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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 793 records · Page 44
All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

RKH space approximations for the feedback operator in a linear hereditary control system

Computational implementation of feedback control laws for linear hereditary systems requires the approximation of infinite dimensional feedback operators with finite dimensional operators. The dense subspaces of K-polygonal functions in reproducing kernel Hilbert spaces, RKH spaces, suggest finite dimensional approximations of the matrix representations of the control operators. A convergence theorem is developed for the approximations and the numerical implementation of the approximations is discussed.

Reneke, J. A.↗
NASA NTRS1936

Investigations on the amount of downwash behind rectangular and elliptical wings

The downwash behind a wing may be computed from the system of vortices created by the wing and which can be substituted for the latter. If the actual rolling-up process of the free vortex sheet is disregarded, the establishment of boundaries for the downwash factors is contingent upon the premise that no rolling up takes place or else that the developed tip vortices start direct on the effective line. The actual downwash factors for the rectangular wing are rather of the approximate magnitude of the values computable with the developed tip vortices starting direct on the wing.

Muttray, H↗
NASA NTRS2011

A Boundary Condition Relaxation Algorithm for Strongly Coupled, Ablating Flows Including Shape Change

Implementations of a model for equilibrium, steady-state ablation boundary conditions are tested for the purpose of providing strong coupling with a hypersonic flow solver. The objective is to remove correction factors or film cooling approximations that are usually applied in coupled implementations of the flow solver and the ablation response. Three test cases are considered - the IRV-2, the Galileo probe, and a notional slender, blunted cone launched at 10 km/s from the Earth's surface. A successive substitution is employed and the order of succession is varied as a function of surface temperature to obtain converged solutions. The implementation is tested on a specified trajectory for the IRV-2 to compute shape change under the approximation of steady-state ablation. Issues associated with stability of the shape change algorithm caused by explicit time step limits are also discussed.

Gnoffo, Peter A.↗
DOE OSTI2023

Dimension Reduction and Redundancy Removal through Successive Schmidt Decompositions

Quantum computers are believed to have the ability to process huge data sizes, which can be seen in machine learning applications. In these applications, the data, in general, are classical. Therefore, to process them on a quantum computer, there is a need for efficient methods that can be used to map classical data on quantum states in a concise manner. On the other hand, to verify the results of quantum computers and study quantum algorithms, we need to be able to approximate quantum operations into forms that are easier to simulate on classical computers with some errors. Motivated by these needs, in this paper, we study the approximation of matrices and vectors by using their tensor products obtained through successive Schmidt decompositions. We show that data with distributions such as uniform, Poisson, exponential, or similar to these distributions can be approximated by using only a few terms, which can be easily mapped onto quantum circuits. The examples include random data with different distributions, the Gram matrices of iris flower, handwritten digits, 20newsgroup, and labeled faces in the wild. Similarly, some quantum operations, such as quantum Fourier transform and variational quantum circuits with a small depth, may also be approximated with a few terms that are easier to simulate on classical computers. Furthermore, we show how the method can be used to simplify quantum Hamiltonians: In particular, we show the application to randomly generated transverse field Ising model Hamiltonians. The reduced Hamiltonians can be mapped into quantum circuits easily and, therefore, can be simulated more efficiently.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A randomized sketching trust-region secant method for low-memory dynamic optimization

The numerical solution of dynamic optimization problems is often limited by the memory required to store the state trajectory, which is used to evaluate the objective function and its derivatives. Recently, [R. Muthukumar et al., SIAM Journal on Optimization 31(2), pp. 1242–1275 (2021)] introduced a trust-region method for dynamic optimization that employs randomized sketching to compress the state trajectory, resulting in inexact derivative computations. By adaptively learning the sketch rank, the trust-region algorithm achieves rigorous convergence guarantees. Here, we extend this approach to use secant Hessian approximations. Due to the randomness introduced by the sketch, the traditional secant update formulae can produce poor Hessian approximations. In particular, the difference of two gradients, computed from two different sketches, may be inconsistent. To overcome this, we employ a sketched approximation of the Hessian application, in lieu of computing the gradient difference. We numerically demonstrate the improved stability of this approach on an example from PDE-constrained optimization.

dynamic optimization↗
DOE OSTI2022

Efficient data acquisition and training of collisional-radiative model artificial neural network surrogates through adaptive parameter space sampling

Abstract Effective plasma transport modeling of magnetically confined fusion devices relies on having an accurate understanding of the ion composition and radiative power losses of the plasma. Generally, these quantities can be obtained from solutions of a collisional-radiative (CR) model at each time step within a plasma transport simulation. However, even compact, approximate CR models can be computationally onerous to evaluate, and in-situ evaluation of these models within a larger plasma transport code can lead to a rigid bottleneck. As a way to bypass this bottleneck, we propose deploying artificial neural network (ANN) surrogates to allow rapid evaluation of the necessary plasma quantities. However, one issue with training an accurate ANN surrogate is the reliance on a sufficiently large and representative training and validation data set, which can be time-consuming to generate. In this work we explore a data-driven active learning and training routine to allow autonomous adaptive sampling of the problem parameter space to ensure a sufficiently large and meaningful set of training data is assembled for the network training. As a result, we can demonstrate approximately order-of-magnitude savings in required training data samples to produce an accurate surrogate.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1979

On the distribution of computation for sequential decoding using the stack algorithm

A method is developed for estimating the computational distribution for the stack algorithm for sequential decoding, that is, the probability that the computation required to decode the first branch of the tree is greater than or equal to N, for small N. The analysis relies heavily on the theory of multitype branching processes. A step in the analysis is the determination of the distribution of the minimum of the cumulative metrics along the transmitted path in the code tree. This is used to obtain the distribution of the number of computations made by the decoder in order to decode the first branch in the tree, and this random variable serves as an approximation of the average number of computations per decoded branch. At information rates below the cutoff rate, the calculated computational performance is virtually identical to that obtained by time-consuming simulations.

Johannesson, R.↗
NASA NTRS1987

IOS and ECS line coupling calculation for the CO-He system - Influence on the vibration-rotation band shapes

Line coupling coefficients resulting from rotational excitation of CO perturbed by He are computed within the infinite order sudden approximation (IOSA) and within the energy corrected sudden approximation (ECSA). The influence of this line coupling on the 1-0 CO-He vibration-rotation band shape is then computed for the case of weakly overlapping lines in the 292-78 K temperature range. The IOS and ECS results differ only at 78 K by a weak amount at high frequencies. Comparison with an additive superposition of Lorentzian lines shows strong modifications in the troughs between the lines. These calculated modifications are in excellent quantitative agreement with recent experimental data for all the temperatures considered. The applicability of previous approaches to CO-He system, based on either the strong collision model or exponential energy gap law, is also discussed.

Boissoles, J.↗
NASA NTRS2011

On Time Delay Margin Estimation for Adaptive Control and Optimal Control Modification

This paper presents methods for estimating time delay margin for adaptive control of input delay systems with almost linear structured uncertainty. The bounded linear stability analysis method seeks to represent an adaptive law by a locally bounded linear approximation within a small time window. The time delay margin of this input delay system represents a local stability measure and is computed analytically by three methods: Pade approximation, Lyapunov-Krasovskii method, and the matrix measure method. These methods are applied to the standard model-reference adaptive control, s-modification adaptive law, and optimal control modification adaptive law. The windowing analysis results in non-unique estimates of the time delay margin since it is dependent on the length of a time window and parameters which vary from one time window to the next. The optimal control modification adaptive law overcomes this limitation in that, as the adaptive gain tends to infinity and if the matched uncertainty is linear, then the closed-loop input delay system tends to a LTI system. A lower bound of the time delay margin of this system can then be estimated uniquely without the need for the windowing analysis. Simulation results demonstrates the feasibility of the bounded linear stability method for time delay margin estimation.

Nguyen, Nhan T.↗
NASA NTRS1983

The treatment of convected vortices in compressible potential flow

A method is described for incorporating line vortices into the three dimensional compressible potential flow equation. A modified Biot-Savart law is used to compute a vortical velocity field, which is added to the gradient of the potential to form a total velocity. A rapidly converging approximate factorization (AFZ) scheme is then used to compute a potential such that the modified potential flow equation as well as the appropriate boundary conditions, based on total velocity, are satisfied. As part of a coupled iteration procedure, the positions of the line vortices are computed so that they convect with the total flow. The method is used to compute the field due to a single line vortex convecting past a wing. This represents an approximation of the effect of a canard or other lifting surface ahead of the wing, which sheds a tip vortex. It is seen that the flow field is substantially modified by the passage of the vortex. Unlike Euler equation schemes, which are also used to compute these flows, the solutions exhibit no numerical diffusion: The convected vortices retain their initial upstream width. Euler solutions, on the other hand, involve a vorticity which is numerically convected in an Eulerian frame and, unless extensive adaptive grid refinement is used they result in vortices with spread as they convect. Also, the potential flow method requires approximately two orders of magnitude less computing time and much less computer storage than the Euler methods.

Steinhoff, J.↗
DOE OSTI2024

A new “gold standard”: Perturbative triples corrections in unitary coupled cluster theory and prospects for quantum computing

A major difficulty in quantum simulation is the adequate treatment of a large collection of entangled particles, synonymous with electron correlation in electronic structure theory, with coupled cluster (CC) theory being the leading framework for dealing with this problem. Augmenting computationally affordable low-rank approximations in CC theory with a perturbative account of higher-rank excitations is a tractable and effective way of accounting for the missing electron correlation in those approximations. This is perhaps best exemplified by the “gold standard” CCSD(T) method, which bolsters the baseline CCSD with the effects of triple excitations using considerations from many-body perturbation theory (MBPT). Despite this established success, such a synergy between MBPT and the unitary analog of CC theory (UCC) has not been explored. In this work, we propose a similar approach wherein converged UCCSD amplitudes are leveraged to evaluate energy corrections associated with triple excitations, leading to the UCCSD[T] method. In terms of quantum computing, this correction represents an entirely classical post-processing step that improves the energy estimate by accounting for triple excitation effects without necessitating new quantum algorithm developments or increasing demand for quantum resources. The rationale behind this choice is shown to be rigorous by studying the properties of finite-order UCC energy functionals, and our efforts do not support the addition of the fifth-order contributions as in the (T) correction. We assess the performance of these approaches on a collection of small molecules and demonstrate the benefits of harnessing the inherent synergy between MBPT and UCC theories.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1948

The Problem of Torsion in Prismatic Members of Circular Segmental Cross Section

The problem is solved by approximation, by setting up a function complying with the differential equation of the stress function, and determining the coefficients appearing in it in such a way that the boundary condition is fulfilled as nearly as possible. For the semicircle, for which the solution is known, the method yields very accurate values; the approximated stress distribution is in good agreement with the accurately computed distribution. Stress and strain measurements indicate that the approximate solution is in sufficiently exact agreement with reality for segmental cross sections.

Weigand, A.↗
DOE OSTI2025

Accelerating Embedding Potential Optimization by Reconstructing the Pseudo-Valence Electron Density

Density functional embedding theory (DFET) enables use of electronic structure methods with higher accuracy than density functional theory in a local region, with applications thus far ranging from (photo/electro)catalysis to reactions in solution. DFET partitions a large collection of atoms into smaller groups that interact via a shared embedding (interaction) potential V emb , determined via functional optimization. The optimized effective potential (OEP) process used to optimize V emb is time-consuming and becomes a computational bottleneck due to sharp, oscillating features of V emb near nuclei. Here, similar to pseudopotential theory, by reconstructing electron densities used in the OEP process from smoother pseudo-valence-only (PVO) electron densities as proxies for total densities of the full system and subsystems, we can retain accuracy in the embedded electronic structure calculations while potentially reducing the overhead of V emb construction, within the projector augmented-wave (PAW) formalism. We explore three different chemical reactions as exemplars to test PVO–DFET, namely, H 2 dissociative adsorption on a Cu(111) surface, H 2 O adsorption on a Pt(111) surface, and aqueous [Ca 2+ –SO 4 2– ] ion-pair formation. The PVO approximation works well for all three systems with minimal loss of accuracy (∼10–70 meV error relative to the original exact-derivative (ED) approach) while accelerating V emb generation for the Cu and Pt systems respectively by 20× and 5×. Given proper numerical convergence parameters, the spatial distributions of differences between PVO- and ED-based V emb outside the core regions are small, explaining the exceptional agreement between the two approaches. Finally, we anticipate that this more efficient PVO–DFET approximation will be useful whenever computation of V emb is much more expensive than subsequent embedded high-level electron correlation calculations.

approximation↗
DOE OSTI2026

Connection between classical and quantum descriptions of spin waves using quantum circuits

A quantum computing circuit is presented that approximates a single spin wave quantum on a linear chain of spin 1/2 particles described by a Heisenberg Hamiltonian. The circuit is a product state where each qubit represents a spin. The spin wave motion is represented by opening the cone angle using Y rotations and then adding progressive Z rotations along the chain to represent wave propagation. We show analytically that this product state yields the correct dispersion relation in the limit of an unbounded chain. This observation is confirmed using both a simulator and various quantum processors. The use of the quantum computing paradigm in this case does not lead to a computational advantage, but rather leads to a novel conceptual connection between classical and quantum descriptions of spin waves, and may also be useful for characterizing the error in quantum processors.

magnons↗
DOE OSTI2026

Comparison between explicit and implicit discretization strategies for a dissipative thermal environment

We investigate strategies for simulating open quantum systems coupled to dissipative baths by comparing explicit wave function-based discretization [via multi-layer multi-configuration time-dependent Hartree (ML-MCTDH)] and the implicit density matrix-based master equation method [via tree tensor network hierarchical equations of motion (TTN-HEOM)]. For dissipative baths characterized by exponentially decaying bath correlation functions, the implicit discretization approach of HEOM—rooted in bath correlation function decompositions—proves significantly more efficient than explicit discretization of the bath into discrete harmonic modes. Explicit methods, like ML-MCTDH, require extensive mode discretization to approximate continuum baths, leading to computational bottlenecks. Case studies for two-level systems and a Fenna–Matthews–Olson complex model highlight TTN-HEOM’s superiority in capturing dissipative dynamics with relaxations with a minimal number of auxiliary modes, while the explicit methods are as exact as the HEOM in pure dephasing regimes. This comparison is enabled by the TENSO package, which has both ML-MCTDH and TTN-HEOM implemented using the same computational structure and propagation strategy.

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

Theory and numerics of subspace approximation of eigenvalue problems

Large-scale eigenvalue problems arise in various fields of science and engineering and demand computationally efficient solutions. In this study, we investigate the subspace approximation for parametric linear eigenvalue problems, aiming to mitigate the computational burden associated with high-fidelity systems. Furthermore, we provide general error estimates under non-simple eigenvalue conditions, establishing some theoretical foundations for understanding the convergence behavior of subspace approximations. Numerical examples, including problems with one-dimensional to three-dimensional spatial domain and one-dimensional to two-dimensional parameter domain, are presented to demonstrate the efficacy of reduced basis method in handling parametric variations in boundary conditions and coefficient fields to achieve significant computational savings while maintaining high accuracy, making them promising tools for practical applications in large-scale eigenvalue computations.

Eigenvalue problems↗
DOE OSTI2023

A localized ensemble of approximate Gaussian processes for fast sequential emulation

More attention has been given to the computational cost associated with the fitting of an emulator. Substantially less attention is given to the computational cost of using that emulator for prediction. This is primarily because the cost of fitting an emulator is usually far greater than that of obtaining a single prediction, and predictions can often be obtained in parallel. In many settings, especially those requiring Markov Chain Monte Carlo, predictions may arrive sequentially and parallelization is not possible. In this case, using an emulator procedure which can produce accurate predictions efficiently can lead to substantial time savings in practice. In this paper, we propose a global model approximate Gaussian process framework via extension of a popular local approximate Gaussian process (laGP) framework. Our proposed emulator can be viewed as a treed Gaussian process where the leaf nodes are laGP models, and the tree structure is learned greedily as a function of the prediction stream. The suggested method (called leapGP) has interpretable tuning parameters which control the time‐memory trade‐off. One reasonable choice of settings leads to an emulator with a training cost and makes predictions rapidly with an asymptotic amortized cost of .

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1986

Monte Carlo turbulence simulation using rational approximations to von Karman spectra

Turbulence simulation is computationally much simpler using rational spectra, but turbulence falls off as f exp -5/3 in frequency ranges of interest to aircraft response and as predicted by von Karman's model. Rational approximations to von Karman spectra should satisfy three requirements: (1) the rational spectra should provide a good approximation to the von Karman spectra in the frequency range of interest; (2) for stability, the resulting rational transfer function should have all its poles in the left half-plane; and (3) at high frequencies, the rational spectra must fall off as an integer power of frequency, and since the -2 power is closest to the -5/3 power, the rational approximation should roll off as the -2 power at high frequencies. Rational approximations to von Karman spectra that satisfy these three criteria are presented, along with spectra from simulated turbulence. Agreement between the spectra of the simulated turbulence and von Karman spectra is excellent.

Campbell, C. W.↗