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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 487 records · Page 27
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Deliberate Motion Analytics Fused Radar and Video Test Results Deployed Beyond the Perimeter Fence in a High Noise Environment

Security systems that protect the nation’s critical facilities must be capable of detecting physical intrusions in all weather conditions. Intrusion detection sensors in a perimeter with a high nuisance alarm rate (NAR) significantly undermine detection performance and degrade security system effectiveness. This research demonstrated a fused sensor system that can differentiate foliage and weather-induced nuisance alarms from those caused by intruders, providing reliable detection within a two-fence perimeter or beyond the fence. A key element of this work is the creation and application of a “deliberate motion algorithm” that fuses alarm data from radar and video analytics to create video motion detection fused radar system. The two-layer architecture of the algorithm uses machine learning, multi-hypothesis tracking, and Dynamic Bayes Nets to differentiate intruder alarms from weather induced alarms.

47 OTHER INSTRUMENTATION↗
NASA NTRS2019

Real-Time Modeling of Thermal Interactions in Cryogenic Ball Bearings

Based on the integration of classical differential equations of motion of bearing elements, a real-time dynamic simulation of ball bearing performance is coupled with simultaneous modeling of thermal interactions between the bearing elements. The transient heat generations are time averaged over a significantly larger time step before they are used to compute the changes in bearing temperature fields. Such an averaging algorithm eliminates the numerical difficulties associated with simultaneous integration of mechanical thermal differential equations with vastly different time scales. Under stable operation, the step change in temperatures at each thermal time step converges to a steady-state solution. Following is a list of accomplishments in the present investigation: (1) A real-time dynamic performance of both 440C and hybrid ball bearings in a LOX environment is modeled in both transient and steady-state time domains, as the inner race accelerates to a prescribed operating speed. (2) The frictional interactions at the ball to race contacts are modeled by experimentally measured traction coefficients as a function of slide-to-roll ratios. (3) Bearing heat generation, as defined by the heat transferred to circulating LOX, is validated against experimental values determined by measured LOX temperatures under prescribed pressures and flow rates. The predicted heat generation is in good agreement with the experimental values. (4) The steady-state solutions are shown to be independent of initial conditions. This establishes convergence of the numerical integration of a differential equation of motion of the bearing elements. (5) Churning and drag losses in the circulating LOX constitutes the majority of bearing heat generation under the experimental test conditions. (6) The heat dissipated in frictional interactions in hybrid bearings is significantly lower in hybrid bearings in comparison to that simulated in all-steel bearings, while the churning and drag losses are relatively unchanged.

Gupta, P. K.↗
DOE OSTI2022

Discovering causal structure with reproducing-kernel Hilbert space ε -machines

We merge computational mechanics’ definition of causal states (predictively equivalent histories) with reproducing-kernel Hilbert space (RKHS) representation inference. The result is a widely applicable method that infers causal structure directly from observations of a system’s behaviors whether they are over discrete or continuous events or time. A structural representation—a finite- or infinite-state kernel ϵ-machine—is extracted by a reduced-dimension transform that gives an efficient representation of causal states and their topology. In this way, the system dynamics are represented by a stochastic (ordinary or partial) differential equation that acts on causal states. We introduce an algorithm to estimate the associated evolution operator. Paralleling the Fokker–Planck equation, it efficiently evolves causal-state distributions and makes predictions in the original data space via an RKHS functional mapping. We demonstrate these techniques, together with their predictive abilities, on discrete-time, discrete-value infinite Markov-order processes generated by finite-state hidden Markov models with (i) finite or (ii) uncountably infinite causal states and (iii) continuous-time, continuous-value processes generated by thermally driven chaotic flows. The method robustly estimates causal structure in the presence of varying external and measurement noise levels and for very high-dimensional data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Hyporheic-zone Processes and Stream Oxygen Dynamics: Insights from a Multiscale Reactive Transport Model: Modeling Archive

This archive contains the data and Python scripts required to reproduce the analyses and figures in the study: Gomez-Velez, J. D., Rathore, S. S., Cohen, M. J., & Painter, S. L. (2025). Hyporheic-zone Processes and Stream Oxygen Dynamics: Insights from a Multiscale Reactive Transport Model. Submitted to Water Resources Research. The analysis utilizes the subgrid model Advection Dispersion Equation with Lagrangian Subgrids (ADELS) implemented in the Advanced Terrestrial Simulator (ATS; https://amanzi.github.io/ats/stable/). In this case, the ATS and Amanzi versions are (1) ATS version 1.5.1_f5ba18f8 and (2) Amanzi version 1.6-dev_53444cca4. The repository includes a Jupyter Notebook and the necessary data (Pandas DataFrames stored as pickle files) to generate the figures for the manuscript. Additionally, it contains Python scripts to create ATS input files, run the ATS simulations, and post-process the results. Finally, it provides routines for parameter estimation using the Single-Station Metabolism (SSM) model with the Differential Evolution Adaptive Metropolis (DREAM) Markov Chain Monte Carlo (MCMC) algorithm with ZS enhancements (DREAM-ZS).

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

JAXtronomy: A JAX port of lenstronomy

Gravitational lensing is a phenomenon where light bends around massive objects, resulting in distorted images seen by an observer. Studying gravitationally lensed systems provides insights into cosmology and astrophysics, including constraints of the expansion rate of the Universe and the distribution of dark matter. Thus, we introduce JAXtronomy, a re-implementation of the gravitational lensing software package lenstronomy (Birrer, 2021; Birrer & Amara, 2018) using JAX (Bradbury et al., 2018). JAX is a Python library that uses an accelerated linear algebra (XLA) compiler to improve the performance of computing software. Our core design principle of JAXtronomy is to maintain an identical API to that of lenstronomy. The main JAX features utilized in JAXtronomy are just-in-time compilation, which can lead to significant reductions in execution time, and automatic differentiation, which allows for the implementation of gradient-based algorithms that were previously impossible. Additionally, JAX allows code to be run on GPUs or parallelized across CPU cores, further boosting the performance of JAXtronomy.

astronomy↗
NASA NTRS1974

Equations of condition for high order Runge-Kutta-Nystrom formulae

Derivation of the equations of condition of order eight for a general system of second-order differential equations approximated by the basic Runge-Kutta-Nystrom algorithm. For this general case, the number of equations of condition is considerably larger than for the special case where the first derivative is not present. Specifically, it is shown that, for orders two through eight, the number of equations for each order is 1, 1, 1, 2, 3, 5, and 9 for the special case and is 1, 1, 2, 5, 13, 34, and 95 for the general case.

Bettis, D. G.↗
NASA NTRS1980

An approximate factorization solution of the Navier-Stokes equations for transonic flow using body-fitted coordinates with application to NACA 64A010 airfoils

The implementation of the approximate factorization algorithm and its ability to efficiently and accurately describe transonic flow about an NACA 64A010 airfoil section is examined. The approximate factorization algorithm is developed from the nondimensional, conservative, vectorized Navier-Stokes equations expressed in curvilinear coordinates. Equations of state and transport coefficient relations appropriate to atmospheric air are appended to close the system of partial differential equations. An algebraic turbulence model is also incorporated into the equation set. This algorithm was verified by investigating the flow about an NACA 64A010 airfoil at 0, 2, and 3.5 deg angle of attack for free-stream conditions of 2,000,000 Reynolds number and 0.8 Mach number. Overall results were in good qualitative agreement with wind tunnel data sets. However, while nondimensional times of six were attained, numerical difficulties prevented any case from reaching a true steady state.

Copper, G. K.↗
NASA NTRS1982

Survey of new vector computers: The CRAY 1S from CRAY research; the CYBER 205 from CDC and the parallel computer from ICL - architecture and programming

Problems which can arise with vector and parallel computers are discussed in a user oriented context. Emphasis is placed on the algorithms used and the programming techniques adopted. Three recently developed supercomputers are examined and typical application examples are given in CRAY FORTRAN, CYBER 205 FORTRAN and DAP (distributed array processor) FORTRAN. The systems performance is compared. The addition of parts of two N x N arrays is considered. The influence of the architecture on the algorithms and programming language is demonstrated. Numerical analysis of magnetohydrodynamic differential equations by an explicit difference method is illustrated, showing very good results for all three systems. The prognosis for supercomputer development is assessed.

Gentzsch, W.↗
NASA NTRS1983

Implicit, nonswitching, vector-oriented algorithm for steady transonic flow

A rapid computation of a sequence of transonic flow solutions has to be performed in many areas of aerodynamic technology. The employment of low-cost vector array processors makes the conduction of such calculations economically feasible. However, for a full utilization of the new hardware, the developed algorithms must take advantage of the special characteristics of the vector array processor. The present investigation has the objective to develop an efficient algorithm for solving transonic flow problems governed by mixed partial differential equations on an array processor.

Lottati, I.↗
NASA NTRS1987

Parallel processing architecture for computing inverse differential kinematic equations of the PUMA arm

In advanced robot control problems, on-line computation of inverse Jacobian solution is frequently required. Parallel processing architecture is an effective way to reduce computation time. A parallel processing architecture is developed for the inverse Jacobian (inverse differential kinematic equation) of the PUMA arm. The proposed pipeline/parallel algorithm can be inplemented on an IC chip using systolic linear arrays. This implementation requires 27 processing cells and 25 time units. Computation time is thus significantly reduced.

Hsia, T. C.↗
NASA NTRS1992

Scheme For Finite-Difference Computations Of Waves

Compact algorithms generating and solving finite-difference approximations of partial differential equations for propagation of waves obtained by new method. Based on concept of discrete dispersion relation. Used in wave propagation to relate frequency to wavelength and is key measure of wave fidelity.

Davis, Sanford↗
NASA NTRS2003

Analysis Method for Inelastic, Adhesively Bonded Joints with Anisotropic Adherends

A one-dimensional analysis method for evaluating adhesively bonded joints composed of anisotropic adherends and adhesives with nonlinear material behavior is presented in the proposed paper. The strain and resulting stress field in a general, bonded joint overlap are determined by using a variable-step, finite-difference solution algorithm to iteratively solve a system of first-order differential equations. Applied loading is given by a system of combined extensional, bending, and shear forces that are applied to the edge of the joint overlap. Adherends are assumed to behave as linear, cylindrically bent plates using classical laminated plate theory that includes the effects of first-order transverse shear deformation. Using the deformation theory of plasticity and a modified von-Mises yield criterion, inelastic material behavior is modeled in the adhesive layer. Results for the proposed method are verified against previous results from the literature and shown to be in excellent agreement. An additional case that highlights the effects of transverse shear deformation between similar adherends is also presented.

Smeltzer, Stanley S., III↗
NASA NTRS2004

Multiobjective Aerodynamic Shape Optimization Using Pareto Differential Evolution and Generalized Response Surface Metamodels

Differential Evolution (DE) is a simple, fast, and robust evolutionary algorithm that has proven effective in determining the global optimum for several difficult single-objective optimization problems. The DE algorithm has been recently extended to multiobjective optimization problem by using a Pareto-based approach. In this paper, a Pareto DE algorithm is applied to multiobjective aerodynamic shape optimization problems that are characterized by computationally expensive objective function evaluations. To improve computational expensive the algorithm is coupled with generalized response surface meta-models based on artificial neural networks. Results are presented for some test optimization problems from the literature to demonstrate the capabilities of the method.

Madavan, Nateri K.↗
NASA NTRS2007

White-light Interferometry using a Channeled Spectrum: II. Calibration Methods, Numerical and Experimental Results

In the companion paper, [Appl. Opt. 46, 5853 (2007)] a highly accurate white light interference model was developed from just a few key parameters characterized in terms of various moments of the source and instrument transmission function. We develop and implement the end-to-end process of calibrating these moment parameters together with the differential dispersion of the instrument and applying them to the algorithms developed in the companion paper. The calibration procedure developed herein is based on first obtaining the standard monochromatic parameters at the pixel level: wavenumber, phase, intensity, and visibility parameters via a nonlinear least-squares procedure that exploits the structure of the model. The pixel level parameters are then combined to obtain the required 'global' moment and dispersion parameters. The process is applied to both simulated scenarios of astrometric observations and to data from the microarcsecond metrology testbed (MAM), an interferometer testbed that has played a prominent role in the development of this technology.

phase correction↗
NASA NTRS2010

Multiscale Simulations of Magnetic Island Coalescence

We describe a new interactive parallel Adaptive Mesh Refinement (AMR) framework written in the Python programming language. This new framework, PyAMR, hides the details of parallel AMR data structures and algorithms (e.g., domain decomposition, grid partition, and inter-process communication), allowing the user to focus on the development of algorithms for advancing the solution of a systems of partial differential equations on a single uniform mesh. We demonstrate the use of PyAMR by simulating the pairwise coalescence of magnetic islands using the resistive Hall MHD equations. Techniques for coupling different physics models on different levels of the AMR grid hierarchy are discussed.

Dorelli, John C.↗
NASA NTRS2010

High-resolution three-dimensional imaging radar

A three-dimensional imaging radar operating at high frequency e.g., 670 GHz, is disclosed. The active target illumination inherent in radar solves the problem of low signal power and narrow-band detection by using submillimeter heterodyne mixer receivers. A submillimeter imaging radar may use low phase-noise synthesizers and a fast chirper to generate a frequency-modulated continuous-wave (FMCW) waveform. Three-dimensional images are generated through range information derived for each pixel scanned over a target. A peak finding algorithm may be used in processing for each pixel to differentiate material layers of the target. Improved focusing is achieved through a compensation signal sampled from a point source calibration target and applied to received signals from active targets prior to FFT-based range compression to extract and display high-resolution target images. Such an imaging radar has particular application in detecting concealed weapons or contraband.

Cooper, Ken B.↗