2023

Sparsity of the electron repulsion integral tensor using different localized virtual orbital representations in local second-order Møller–Plesset theory

Utilizing localized orbitals, local correlation theory can reduce the unphysically high system-size scaling of post-Hartree–Fock (post-HF) methods to linear scaling in insulating molecules. The sparsity of the four-index electron repulsion integral (ERI) tensor is central to achieving this reduction. For second-order Møller–Plesset theory (MP2), one of the simplest post-HF methods, only the (ia|jb) ERIs are needed, coupling occupied orbitals i, j and virtuals a, b. In this paper, we compare the numerical sparsity (called the “ragged list”) and two other approaches revealing the low-rank sparsity of the ERI. The ragged list requires only one set of (localized) virtual orbitals, and we find that the orthogonal valence virtual-hard virtual set of virtuals originally proposed by Subotnik et al. gives the sparsest ERI tensor. To further compress the ERI tensor, the pair natural orbital (PNO) type representation uses different sets of virtual orbitals for different occupied orbital pairs, while the occupied-specific virtual (OSV) approach uses different virtuals for each occupied orbital. Here, our results indicate that while the low-rank PNO representation achieves significant rank reduction, it also requires more memory than the ragged list. The OSV approach requires similar memory to that of the ragged list, but it involves greater algorithmic complexity. An approximation (called the “fixed sparsity pattern”) for solving the local MP2 equations using the numerically sparse ERI tensor is proposed and tested to be sufficiently accurate and to have highly controllable error. A low-scaling local MP2 algorithm based on the ragged list and the fixed sparsity pattern is therefore promising.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2006

Compressible Flow Toolbox

The Compressible Flow Toolbox is primarily a MATLAB-language implementation of a set of algorithms that solve approximately 280 linear and nonlinear classical equations for compressible flow. The toolbox is useful for analysis of one-dimensional steady flow with either constant entropy, friction, heat transfer, or Mach number greater than 1. The toolbox also contains algorithms for comparing and validating the equation-solving algorithms against solutions previously published in open literature. The classical equations solved by the Compressible Flow Toolbox are as follows: The isentropic-flow equations, The Fanno flow equations (pertaining to flow of an ideal gas in a pipe with friction), The Rayleigh flow equations (pertaining to frictionless flow of an ideal gas, with heat transfer, in a pipe of constant cross section), The normal-shock equations, The oblique-shock equations, and The expansion equations.

Melcher, Kevin J.↗