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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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Combining Sparse Approximate Factorizations with Mixed-precision Iterative Refinement

The standard LU factorization-based solution process for linear systems can be enhanced in speed or accuracy by employing mixed-precision iterative refinement. Most recent work has focused on dense systems. We investigate the potential of mixed-precision iterative refinement to enhance methods for sparse systems based on approximate sparse factorizations. In doing so, we first develop a new error analysis for LU- and GMRES-based iterative refinement under a general model of LU factorization that accounts for the approximation methods typically used by modern sparse solvers, such as low-rank approximations or relaxed pivoting strategies. We then provide a detailed performance analysis of both the execution time and memory consumption of different algorithms, based on a selected set of iterative refinement variants and approximate sparse factorizations. Our performance study uses the multifrontal solver MUMPS, which can exploit block low-rank factorization and static pivoting. We evaluate the performance of the algorithms on large, sparse problems coming from a variety of real-life and industrial applications showing that mixed-precision iterative refinement combined with approximate sparse factorization can lead to considerable reductions of both the time and memory consumption.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Massively parallel and universal approximation of nonlinear functions using diffractive processors

Nonlinear computation is essential for a wide range of information processing tasks, yet implementing nonlinear functions using optical systems remains a challenge due to the weak and power-intensive nature of optical nonlinearities. Overcoming this limitation without relying on nonlinear optical materials could unlock unprecedented opportunities for ultrafast and parallel optical computing systems. Here, we demonstrate that large-scale nonlinear computation can be performed using linear optics through optimized diffractive processors composed of passive phase-only surfaces. In this framework, the input variables of nonlinear functions are encoded into the phase of an optical wavefront—e.g., via a spatial light modulator (SLM)—and transformed by an optimized diffractive structure with spatially varying point-spread functions to yield output intensities that approximate a large set of unique nonlinear functions–all in parallel. We provide proof establishing that this architecture serves as a universal function approximator for an arbitrary set of bandlimited nonlinear functions, also covering wavelength-multiplexed nonlinear functions as well as multi-variate and complex-valued functions that are all-optically cascadable. Our analysis also indicates the successful approximation of typical nonlinear activation functions commonly used in neural networks, including the sigmoid, tanh, ReLU (rectified linear unit), and softplus. We numerically demonstrate the parallel computation of one million distinct nonlinear functions, accurately executed at wavelength-scale spatial density at the output of a diffractive optical processor. Furthermore, we experimentally validated this framework using in situ optical learning and approximated 35 unique nonlinear functions in a single shot using a compact setup consisting of an SLM and an image sensor. These results establish diffractive optical processors as a scalable platform for massively parallel universal nonlinear function approximation, paving the way for new capabilities in analog optical computing based on linear materials.

Rahman, Md Sadman Sakib [University of California,↗
DOE OSTI2018

Neutron Capture Energies for Flux Normalization and Approximate Model for Gamma-Smeared Power

The Consortium for Advanced Simulation of Light Water Reactors (CASL) Virtual Environment for Reactor Applications (VERA) neutronics simulator MPACT has used a single recoverable fission energy for each fissionable nuclide assuming that all recoverable energies come only from fission reaction, for which capture energy is merged with fission energy. This approach includes approximations and requires improvement by separating capture energy from the merged effective recoverable energy. This report documents the procedure to generate recoverable neutron capture energies and the development of a program called CapKappa to generate capture energies. Recoverable neutron capture energies have been generated by using CapKappa with the evaluated nuclear data file (ENDF)/B-7.0 and 7.1 cross section and decay libraries. The new capture kappas were compared to the current SCALE-6.2 and the CASMO-5 capture kappas. These new capture kappas have been incorporated into the Simplified AMPX 51- and 252-group libraries, and they can be used for the AMPX multigroup (MG) libraries and the SCALE code package. The CASL VERA neutronics simulator MPACT does not include a gamma transport capability, which limits it to explicitly estimating local energy deposition from fission, neutron, and gamma slowing down and capture. Since the mean free path of gamma rays is typically much longer than that for the neutron, and the total gamma energy is about 10% to the total energy, the gamma-smeared power distribution is different from the fission power distribution. Explicit local energy deposition through neutron and gamma transport calculation is significantly important in multi-physics whole core simulation with thermal-hydraulic feedback. Therefore, the gamma transport capability should be incorporated into the CASL neutronics simulator MPACT. However, this task will be timeconsuming in developing the neutron induced gamma production and gamma cross section libraries. This study is to investigate an approximate model to estimate gammasmeared power distribution without performing any gamma transport calculation. A simple approximate gamma smearing model has been investigated based on the facts that pinwise gamma energy depositions are almost flat over a fuel assembly, and assembly-wise gamma energy deposition is proportional to kappa-fission energy deposition. The approximate gamma smearing model works well for single assembly cases, and can partly improve the gamma smeared power distribution for the whole core model. Although the power distributions can be improved by the approximate gamma smearing model, still there is an issue to explicitly obtain local energy deposition. A new simple approach or gamma transport/diffusion capability may need to be incorporated into MPACT to estimate local energy deposition for more robust multi-physics simulation.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2019

Exploring the Random Phase Approximation for Materials and Chemical Physics

In this work we test the performance of the fully nonlocal random phase approximation (RPA) for challenging problems in materials chemistry and physics. In this work we assessed the fully nonlocal random phase approximation (RPA) for the delicate energy differences of interest in materials chemistry and physics. The applications in this proposal are challenges for the simpler approximations of Kohn-Sham density functional theory, which are part of the current “standard model” for quantum chemistry and condensed matter physics. Direct RPA includes the full exact exchange energy and a nonlocal correlation energy from the occupied and unoccupied Kohn-Sham orbitals and orbital energies, with an approximate but universal description of long-range van der Waals attraction. RPA still cannot be a benchmark electronic structure method without a correction for its short-range correlation energy which is too deep. The short-range error of RPA can be corrected by a spatially nonlocal, exchange-only kernel. Such kernels could be a more reliable and “intrinsic” approximation to capture accurate ground-state energy differences than the expensive SOSEX and other beyond-RPA corrections. In this project we revealed the strengths and limitations of some model kernels through some materials problems focusing on structural phase transitions and transition metal chemistry. In addition we demonstrated the accuracy of the Renormalized RPA for total correlation energies of simple solids, and the pressure-induced phase transitions.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Completely Positive, Simple, and Possibly Highly Accurate Approximation of the Redfield Equation

Here we present a Lindblad master equation that approximates the Redfield equation, a well known master equation derived from first principles, without significantly compromising the range of applicability of the Redfield equation. Instead of full-scale coarse-graining, this approximation only truncates terms in the Redfield equation that average out over a time-scale typical of the quantum system. The first step in this approximation is to properly renormalize the system Hamiltonian, to symmetrize the gains and losses of the state due to the environmental coupling. In the second step, we swap out an arithmetic mean of the spectral density with a geometric one, in these gains and losses, thereby restoring complete positivity. This completely positive approximation, GAME (geometric-arithmetic master equation), is adaptable between its time-independent, time-dependent, and Floquet form. In the exactly solvable, three-level, Jaynes-Cummings model, we find that the error of the approximate state is almost an order of magnitude lower than that obtained by solving the coarse-grained stochastic master equation. As a test-bed, we use a ferromagnetic Heisenberg spin-chain with long-range dipole-dipole coupling between up to 25-spins, and study the differences between various master equations. We find that GAME has the highest accuracy per computational resource.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

The Effect of the Flux Separability Approximation on Multigroup Neutron Transport

The angular dependence of flux-weighted multigroup cross sections is commonly neglected when generating multigroup libraries. The error of this flux separability approximation is typically not isolated from other error sources due to a lack of availability of library generation and corresponding solvers that cannot relax this approximation. These errors can now be isolated and quantified with the availability of a multigroup Monte Carlo transport and multigroup library-generation capability in the OpenMC Monte Carlo transport code. This work will discuss relevant details of the OpenMC implementation, provide an example case useful for detailing the type of errors one can expect from making the flux separability approximation, and end with more realistic problems which show the impact of the approximation and highlight how it can strongly arise from an energy-dependent resonance absorption effect. Since the angle-dependence is intrinsically linked to the energy group structure, these examples also show that relaxing the flux separability approximation with angle-dependent cross sections could be used to reduce either the fine-tuning required to set a multigroup energy structure for a specific reactor type or the number of energy groups required to obtain a desired level of accuracy for a given problem. This trade-off could increase the costs of generating multigroup cross sections, and has the potential to require more memory for storing the multigroup library during the transport calculations, but it can significantly reduce the computational time required since the runtime of a discrete ordinates or method of characteristics neutron transport solver scales roughly linearly with the number of groups.

42 ENGINEERING↗
DOE OSTI2023

Finite-Time Analysis of Whittle Index based Q-Learning for Restless Multi-Armed Bandits with Neural Network Function Approximation

Whittle index policy is a heuristic to the intractable restless multi-armed bandits (RMAB) problem. Although it is provably asymptotically optimal, finding Whittle indices remains difficult. In this paper, we present Neural-Q-Whittle, a Whittle index based Q-learning algorithm for RMAB with neural network function approximation, which is an example of nonlinear two-timescale stochastic approximation with Q-function values updated on a faster timescale and Whittle indices on a slower timescale. Despite the empirical success of deep Q-learning, the non-asymptotic convergence rate of Neural-Q-Whittle, which couples neural networks with two-timescale Q-learning largely remains unclear. This paper provides a finite-time analysis of Neural-Q-Whittle, where data are generated from a Markov chain, and Q-function is approximated by a ReLU neural network. Our analysis leverages a Lyapunov drift approach to capture the evolution of two coupled parameters, and the nonlinearity in value function approximation further requires us to characterize the approximation error. Combing these provide Neural-Q-Whittle with convergence rate, where is the number of iterations.

reinforcement learning, structured learning, conve↗
DOE OSTI2021

An adaptive Hessian approximated stochastic gradient MCMC method

Bayesian approaches have been successfully integrated into training deep neural networks. One popular family is stochastic gradient Markov chain Monte Carlo methods (SG-MCMC), which have gained increasing interest due to their ability to handle large datasets and the potential to avoid overfitting. Although standard SG-MCMC methods have shown great performance in a variety of problems, they may be inefficient when the random variables in the target posterior densities have scale differences or are highly correlated. Here, we present an adaptive Hessian approximated stochastic gradient MCMC method to incorporate local geometric information while sampling from the posterior. The idea is to apply stochastic approximation (SA) to sequentially update a preconditioning matrix at each iteration. The preconditioner possesses second-order information and can guide the random walk of a sampler efficiently. Instead of computing and saving the full Hessian of the log posterior, we use limited memory of the samples and their stochastic gradients to approximate the inverse Hessian-vector multiplication in the updating formula. Moreover, by smoothly optimizing the preconditioning matrix via SA, our proposed algorithm can asymptotically converge to the target distribution with a controllable bias under mild conditions. To reduce the training and testing computational burden, we adopt a magnitude-based weight pruning method to enforce the sparsity of the network. Our method is user-friendly and demonstrates better learning results compared to standard SG-MCMC updating rules. The approximation of inverse Hessian alleviates storage and computational complexities for large dimensional models. Numerical experiments are performed on several problems, including sampling from 2D correlated distribution, synthetic regression problems, and learning the numerical solutions of heterogeneous elliptic PDE. The numerical results demonstrate great improvement in both the convergence rate and accuracy.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Biased degenerate ground-state sampling of small Ising models with converged quantum approximate optimization algorithm

The quantum alternating operator ansatz, a generalization of the quantum approximate optimization algorithm (QAOA), is a quantum algorithm used for approximately solving combinatorial optimization problems. QAOA typically uses the transverse field mixer as the driving Hamiltonian. One of the interesting properties of the transverse field driving Hamiltonian is that it results in nonuniform sampling of degenerate ground states of optimization problems. In this study, we numerically examine the fair sampling properties of the transverse field mixer QAOA, and Grover mixer QAOA (GM-QAOA), which provides theoretical guarantees of fair sampling of degenerate optimal solutions, up to a large enough p such that the mean expectation value converges to an optimal approximation ratio of 1. This comparison is performed with high-quality heuristically computed, but not necessarily optimal, QAOA angles, which give strictly monotonically improving solution quality as p increases. These angles are computed using the Julia based numerical simulation software JuliQAOA. Fair sampling of degenerate ground states is quantified using the Shannon entropy of the ground-state amplitudes distribution. The fair sampling properties are reported on several quantum signature Hamiltonians from previous quantum annealing fair sampling studies. Small random fully connected spin glasses are shown, which exhibit exponential suppression of some degenerate ground states with transverse field mixer QAOA. The transverse field mixer QAOA simulations show that some problem instances clearly saturate the Shannon entropy of 0 with a maximally biased distribution that occurs when the learning converges to an approximation ratio of 1 while other problem instances never deviate from a maximum Shannon entropy (uniform distribution) at any p step. Published by the American Physical Society 2025

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Construction and Investigation of the Third-Order Approximation to the Solution of the Heat-Conduction Equation for Thin Shallow Shells by Using Legendre Polynomials in the Case of Stationary Heat Exchange

By using the N th order approximation of temperature function and its first derivative by Legendre polynomials, we construct the solution of problem of heat conduction for a thin-walled shallow isotropic shell and deduce the system of resolving equations for the N th approximation. For the first and third approximations, we solve this problem for the case of concentrated heat sources. In the third approximation, we also construct the plots of the dependences of temperature on the distance to the heat source and on the curvature of the shell under the conditions of symmetric or asymmetric stationary heat exchange.

42 ENGINEERING↗
DOE OSTI2018

Criteria for the Best Approximation by Simple Partial Fractions on Semi-Axis and Axis

We study uniform approximation of real-valued functions f, f(∞) = 0, on ℝ{sup +} and ℝ by real-valued simple partial fractions (the logarithmic derivatives of polynomials). We obtain a criterion for the best approximation on ℝ{sup +} and ℝ in terms of the Chebyshev alternance. This criterion is similar to the known criterion on finite segments. For the problem of approximating odd functions on ℝ we construct an alternance criterion with a weakened condition on the poles of fractions. We present a criterion for the best approximation by simple partial fractions on ℝ{sup +} and ℝ in terms of Kolmogorov. We prove analogs of the de la Vallee-Poussin alternation theorem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Empirical performance bounds for quantum approximate optimization

The quantum approximate optimization algorithm (QAOA) has been put forth as a method for near-term quantum computers to solve optimization problems. However, assessments of QAOA performance have mostly focused on small structured problem instances while performance on more general instances is less clear. Here, we numerically simulate QAOA pure state dynamics for every instance of MaxCut on non-isomorphic unweighted graphs with nine or fewer vertices with depth parameters p ≤ 3. We find the approximation ratios and optimized circuit parameters concentrate across graphs of a given size and empirically show increases in concentration as graph size increases. The parameter concentration leads to two median-angle heuristics that overcome difficulties in QAOA parameter optimization and obtain mean approximation ratios within 3% and 0.2% of the optimal. We also analyze the probability to measure an optimal solution and find increasing variations between graphs as depth increases, in stark contrast to the approximation ratios which concentrate as depth increases. Furthermore, the resulting benchmark data set gives empirical bounds for on-going experimental realizations and lays groundwork for theoretical extensions to greater problem sizes and depths where QAOA may prove important for practically relevant problems.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Cluster truncated Wigner approximation in strongly interacting systems

We present a general method by which linear quantum Hamiltonian dynamics with exponentially many degrees of freedom is replaced by approximate classical nonlinear dynamics with the number of degrees of freedom (phase space dimensionality) scaling polynomially in the system size. This method is based on generalization of the truncated Wigner approximation (TWA) to a higher dimensional phase space, where phase space variables are associated with a complete set of quantum operators spanning finite size clusters. The method becomes asymptotically exact with increasing cluster size. The crucial feature of TWA is fluctuating initial conditions, which we approximate by a Gaussian distribution. We show that such fluctuations dramatically increase accuracy of TWA over traditional cluster mean-field approximations. In this way we can treat on equal footing quantum and thermal fluctuations as well as compute entanglement and various equal and non-equal time correlation functions. The main limitation of the method is exponential scaling of the phase space dimensionality with the cluster size, which can be significantly reduced by using the language of Schwinger bosons and can likely be further reduced by truncating the local Hilbert space variables. We demonstrate the power of this method analyzing dynamics in various spin chains with and without disorder and show that we can capture such phenomena as long time hydrodynamic relaxation, many-body localization and the ballistic spread of entanglement.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

A Meta-Generalized Gradient Approximation for the Cavity-Dependent Exchange-Correlation Interaction in Strongly Coupled Light–Matter Systems

Strong light–matter coupling in optical cavities enables the manipulation of chemical and physical properties without altering molecular composition. Theoretical modeling of such phenomena requires exchange-correlation (XC) functionals that account for both electron–electron and electron–photon (ep) interactions within quantum electrodynamical density functional theory (QEDFT). In this work, we develop a meta-generalized gradient approximation (meta-GGA) specifically targeting the cavity-dependent XC interaction in strongly coupled light–matter systems. This novel approximation is built upon a new semilocal polarizability approximation, which draws from the jellium-with-a-gap model, and can be extended to a “global hybrid” variant that goes beyond the isotropic model from previous approximations. The polarizability model yields significantly improved dispersion coefficients and benchmark calculations with the cavity-dependent XC functional demonstrate improved agreement with QED Hartree–Fock (QED-HF) reference energies. Application to the regioselectivity of brominated nitrobenzene intermediates reveals the functional’s capacity to capture cavity-induced energetic shifts. In conclusion, our results advance the Jacob’s ladder of functionals for QEDFT and provide a practical tool for modeling polaritonic chemistry.

Approximation↗
DOE OSTI2022

Approximate bounds and temperature dependence of adiabatic connection integrands for the uniform electron gas

Thermal density functional theory is commonly used in simulations of warm dense matter, a highly energetic phase characterized by substantial thermal effects and by correlated electrons demanding quantum mechanical treatment. Methods that account for temperature dependence, such as Mermin–Kohn–Sham finite-temperature density functional theory and free energy density functional theory, are now employed with more regularity and available in many standard code packages. However, approximations from zero-temperature density functional theory are still often used in temperature-dependent simulations using thermally weighted electronic densities as an input to exchange–correlation functional approximations, a practice known to miss temperature-dependent effects in the exchange–correlation free energy of these systems. Here, in this work, the temperature-dependent adiabatic connection is demonstrated and analyzed using a well-known parameterization of the uniform electron gas free energy. Useful tools based on this formalism for analyzing and constraining approximations of the exchange–correlation at zero temperature are leveraged for the finite-temperature case. Inspired by the Lieb–Oxford inequality, which provides a lower bound for the ground-state exchange–correlation energy, bounds for the exchange–correlation at finite temperatures are approximated for various degrees of electronic correlation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Embedded random phase approximation for magnetic systems: H 2 dissociative adsorption on Fe(110)

The random phase approximation (RPA), a method for treating electron correlation, has been shown to be superior to standard density functional theory (DFT) approximations in numerous cases. However, the RPA’s computational cost is substantially higher than that of DFT, particularly restricting its application to extended surfaces. The recently introduced embedded RPA (emb-RPA) approach [Wei et al., J. Chem. Phys. 159(19), 194108 (2023)] reduces this computational cost by approximately two orders of magnitude. While previous applications of emb-RPA focused on non-spin-polarized systems, here we extend the approach to ferromagnetic ones. Unlike other embedded correlated wavefunction methods, such as embedded complete active space self-consistent field theory, emb-RPA is advantageous for spin-polarized systems because the RPA is compatible with unrestricted DFT solutions, which are eigenfunctions of the spin angular momentum operator S z but not the total spin-squared operator S 2 . By applying emb-RPA with specific magnetization constraints, we achieved a speedup of two to three orders of magnitude (one order when accounting for the one-time embedding potential optimization cost) with only small errors (∼50 meV) compared to full periodic RPA. Moreover, emb-RPA significantly reduces the over-binding errors of DFT approximations. In conclusion, we anticipate that the acceleration enabled by the spin-polarized emb-RPA approach will broaden the applicability of RPA to magnetic materials.

Density functional theory↗
DOE OSTI2018

Constructing Convex Inner Approximations of Steady-State Security Regions

Here, we propose a scalable optimization framework for estimating convex inner approximations of the steady-state security sets. The framework is based on Brouwer fixed point theorem applied to a fixed-point form of the power flow equations. It establishes a certificate for the self-mapping of a polytope region constructed around a given feasible operating point. This certificate is based on the explicit bounds on the nonlinear terms that hold within the self-mapped polytope. The shape of the polytope is adapted to find the largest approximation of the steady-state security region. While the corresponding optimization problem is nonlinear and non-convex, every feasible solution found by local search defines a valid inner approximation. The number of variables scales linearly with the system size, and the general framework can naturally be applied to other nonlinear equations with affine dependence on inputs. Test cases, with the system sizes up to 1354 buses, are used to illustrate the scalability of the approach. The results show that the approximated regions are not unreasonably conservative and that they cover substantial fractions of the true steady-state security regions for most medium-sized test cases.

42 ENGINEERING↗
DOE OSTI2021

Ensemble Learning Based Convex Approximation of Three-Phase Power Flow

Though the convex optimization has been widely used in power systems, it still cannot guarantee to yield a tight (accurate) solution to some problems. To mitigate this issue, this paper proposes an ensemble learning based convex approximation for alternating current (AC) power flow equations that differs from the existing convex relaxations. The proposed approach is based on three-phase quadratic power flow equations in rectangular coordinates. To develop this data-driven convex approximation of power flows, the polynomial regression (PR) is first deployed as a basic learner to fit convex relationships between the independent and dependent variables. Then, ensemble learning algorithms such as gradient boosting (GB) and bagging are introduced to combine learners to boost model performance. Based on the learned convex approximation of power flow, optimal power flow (OPF) is formulated as a convex quadratic programming problem. The simulation results on IEEE standard cases of both balanced and unbalanced systems show that, in the context of solving OPF, the proposed data-driven convex approximation outperforms the conventional semi-definite programming (SDP) relaxation in both accuracy and computational efficiency, especially in the cases that the conventional SDP relaxation fails

Convex approximation↗