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Results for “Operator approximation”

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 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
NASA NTRS1981

Straight and chopped DC performance data for a reliance EV-250AT motor with a General Electric EV-1 controller

Straight and chopped DC motor performances for a Reliance EV-250AT motor with an EV-1 controller were examined. Effects of motor temperature and operating voltage are shown. It is found that the maximum motor efficiency is approximately 85% at low operating temperatures in the straight DC mode. Chopper efficiency is 95% under all operating conditions. For equal speeds, the motor operated in the chopped mode develops slightly more torque and draws more current than it does in the straight DC mode.

Edie, P. C.↗
NASA NTRS1979

Implicit finite-difference simulations of steady and unsteady transonic flows

Implicit methods for several fluid dynamic formulations have been developed and applied to steady-state and low-frequency transonic flows. The basic steps involved in the construction of implicit schemes include: selection of linearly stable accurate implicit difference operators, time-linearization of nonlinear terms, and approximate factorization of the implicit operators into easily solved systems of equations. The proposed schemes are found very efficient for the simpler formulations.

Ballhaus, W. F.↗
DOE OSTI2020

Algorithms for Efficient Reproducible Floating Point Summation

We define “reproducibility” as getting bitwise identical results from multiple runs of the same program, perhaps with different hardware resources or other changes that should not affect the answer. Many users depend on reproducibility for debugging or correctness. However, dynamic scheduling of parallel computing resources, combined with nonassociative floating point addition, makes reproducibility challenging even for summation, or operations like the BLAS. We describe a “reproducible accumulator” data structure (the “binned number”) and associated algorithms to reproducibly sum binary floating point numbers, independent of summation order. We use a subset of the IEEE Floating Point Standard 754-2008 and bitwise operations on the standard representations in memory. Our approach requires only one read-only pass over the data, and one reduction in parallel, using a 6-word reproducible accumulator (more words can be used for higher accuracy), enabling standard tiling optimization techniques. Summing n words with a 6-word reproducible accumulator requires approximately 9 n floating point operations (arithmetic, comparison, and absolute value) and approximately 3 n bitwise operations. The final error bound with a 6-word reproducible accumulator and our default settings can be up to 2 29 times smaller than the error bound for conventional (recursive) summation on ill-conditioned double-precision inputs.

Computer Science↗
NASA NTRS1979

Concept for UF6-fueled self-critical DNPL reactor system

An analytical study of a self-critical nuclear pumped laser system concept was performed. The primary emphasis was on a reactor concept which would use gaseous uranium hexafluoride (UF6) as the fissioning material. A reference configuration was selected which has a 3.2 cu m lasing volume as the reactor core. The core is composed of a series of hexagonal graphite tubes which are surrounded by a reflector-moderator composed either of heavy water or beryllium. Laser transitions requiring average fission power densities less than approximately 1 kW/cu cm for excitation are most attractive. Operation at wavelengths greater than approximately 400 nm may be required because of limitations imposed by the opacity of gaseous UF6. Further research directed toward identification of UF6 compatible lasing transitions is required.

Rodgers, R. J.↗
NASA NTRS1980

Performance characterization of a Bosch CO sub 2 reduction subsystem

The performance of Bosch hardware at the subsystem level (up to five-person capacity) in terms of five operating parameters was investigated. The five parameters were: (1) reactor temperature, (2) recycle loop mass flow rate, (3) recycle loop gas composition (percent hydrogen), (4) recycle loop dew point and (5) catalyst density. Experiments were designed and conducted in which the five operating parameters were varied and Bosch performance recorded. A total of 12 carbon collection cartridges provided over approximately 250 hours of operating time. Generally, one cartridge was used for each parameter that was varied. The Bosch hardware was found to perform reliably and reproducibly. No startup, reaction initiation or carbon containment problems were observed. Optimum performance points/ranges were identified for the five parameters investigated. The performance curves agreed with theoretical projections.

Heppner, D. B.↗
NASA NTRS1989

Monotonically improving approximate answers to relational algebra queries

We present here a query processing method that produces approximate answers to queries posed in standard relational algebra. This method is monotone in the sense that the accuracy of the approximate result improves with the amount of time spent producing the result. This strategy enables us to trade the time to produce the result for the accuracy of the result. An approximate relational model that characterizes appromimate relations and a partial order for comparing them is developed. Relational operators which operate on and return approximate relations are defined.

Smith, Kenneth P.↗
DOE OSTI2021

A Sparse-Grid Probabilistic Scheme for Approximation of the Runaway Probability of Electrons in Fusion Tokamak Simulation

Runaway electrons (RE) generated during magnetic disruptions present a major threat to the safe operation of plasma nuclear fusion reactors. A critical aspect of understanding RE dynamics is to calculate the runaway probability, i.e., the probability that an electron in the phase space will runaway on, or before, a prescribed time. Such probability can be obtained by solving the adjoint equation of the underlying Fokker-Planck equation that controls the electron dynamics. In this effort, we present a sparse-grid probabilistic scheme for computing the runaway probability. The key ingredient of our approach is to represent the solution of the adjoint equation as a conditional expectation, such that discretizing the differential operator reduces to the approximation of a set of integrals. Adaptive sparse grid interpolation is utilized to approximate the map from the phase space to the runaway probability. The main novelties of this effort are the integration of the sparse-grid method into the probabilistic numerical scheme for computing escape probability, and the application of the proposed method in computing RE probabilities. Two numerical examples are given to illustrate that the proposed method can achieve O(Δt) convergence, and that the local anisotropic adaptive refinement strategy (M. Stoyanov, Adaptive sparse grid construction in a context of local anisotropy and multiple hierarchical parents. In: Sparse Grids and Applications-Miami 2016, Springer, Berlin, 2018, pp. 175–199) can effectively handle the sharp transition layer between the runaway and non-runaway regions.

Yang, Minglei↗
DOE OSTI2024

RandONets: Shallow networks with random projections for learning linear and nonlinear operators

Deep neural networks have been extensively used for the solution of both the forward and the inverse problem for dynamical systems. However, their implementation necessitates optimizing a high-dimensional space of parameters and hyperparameters. This fact, along with the requirement of substantial computational resources, pose a barrier to achieving high numerical accuracy, but also interpretability. Here, to address the above challenges, we present Random Projection-based Operator Networks (RandONets): shallow networks with random projections and tailor-made numerical analysis methods that learn accurately and fast linear and nonlinear operators. Building on previous works, we prove that RandOnets are universal approximators of linear and nonlinear operators. Due to their simplicity, RandONets provide a one-step transformation of the input space, facilitating interpretability. For the evaluation of their performance, we focus on operators of PDEs. We show, that RandONets outperform by several orders of magnitude, both in terms of numerical approximation accuracy and computational cost, the “vanilla” DeepONets. Hence, we believe that our method will trigger further developments in the field of scientific machine learning, for the development of new ‘’light”schemes that will provide high accuracy while reducing dramatically the computational cost. A MATLAB toolbox for RandONets, including demos, is available on GitHub at https://github.com/GianlucaFabiani/RandONets.

Interpretable machine learning↗
DOE OSTI2023

On the influence of over-parameterization in manifold based surrogates and deep neural operators

Constructing accurate and generalizable approximators (surrogate models) for complex physico-chemical processes exhibiting highly non-smooth dynamics is challenging. The main question is what type of surrogate models we should construct and should these models be under-parameterized or over-parameterized. In this work, we propose new developments and perform comparisons for two promising approaches: manifold-based polynomial chaos expansion (m-PCE) and the deep neural operator (DeepONet), and we examine the effect of over-parameterization on generalization. While m-PCE enables the construction of a mapping by first identifying low-dimensional embeddings of the input functions, parameters, and quantities of interest (QoIs), a neural operator learns the nonlinear mapping via the use of deep neural networks. Here, we demonstrate the performance of these methods in terms of generalization accuracy by solving the 2D time-dependent Brusselator reaction-diffusion system with uncertainty sources, modeling an autocatalytic chemical reaction between two species. We first propose an extension of the m-PCE by constructing a mapping between latent spaces formed by two separate embeddings of the input functions and the output QoIs. To further enhance the accuracy of the DeepONet, we introduce weight self-adaptivity in the loss function. We demonstrate that the performance of m-PCE and DeepONet is comparable for cases of relatively smooth input-output mappings. However, when highly non-smooth dynamics is considered, DeepONet shows higher approximation accuracy. We also find that for m-PCE, modest over-parameterization leads to better generalization, both within and outside of distribution, whereas aggressive over-parameterization leads to over-fitting. In contrast, an even highly over-parameterized DeepONet leads to better generalization for both smooth and non-smooth dynamics. Furthermore, we compare the performance of the above models with another recently proposed operator learning model, the Fourier Neural Operator, and show that its over-parameterization also leads to better generalization. Taken together, our studies show that m-PCE can provide very good accuracy at very low training cost, whereas a highly over-parameterized DeepONet can provide better accuracy and robustness to noise but at higher training cost. In both methods, the inference cost is negligible.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Data-Driven Approach for Uncertainty Propagation and Reachability Analysis in Dynamical Systems

In this paper, we propose a data-driven approach for uncertainty propagation and reachability analysis in a dynamical system. The proposed approach relies on the linear lifting of a nonlinear system using linear Perron-Frobenius (P-F) and Koopman operators. Here, the uncertainty can be characterized in terms of the moments of a probability density function. We demonstrate how the P-F and Koopman operators are used for propagating the moments. Time-series data is used for the finite-dimensional approximation of the linear operators, thereby enabling data-driven approach for moment propagation. Simulation results are presented to demonstrate the effectiveness of the proposed method.

42 ENGINEERING↗
NASA NTRS2018

XY vs X Mixer in Quantum Alternating Operator Ansatz for Optimization Problems with Constraints

Quantum Approximate Optimization Algorithm, further generalized as Quantum Alternating Operator Ansatz (QAOA), is a family of algorithms for combinatorial optimization problems. It is a leading candidate to run on emerging universal quantum computers to gain insight into quantum heuristics. In constrained optimization, penalties are often introduced so that the ground state of the cost Hamiltonian encodes the solution (a standard practice in quantum annealing). An alternative is to choose a mixing Hamiltonian such that the constraint corresponds to a constant of motion and the quantum evolution stays in the feasible subspace. Better performance of the algorithm is speculated due to a much smaller search space. We consider problems with a constant Hamming weight as the constraint. We also compare different methods of generating the generalized W-state, which serves as a natural initial state for the Hamming-weight constraint. Using graph-coloring as an example, we compare the performance of using XY model as a mixer that preserves the Hamming weight with the performance of adding a penalty term in the cost Hamiltonian.

quantum computing↗
DOE OSTI2023

Recognizability of Demographically Altered Computerized Facial Approximations in an Automated Facial Recognition Context for Potential Application in Unidentified Persons Data Repositories

This study examined the recognizability of demographically altered facial approximations for potential utility in unidentified persons tracking systems. Five computer-generated approximations were generated for each of 26 African male participants using the following demographic parameters: (i) African male (true demographics), (ii) African female, (iii) Caucasian male, (iv) Asian male, and (v) Hispanic male. Overall, 62% of the true demographic facial approximations for the 26 African male participants examined were matched to a corresponding life photo within the top 50 images of a candidate list generated from an automated blind search of an optimally standardized gallery of 6159 photographs. When the African male participants were processed as African females, the identification rate was 50%. In contrast, less congruent identification rates were observed when the African male participants were processed as Caucasian (42%), Asian (35%), and Hispanic (27%) males. The observed results suggest that approximations generated using the opposite sex may be operationally informative if sex is unknown. The performance of approximations generated using alternative ancestry assignments, however, was less congruent with the performance of the true demographic approximation (African male) and may not yield as operationally constructive data as sex-altered approximations.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS1991

Approximate reasoning-based learning and control for proximity operations and docking in space

A recently proposed hybrid-neutral-network and fuzzy-logic-control architecture is applied to a fuzzy logic controller developed for attitude control of the Space Shuttle. A model using reinforcement learning and learning from past experience for fine-tuning its knowledge base is proposed. Two main components of this approximate reasoning-based intelligent control (ARIC) model - an action-state evaluation network and action selection network are described as well as the Space Shuttle attitude controller. An ARIC model for the controller is presented, and it is noted that the input layer in each network includes three nodes representing the angle error, angle error rate, and bias node. Preliminary results indicate that the controller can hold the pitch rate within its desired deadband and starts to use the jets at about 500 sec in the run.

Berenji, Hamid R.↗
DOE OSTI2024

Comparison of second-order spectral line widths formulae

Frequently used second-order spectral line width formulae from the projector operator and kinetic theory methods have not been formally compared previously. Here it is shown that a systematic second-order expansion of the projection operator expression including initial correlations agrees with the second-order kinetic theory result. The agreement assumes a common approximation in the projector operator method that introduces a screened radiator–perturber interaction to account for neglected electron–electron correlations. On the other hand, it is shown that the usual width expression from the projection operator approach neglecting initial correlations differs from kinetic theory. The differences, however, are at least third order in the radiator–perturber interaction. The comparisons suggest using the more compact width expression from kinetic theory, which includes initial correlations and a systematic screening of the radiator–perturber interactions, as the starting point for second-order width calculations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Hamiltonian variational ansatz without barren plateaus

Variational quantum algorithms, which combine highly expressive parameterized quantum circuits (PQCs) and optimization techniques in machine learning, are one of the most promising applications of a near-term quantum computer. Despite their huge potential, the utility of variational quantum algorithms beyond tens of qubits is still questioned. One of the central problems is the trainability of PQCs. The cost function landscape of a randomly initialized PQC is often too flat, asking for an exponential amount of quantum resources to find a solution. This problem, dubbed barren plateaus , has gained lots of attention recently, but a general solution is still not available. In this paper, we solve this problem for the Hamiltonian variational ansatz (HVA), which is widely studied for solving quantum many-body problems. After showing that a circuit described by a time-evolution operator generated by a local Hamiltonian does not have exponentially small gradients, we derive parameter conditions for which the HVA is well approximated by such an operator. Based on this result, we propose an initialization scheme for the variational quantum algorithms and a parameter-constrained ansatz free from barren plateaus.

Physics↗
NASA NTRSDate not supplied

Edge Wear of the Advanced Electric Propulsion System Pole Covers

This work summarizes a wear test focused on characterizing the erosion of the edges and side walls of the 12-kW Advanced Electric Propulsion System (AEPS) pole covers as well as the impact of magnetic field strength on component erosion for operation at a discharge voltage of 600 V. Testing was performed with the AEPS Engineering Test Unit 2 (ETU-2) thruster and accumulated approximately 325 hours of operation at the 600 V/12 kW condition with the magnetic field strength set to 75% of its nominal value. Thruster performance was invariant throughout the wear test for all thruster throttle conditions and matched previous measurements at the nominal magnetic field strength. Contrary to past results, inner front pole cover erosion rates were invariant to magnetic field strength at the 600 V/12 kW condition and no erosion was measured on the outer front pole cover. The erosion profile of the downstream inner front pole cover faces was continuous across the cover, indicating no significant change in erosion processes at the pole cover edges. Side wall erosion was only detected on the cathode-facing surfaces of the inner front pole cover and was equal in magnitude to the rates measured on the adjacent downstream edges. Taken together, these results suggest that erosion of the pole cover edges and sidewalls is driven by cathode-borne ions and will ultimately not impact AEPS life estimates.

Hall thrusters↗
DOE OSTI2022

MIONet: Learning Multiple-Input Operators via Tensor Product

As an emerging paradigm in scientific machine learning, neural operators aim to learn operators, via neural networks, that map between infinite-dimensional function spaces. Several neural operators have been recently developed. However, all the existing neural operators are only designed to learn operators defined on a single Banach space; i.e., the input of the operator is a single function. Here, for the first time, we study the operator regression via neural networks for multiple-input operators defined on the product of Banach spaces. We first prove a universal approximation theorem of continuous multiple-input operators. We also provide a detailed theoretical analysis including the approximation error, which provides guidance for the design of the network architecture. Based on our theory and a low-rank approximation, we propose a novel neural operator, MIONet, to learn multiple-input operators. MIONet consists of several branch nets for encoding the input functions and a trunk net for encoding the domain of the output function. Here, we demonstrate that MIONet can learn solution operators involving systems governed by ordinary and partial differential equations. In our computational examples, we also show that we can endow MIONet with prior knowledge of the underlying system, such as linearity and periodicity, to further improve accuracy.

97 MATHEMATICS AND COMPUTING↗