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Results for “Approximate Computing”

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 1,189 records · Page 66
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Using hybrid implicit Monte Carlo diffusion to simulate gray radiation hydrodynamics

This work describes how to couple a hybrid Implicit Monte Carlo Diffusion (HIMCD) method with a Lagrangian hydrodynamics code to evaluate the coupled radiation hydrodynamics equations. This HIMCD method dynamically applies Implicit Monte Carlo Diffusion (IMD) [1] to regions of a problem that are opaque and diffusive while applying standard Implicit Monte Carlo (IMC) [2] to regions where the diffusion approximation is invalid. We show that this method significantly improves the computational efficiency as compared to a standard IMC/Hydrodynamics solver, when optically thick diffusive material is present, while maintaining accuracy. Two test cases are used to demonstrate the accuracy and performance of HIMCD as compared to IMC and IMD. The first is the Lowrie semi-analytic diffusive shock [3]. The second is a simple test case where the source radiation streams through optically thin material and heats a thick diffusive region of material causing it to rapidly expand. We found that HIMCD proves to be accurate, robust, and computationally efficient for these test problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Adaptive resource allocation for surrogate modeling of systems comprised of multiple disciplines with varying fidelity

We present an adaptive algorithm for constructing surrogate models for integrated systems composed of a set of coupled components. With this goal we introduce ‘coupling’ variables with a priori unknown distributions that allow approximations of each component to be built independently. Once built, the surrogates of the components are combined and used to predict system-level quantities of interest (QoI) at a fraction of the cost of interrogating the full system model. We use a greedy experimental design procedure, based upon a modification of Multi-Index Stochastic Collocation (MISC), to minimize the error of the combined surrogate. This is achieved by refining each component surrogate in accordance with its relative contribution to error in the approximation of the system-level QoI. Our adaptation of MISC is a multi-fidelity procedure that can leverage ensembles of models of varying cost and accuracy, for one or more components, to produce estimates of system-level QoI. Several numerical examples demonstrate the efficacy of the proposed approach on systems involving feed-forward and feedback coupling. For a fixed computational budget, the proposed algorithm is able to produce approximations that are orders of magnitude more accurate than approximations that treat the integrated system as a black-box.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Change detection and classification of land cover in multispectral satellite imagery using clustering of sparse approximations (CoSA) over learned feature dictionaries

Neuromimetic machine vision and pattern recognition algorithms are of great interest for landscape characterization and change detection in satellite imagery in support of global climate change science and modeling. We present results from an ongoing effort to extend machine vision methods to the environmental sciences, using adaptive sparse signal processing combined with machine learning. A Hebbian learning rule is used to build multispectral, multiresolution dictionaries from regional satellite normalized band difference index data. Land cover labels are automatically generated via our CoSA algorithm: Clustering of Sparse Approximations, using a clustering distance metric that combines spectral and spatial textural characteristics to help separate geologic, vegetative, and hydrologie features. We demonstrate our method on example Worldview-2 satellite images of an Arctic region, and use CoSA labels to detect seasonal surface changes. In conclusion, our results suggest that neuroscience-based models are a promising approach to practical pattern recognition and change detection problems in remote sensing.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

FELIX-1.0: A finite element solver for the time dependent generator coordinate method with the Gaussian overlap approximation

In this study, we describe the software package FELIX that solves the equations of the time-dependent generator coordinate method (TDGCM) in NN-dimensions (N ≥ 1) under the Gaussian overlap approximation. The numerical resolution is based on the Galerkin finite element discretization of the collective space and the Crank–Nicolson scheme for time integration. The TDGCM solver is implemented entirely in C++. Several additional tools written in C++, Python or bash scripting language are also included for convenience. In this paper, the solver is tested with a series of benchmarks calculations. We also demonstrate the ability of our code to handle a realistic calculation of fission dynamics.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Solving the Dynamics-Aware Economic Dispatch Problem with the Koopman Operator

The dynamics-aware economic dispatch (DED) problem embeds low-level generator dynamics and operational constraints to enable near real-time scheduling of generation units in a power network. DED produces a more dynamic supervisory control policy than traditional economic dispatch (T-ED) that reduces overall generation costs. However, in contrast to T-ED, DED is a nonlinear, non-convex optimization problem that is computationally prohibitive to solve. We introduce a machine learning-based operator-theoretic approach for solving the DED problem efficiently. Specifically, we develop a novel discrete-time Koopman Operator (KO) formulation that embeds domain information into the structure of the KO to learn high-fidelity approximations of the generator dynamics. Using the KO approximation, the DED problem can be reformulated as a computationally tractable linear program (abbreviated DED-KO). We demonstrate the high solution quality and computational-time savings of the DED-KO model over the original DED formulation on a 9-bus test system.

King, Ethan↗
DOE OSTI2016

Hyperspherical Sparse Approximation Techniques for High-Dimensional Discontinuity Detection

This work proposes a hyperspherical sparse approximation framework for detecting jump discontinuities in functions in high-dimensional spaces. The need for a novel approach results from the theoretical and computational inefficiencies of well-known approaches, such as adaptive sparse grids, for discontinuity detection. Our approach constructs the hyperspherical coordinate representation of the discontinuity surface of a function. Then sparse approximations of the transformed function are built in the hyperspherical coordinate system, with values at each point estimated by solving a one-dimensional discontinuity detection problem. Due to the smoothness of the hypersurface, the new technique can identify jump discontinuities with significantly reduced computational cost, compared to existing methods. Several approaches are used to approximate the transformed discontinuity surface in the hyperspherical system, including adaptive sparse grid and radial basis function interpolation, discrete least squares projection, and compressed sensing approximation. Moreover, hierarchical acceleration techniques are also incorporated to further reduce the overall complexity. In conclusion, rigorous complexity analyses of the new methods are provided, as are several numerical examples that illustrate the effectiveness of our approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Simulation of biochemical reactions with time-dependent rates by the rejection-based algorithm

We address the problem of simulating biochemical reaction networks with time-dependent rates and propose a new algorithm based on our rejection-based stochastic simulation algorithm (RSSA) [Thanh et al., J. Chem. Phys. 141(13), 134116 (2014)]. The computation for selecting next reaction firings by our time-dependent RSSA (tRSSA) is computationally efficient. Furthermore, the generated trajectory is exact by exploiting the rejection-based mechanism. We benchmark tRSSA on different biological systems with varying forms of reaction rates to demonstrate its applicability and efficiency. We reveal that for nontrivial cases, the selection of reaction firings in existing algorithms introduces approximations because the integration of reaction rates is very computationally demanding and simplifying assumptions are introduced. The selection of the next reaction firing by our approach is easier while preserving the exactness.

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

Capabilities of multivariate Bayesian inference toward seismic hazard assessment

Multivariate Bayesian analysis can bring significant benefits to seismic hazard analysis: Its multivariate feature enables computing scalar and vector hazard without making any approximations; Correlations between intensity measures are implicitly modeled, permitting direct simulation of ground motion selection tools such as the conditional mean spectrum and the generalized conditioning intensity measure; and Its updating feature enables a seamless integration of new ground motion data into the hazard results. Here, we first develop a multivariate Bayesian ground motion model through the NGA-West2 database. The model functional form considers fault-type, magnitude, and distance dependencies, and also the linear and the rock intensity dependent site response. We use a hybrid Markov Chain Monte Carlo sampling to perform Bayesian inference consisting of Gibbs step and a multilevel Metropolis-Hastings step. We then perform several checks on the model and note that its performance is satisfactory. Finally, we illustrate the merits of this multivariate Bayesian analysis, which include: ground motion model updating with ground motion data recorded in the last four years not part of the NGA-West2 database; computation of scalar and vector seismic hazard using the un-updated and updated ground motion models for Los Angeles, CA; and simulation of the conditional mean spectrum under scalar and vector IM conditioning while accounting for different sources of aleatoric and epistemic uncertainties.

58 GEOSCIENCES↗
DOE OSTI2013

Estimating the Bias of Local Polynomial Approximation Methods Using the Peano Kernel

The determination of uncertainty of an estimate requires both the variance and the bias of the estimate. Calculating the variance of local polynomial approximation (LPA) estimates is straightforward. We present a method, using the Peano Kernel Theorem, to estimate the bias of LPA estimates and show how this can be used to optimize the LPA parameters in terms of the bias-variance tradeoff. Figures of merit are derived and values calculated for several common methods. The results in the literature are expanded by giving bias error bounds that are valid for all lengths of the smoothing interval, generalizing the currently available asymptotic results that are only valid in the limit as the length of this interval goes to zero.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Wormholes and black hole microstates in AdS/CFT

It has long been known that the coarse-grained approximation to the black hole density of states can be computed using classical Euclidean gravity. In this work we argue for another entry in the dictionary between Euclidean gravity and black hole physics, namely that Euclidean wormholes describe a coarse-grained approximation to the energy level statistics of black hole microstates. To do so we use the method of constrained instantons to obtain an integral representation of wormhole amplitudes in Einstein gravity and in full-fledged AdS/CFT. These amplitudes are non-perturbative corrections to the two-boundary problem in AdS quantum gravity. The full amplitude is likely UV sensitive, dominated by small wormholes, but we show it admits an integral transformation with a macroscopic, weakly curved saddle-point approximation. The saddle is the “double cone” geometry of Saad, Shenker, and Stanford, with fixed moduli. In the boundary description this saddle appears to dominate a smeared version of the connected two-point function of the black hole density of states, and suggests level repulsion in the microstate spectrum. Using these methods we further study Euclidean wormholes in pure Einstein gravity and in IIB supergravity on Euclidean AdS 5 × S 5 . We address the perturbative stability of these backgrounds and study brane nucleation instabilities in 10d supergravity. In particular, brane nucleation instabilities of the Euclidean wormholes are lifted by the analytic continuation required to obtain the Lorentzian spectral form factor from gravity. Our results indicate a factorization paradox in AdS/CFT.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Nonunitary Variational Quantum Eigensolver with the Localized Active Space Method and Cost Mitigation

Accurately describing strongly correlated systems with affordable quantum resources remains a central challenge for quantum chemistry applications on near and intermediate term quantum computers. The localized active space self-consistent field (LASSCF) approximates the complete active space self-consistent field (CASSCF) by generating active space-based wave functions within specific fragments while treating interfragment correlation with mean-field approach, hence is computationally less expensive. Hardware-efficient ansatzes (HEA) offer affordable and shallower circuits, yet they often fail to capture the necessary correlation. Previously, Jastrow-factor-inspired nonunitary qubit operators were proposed to use with HEA for variational quantum eigensolver (VQE) calculations (so-called nuVQE), as they do not increase circuit depths and recover correlation beyond the mean-field level for Hartree–Fock initial states. Here, in this study, we explore running nuVQE with LASSCF as the initial state. The method, named LAS-nuVQE, is shown to recover interfragment correlations, reach chemical accuracy with a small number of gates (<70) in both H 4 and square cyclobutadiene (C 4 H 4 ), and produces more accurate energetics than its HEA counterparts at all circuit depths. To further address the inherent symmetry-breaking in HEA, we implemented spin-constrained LAS-nuVQE to extend the capabilities of HEA further and show spin-pure results for square cyclobutadiene. We also mitigate the increased measurement overhead of nuVQE via Pauli grouping and shot-frugal sampling, reducing measurement costs by up to 2 orders of magnitude compared to ungrouped operator, and show that one can achieve better accuracy with a small number of shots (10 3–4 ) per one expectation value calculation compared to noiseless simulations with one or two orders of magnitude more shots. Finally, wall clock time estimates show that, with our measurement mitigation protocols, nuVQE becomes a cheaper and more accurate alternative than vanilla VQE with HEA. Taken together, these developments illustrate a practical pathway toward performing multireference chemical simulations with accuracy and affordable resources on today’s quantum hardware, achieving both accuracy and affordability in challenging correlated systems.

Wang, Qiaohong [Univ. of Chicago, IL (United State↗
DOE OSTI2013

Estimating anisotropic diffusion of neutrons near the boundary of a pebble bed random system

Due to the arrangement of the pebbles in a Pebble Bed Reactor (PBR) core, if a neutron is located close to a boundary wall, its path length probability distribution function in directions of flight parallel to the wall is significantly different than in other directions. Hence, anisotropic diffusion of neutrons near the boundaries arises. We describe an analysis of neutron transport in a simplified 3-D pebble bed random system, in which we investigate the anisotropic diffusion of neutrons born near one of the system's boundary walls. While this simplified system does not model the actual physical process that takes place near the boundaries of a PBR core, the present work paves the road to a formulation that may enable more accurate diffusion simulations of such problems to be performed in the future. Monte Carlo codes have been developed for (i) deriving realizations of the 3-D random system, and (ii) performing 3-D neutron transport inside the heterogeneous model; numerical results are presented for three different choices of parameters. These numerical results are used to assess the accuracy of estimates for the mean-squared displacement of neutrons obtained with the diffusion approximations of the Atomic Mix Model and of the recently introduced [1] Non-Classical Theory with angular-dependent path length distribution. The Non-Classical Theory makes use of a Generalized Linear Boltzmann Equation in which the locations of the scattering centers in the system are correlated and the distance to collision is not exponentially distributed. We show that the results predicted using the Non-Classical Theory successfully model the anisotropic behavior of the neutrons in the random system, and more closely agree with experiment than the results predicted by the Atomic Mix Model. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2021

Revisiting the ODE Method for Recursive Algorithms: Fast Convergence Using Quasi Stochastic Approximation

Several decades ago, Profs. Sean Meyn and Lei Guo were postdoctoral fellows at ANU, where they shared interest in recursive algorithms. It seems fitting to celebrate Lei Guo's 60th birthday with a review of the ODE Method and its recent evolution. The method has been regarded as a technique for algorithm analysis. It is argued that this viewpoint is backwards: The original stochastic approximation method was surely motivated by an ODE, and tools for analysis came much later (based on establishing robustness of Euler approximations). The paper presents a brief survey of recent research in machine learning that shows the power of algorithm design in continuous time, following by careful approximation to obtain a practical recursive algorithm. While these methods are usually presented in a stochastic setting, this is not a prerequisite. In fact, recent theory shows that rates of convergence can be dramatically accelerated by applying techniques inspired by quasi Monte-Carlo. Subject to conditions, the optimal rate of convergence can be obtained by applying the averaging technique of Polyak and Ruppert. The conditions are not universal, but theory suggests alternatives to achieve acceleration. The theory is illustrated with applications to gradient-free optimization, and policy gradient algorithms for reinforcement learning.

learning and adaptive systems in artificial intell↗
DOE OSTI2025

Static Subspace Approximation for Random Phase Approximation Correlation Energies: Applications to Materials for Catalysis and Electrochemistry

Modeling complex materials using high-fidelity, ab initio methods at low cost is a fundamental goal for quantum chemical software packages. The GW approximation and random phase approximation (RPA) provide a unified description of both electronic structure and total energies using the same physics in a many-body perturbative approach that can be more accurate than generalized-gradient density functional theory (DFT) methods. However, GW/RPA implementations have historically been limited to either specific materials classes or application toward small chemical systems. Here, the static subspace approximation allows for reduced cost full-frequency GW/RPA calculations and has previously been benchmarked thoroughly for GW calculations. Here, we describe our approach to including partial occupations of electronic orbitals in full-frequency GW and RPA calculations for the study of electrocatalysts. We benchmarked RPA total energy calculations using the subspace approximation across a diverse test suite of materials for a variety of computational parameters. The benchmarking quantifies the impact of different extrapolation procedures for representing the static polarizability at infinite screened cutoff, and shows that using screened cutoffs above 20-25 Ryd result in diminishing accuracy returns for predicting RPA total energies. Additionally, for moderately sized electrocatalytic models, 2-3 times fewer computational resources are used to compute RPA total energies by representing the static polarizability with 20-30% of the static subspace basis, with an error of approximately 0.01 eV or better in RPA adsorption energy calculations. Finally, we show that for these electrochemical models RPA can shift DFT adsorption energy shifts by up to 0.5 eV and that GW can frequently shift DFT eigenvalues of surface and adsorbate states by approximately 0.5-1 eV.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Approximate l-Fold Cross-Validation with Least Squares SVM and Kernel Ridge Regression

Kernel methods have difficulties scaling to large modern data sets. The scalability issues are based on computational and memory requirements for working with a large matrix. These requirements have been addressed over the years by using low-rank kernel approximations or by improving the solvers' scalability. However, Least Squares Support Vector Machines (LS-SVM), a popular SVM variant, and Kernel Ridge Regression still have several scalability issues. In particular, the O(n^3) computational complexity for solving a single model, and the overall computational complexity associated with tuning hyper parameters are still major problems. We address these problems by introducing an O(nlog n) approximate l-fold cross-validation method that uses a multi-level circulant matrix to approximate the kernel. In addition, we prove our algorithm's computational complexity and present empirical runtimes on data sets with approximately one million data points. We also validate our approximate method's effectiveness at selecting hyper parameters on real world and standard benchmark data sets. Lastly, we provide experimental results on using a multi level circulant kernel approximation to solve LS-SVM problems with hyper parameters selected using our method.

Computer Science↗
DOE OSTI2025

Virtual element approximations of the time-fractional nonlinear convection-diffusion equation on polygonal meshes

We extend the Virtual Element Method to a two-dimensional unsteady nonlinear convection-diffusion equation characterized by a fractional-order derivative with respect to the time variable. Our methodology is based on three fundamental technical components: a fractional version of the Grunwald-Letnikov approximation, discrete maximal regularity, and the regularity theory associated with non-linearity. We prove the method's well-posedness, i.e., the approximate solution's existence and uniqueness to the time-fractional convection-diffusion equation with a Lipschitz nonlinear source term. The fully discrete scheme inherently maintains stability and consistency by leveraging the discrete maximal regularity and the energy projection operator. The convergence in the L 2 -norm and H 1 -norm to various mesh configurations is validated by numerical results, underlining the practical effectiveness of the proposed method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

A full-dimensional quantum dynamical study of H{sub 2}+H{sub 2} collisions: Coupled-states versus close-coupling formulation

Collision-induced energy transfer involving H{sub 2} molecules plays an important role in many areas of physics. Kinetic models often require a complete set of state-to-state rate coefficients for H{sub 2}+H{sub 2} collisions in order to interpret results from spectroscopic observations or to make quantitative predictions. Recent progress in full-dimensional quantum dynamics using the numerically exact close-coupling (CC) formulation has provided good agreement with existing experimental data for low-lying states of H{sub 2} and increased the number of state-to-state cross sections that may be reliably determined over a broad range of energies. Nevertheless, there exist many possible initial states (e.g., states with high rotational excitation) that still remain elusive from a computational standpoint even at relatively low collision energies. In these cases, the coupled-states (CS) approximation offers an alternative full-dimensional formulation. We assess the accuracy of the CS approximation for H{sub 2}+H{sub 2} collisions by comparison with benchmark results obtained using the CC formulation. The results are used to provide insight into the orientation effects of the various internal energy transfer mechanisms. A statistical CS approximation is also investigated and cross sections are reported for transitions which would otherwise be impractical to compute.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗