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Results for “algorithmic differentiation”

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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Quantum advantage for differential equation analysis

Quantum algorithms for differential equation solving, data processing, and machine learning potentially offer an exponential speedup over all known classical algorithms. However, there also exist obstacles to obtaining this potential speedup in useful problem instances. The essential obstacle for quantum differential equation solving is that outputting useful information may require difficult postprocessing, and the essential obstacle for quantum data processing and machine learning is that inputting the data is a difficult task just by itself. In this study, we demonstrate that, when combined, these difficulties solve one another. We show how the output of quantum differential equation solving can serve as the input for quantum data processing and machine learning, allowing dynamical analysis in terms of principal components, power spectra, and wavelet decompositions. To illustrate this, we consider continuous-time Markov processes on epidemiological and social networks. These quantum algorithms provide an exponential advantage over existing classical Monte Carlo methods.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Energy-momentum-conserving stochastic differential equations and algorithms for the nonlinear Landau-Fokker-Planck equation

Coulomb collision is a fundamental diffusion process in plasmas that can be described by the Landau-Fokker-Planck (LFP) equation or the stochastic differential equation (SDE). While energy and momentum are conserved exactly in the LFP equation, they are conserved only on average by the conventional corresponding SDEs, suggesting that the underlying stochastic process may not be well defined by such SDEs. Here, in this study, we derive new SDEs with exact energy-momentum conservation for the Coulomb collision by factorizing the collective effect of field particles into individual particles and enforcing Newton's third law. These SDEs, when interpreted in the Stratonovich sense, have a particularly simple form that represents pure diffusion between particles without drag. To demonstrate that the new SDEs correspond to the LFP equation, we develop numerical algorithms that converge to the SDEs and preserve discrete conservation laws. Simulation results are presented in a benchmark of various relaxation processes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Spectrally accurate, reverse-mode differentiable bounce-averaging algorithm and its applications

We present a fast, spectrally (exponentially) accurate, automatically differentiable bounce-averaging algorithm that is used to simplify kinetic models. Using this algorithm, implemented in the DESC stellarator optimisation suite, we can perform efficient optimisation of many objectives to improve stellarator performance, such as the effective ripple 𝜖 eff metric for the neoclassical transport coefficient in the low collisionality regime and proxies for energetic particle confinement. For the first time, we optimise a finite-beta stellarator to directly reduce neoclassical ripple transport using reverse-mode differentiation. This ensures the computational cost of differentiation is independent of the number of controllable parameters.

fusion plasma↗
DOE OSTI2021

Efficient quantum algorithm for dissipative nonlinear differential equations

Significance Nonlinear differential equations appear in many domains and are notoriously difficult to solve. Whereas previous quantum algorithms for general nonlinear differential equations have complexity exponential in the evolution time, we give the first quantum algorithm for dissipative nonlinear differential equations that is efficient provided the dissipation is sufficiently strong relative to nonlinear and forcing terms and the solution does not decay too rapidly. We also establish a lower bound showing that differential equations with sufficiently weak dissipation have worst-case complexity exponential in time, giving an almost tight classification of the quantum complexity of simulating nonlinear dynamics. Furthermore, numerical results for the Burgers equation suggest that our algorithm may potentially address complex nonlinear phenomena even in regimes with weaker dissipation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1972

DDA realizations of attitude algorithms.

Digital differential analyzer (DDA) realization of the direction cosine, Euler angle, and quaternion algorithms. It is shown that, for any one of the three attitude algorithms, 27 DDAs are needed. This number is considerably smaller than those obtained by others for the cases of Euler angle and quaternion algorithms.

Yeh, Y.↗
NASA NTRS1985

Towards developing robust algorithms for solving partial differential equations on MIMD machines

Methods for efficient computation of numerical algorithms on a wide variety of MIMD machines are proposed. These techniques reorganize the data dependency patterns to improve the processor utilization. The model problem finds the time-accurate solution to a parabolic partial differential equation discretized in space and implicitly marched forward in time. The algorithms are extensions of Jacobi and SOR. The extensions consist of iterating over a window of several timesteps, allowing efficient overlap of computation with communication. The methods increase the degree to which work can be performed while data are communicated between processors. The effect of the window size and of domain partitioning on the system performance is examined both by implementing the algorithm on a simulated multiprocessor system.

Saltz, J. H.↗
NASA NTRS1988

Towards developing robust algorithms for solving partial differential equations on MIMD machines

Methods for efficient computation of numerical algorithms on a wide variety of MIMD machines are proposed. These techniques reorganize the data dependency patterns to improve the processor utilization. The model problem finds the time-accurate solution to a parabolic partial differential equation discretized in space and implicitly marched forward in time. The algorithms are extensions of Jacobi and SOR. The extensions consist of iterating over a window of several timesteps, allowing efficient overlap of computation with communication. The methods increase the degree to which work can be performed while data are communicated between processors. The effect of the window size and of domain partitioning on the system performance is examined both by implementing the algorithm on a simulated multiprocessor system.

Saltz, Joel H.↗
DOE OSTI2021

Combinatorial Algorithms in Scientific Computing

We provide the final report for this grant, detailing the publications, software produced, students trained who have joined the DOE workforce, and the impact our work has had on computational mathematics and related disciplines.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Parallel Variable Population Multi-Objective Optimizer (pvpmoo) v1.0

This is a parallel variable population multi-objective optimizer with an adaptive unified differential evolution algorithm or a genetic algorithm. It can also be used for single objective optimization. Some features of this code include: 1) The population size varies from generation to generation to save the total # of objective function evaluations. 2) The population is uniformly distributed to a number of parallel processors for simultaneous objective function evaluation. 3) The objective function evaluation can be attained from an external simulation program with control variables in its input file and objectives calculated from its output files. 4) The optimizer includes an adaptive unified differential evolution algorithm and a real value genetic algorithm. The parameters in the unified differential evolution algorithm can be chosen to attain any mutation schemes in the published literature.

Qiang, Ji↗
NASA NTRS1975

A least mean squares CUBIC algorithm for on-line differential of sampled analog signals

A digital computer algorithm is developed for on-line time differentiation of sampled analog voltage signals. The derivative is obtained by employing a least mean squares technique. The recursive algorithm results in a considerable reduction in computer time compared to a complete new solution of the normal equations each time a new data point is accepted. Implementation of the algorithm on a digital computer is discussed. Examples are simulated on a DEC PDP-8 computer.

Allum, J. H. J.↗
DOE OSTI2023

Improved quantum algorithms for linear and nonlinear differential equations

We present substantially generalized and improved quantum algorithms over prior work for inhomogeneous linear and nonlinear ordinary differential equations (ODE). Specifically, we show how the norm of the matrix exponential characterizes the run time of quantum algorithms for linear ODEs opening the door to an application to a wider class of linear and nonlinear ODEs. In [1], a quantum algorithm for a certain class of linear ODEs is given, where the matrix involved needs to be diagonalizable. The quantum algorithm for linear ODEs presented here extends to many classes of non-diagonalizable matrices including singular matrices. The algorithm here is also exponentially faster than the bounds derived in [1] for certain classes of diagonalizable matrices. Our linear ODE algorithm is then applied to nonlinear differential equations using Carleman linearization (an approach taken recently by us in [2]). The improvement over that result is two-fold. First, we obtain an exponentially better dependence on error. This kind of logarithmic dependence on error has also been achieved by [3], but only for homogeneous nonlinear equations. Second, the present algorithm can handle any sparse matrix (that models dissipation) if it has a negative log-norm (including non-diagonalizable matrices), whereas [2] and [3] additionally require normality.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1981

Symbolic Solution of Linear Differential Equations

An algorithm for solving linear constant-coefficient ordinary differential equations is presented. The computational complexity of the algorithm is discussed and its implementation in the FORMAC system is described. A comparison is made between the algorithm and some classical algorithms for solving differential equations.

Feinberg, R. B.↗
DOE OSTI2020

A catalogue of Locus Algorithm pointings for optimal differential photometry for 23 779 quasars

ABSTRACT This paper presents a catalogue of optimized pointings for differential photometry of 23 779 quasars extracted from the Sloan Digital Sky Survey (SDSS) Catalogue and a Score for each indicating the quality of the Field of View (FoV) associated with that pointing. Observation of millimagnitude variability on a time-scale of minutes typically requires differential observations with reference to an ensemble of reference stars. For optimal performance, these reference stars should have similar colour and magnitude to the target quasar. In addition, the greatest quantity and quality of suitable reference stars may be found by using a telescope pointing which offsets the target object from the centre of the FoV. By comparing each quasar with the stars which appear close to it on the sky in the SDSS Catalogue, an optimum pointing can be calculated, and a figure of merit, referred to as the ‘Score’ is calculated for that pointing. Highly flexible software has been developed to enable this process to be automated and implemented in a distributed computing paradigm, which enables the creation of catalogues of pointings given a set of input targets. Applying this technique to a sample of 40 000 targets from the fourth SDSS quasar catalogue resulted in the production of pointings and Scores for 23 779 quasars based on their magnitudes in the SDSS r-band. This catalogue is a useful resource for observers planning differential photometry studies and surveys of quasars to select those which have many suitable celestial neighbours for differential photometry.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

I-V characterization and parameter extraction tool [SWR-24-59]

GPT-crafted control software and graphical user interface for Keithley 2400 Source Measure Units and global optimization algorithm. It contains Numba-compatible self-adaptive differential evolution algorithm for optimization tasks. This software is comprised of two repositories: https://github.com/NREL/Keithley_GPT https://github.com/NREL/DE

Febba, Davi Marcelo↗