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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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NASA NTRS1972

Precision state and filter weighting matrix extrapolation, revision 3

The matrix extrapolation routine presented is a coded algorithm for the numerical solution of modified forms of the basic differential equations which are satisfied by the geocentric state vector of a spacecraft's center of mass and by the filter-weighting matrix. The equations are described in detail and the various input and output variables designated. The capability is thus established to extrapolate any spacecraft's geocentric state vector, either backwards or forwards in time, through a force field consisting of the earth's primary central-force gravitational attraction, and a superimposed perturbing acceleration.

Robertson, W. M.↗

NASA NTRS1976

Finite element solution of turbulent and reacting compressible three-dimensional flows

Results of detailed numerical evaluation of turbulent and reacting three-dimensional compressible flows are presented. These solutions were obtained using a finite element algorithm to solve the system of explicitly non-linear partial differential equations governing three-dimensional, confined unidirectional turbulent flow of a compressible, reacting fluid. Assessments are made of solution accuracy and convergence, including detailed comparisons to experimental data.

Baker, A. J.↗

NASA NTRS1984

Vibrational relaxation of diatomic molecules in solids at low temperatures

The application of a hemiquantal method to the specific problem of the vibrational relaxation of a diatomic molecule embedded in a one dimensional lattice is presented. The vectorization of a CYBER 205 algorithm which integrates the 1,000 to 10,000 simultaneous hemiquantal differential equations is examined with comments on optimization. Results of the simulations are briefly discussed.

Halcomb, L. L.↗

NASA NTRS1984

A comparison of the efficiency of numerical methods for integrating chemical kinetic rate equations

A comparison of the efficiency of several algorithms recently developed for the efficient numerical integration of stiff ordinary differential equations is presented. The methods examined include two general-purpose codes EPISODE and LSODE and three codes (CHEMEQ, CREK1D, and GCKP84) developed specifically to integrate chemical kinetic rate equations. The codes are applied to two test problems drawn from combustion kinetics. The comparisons show that LSODE is the fastest code currently available for the integration of combustion kinetic rate equations. An important finding is that an iterative solution of the algebraic energy conservation equation to compute the temperature can be more efficient than evaluating the temperature by integrating its time-derivative.

Radhakrishnan, K.↗

NASA NTRS1993

Implementing abstract multigrid or multilevel methods

Multigrid methods can be formulated as an algorithm for an abstract problem that is independent of the partial differential equation, domain, and discretization method. In such an abstract setting, problems not arising from partial differential equations can be treated. A general theory exists for linear problems. The general theory was motivated by a series of abstract solvers (Madpack). The latest version was motivated by the theory. Madpack now allows for a wide variety of iterative and direct solvers, preconditioners, and interpolation and projection schemes, including user callback ones. It allows for sparse, dense, and stencil matrices. Mildly nonlinear problems can be handled. Also, there is a fast, multigrid Poisson solver (two and three dimensions). The type of solvers and design decisions (including language, data structures, external library support, and callbacks) are discussed. Based on the author's experiences with two versions of Madpack, a better approach is proposed. This is based on a mixed language formulation (C and FORTRAN + preprocessor). Reasons for not using FORTRAN, C, or C++ (individually) are given. Implementing the proposed strategy is not difficult.

Douglas, Craig C.↗

NASA NTRS2001

An Analysis of an Automatic Coolant Bypass in the International Space Station Node 2 Internal Active Thermal Control System

A challenging part of International Space Station (ISS) thermal control design is the ability to incorporate design changes into an integrated system without negatively impacting performance. The challenge presents itself in that the typical ISS Internal Active Thermal Control System (IATCS) consists of an integrated hardware/software system that provides active coolant resources to a variety of users. Software algorithms control the IATCS to specific temperatures, flow rates, and pressure differentials in order to meet the user-defined requirements. What may seem to be small design changes imposed on the system may in fact result in system instability or the temporary inability to meet user requirements. The purpose of this paper is to provide a brief description of the solution process and analyses used to implement one such design change that required the incorporation of an automatic coolant bypass in the ISS Node 2 element.

Clanton, Stephen E.↗

NASA NTRS2005

Remote Sensing of Particulate Organic Carbon Pools in the High-Latitude Oceans

The general goal of this project was to characterize spatial distributions at basin scales and variability on monthly to interannual timescales of particulate organic carbon (POC) in the high-latitude oceans. The primary objectives were: (1) To collect in situ data in the north polar waters of the Atlantic and in the Southern Ocean, necessary for the derivation of POC ocean color algorithms for these regions. (2) To derive regional POC algorithms and refine existing regional chlorophyll (Chl) algorithms, to develop understanding of processes that control bio-optical relationships underlying ocean color algorithms for POC and Chl, and to explain bio-optical differentiation between the examined polar regions and within the regions. (3) To determine basin-scale spatial patterns and temporal variability on monthly to interannual scales in satellite-derived estimates of POC and Chl pools in the investigated regions for the period of time covered by SeaWiFS and MODIS missions.

Stramski, Dariusz↗

NASA NTRS1989

Modified Chebyshev pseudospectral method with O(N exp -1) time step restriction

The extreme eigenvalues of the Chebyshev pseudospectral differentiation operator are O(N exp 2) where N is the number of grid points. As a result of this, the allowable time step in an explicit time marching algorithm is O(N exp -2) which, in many cases, is much below the time step dictated by the physics of the partial differential equation. A new set of interpolating points is introduced such that the eigenvalues of the differentiation operator are O(N) and the allowable time step is O(N exp -1). The properties of the new algorithm are similar to those of the Fourier method. The new algorithm also provides a highly accurate solution for non-periodic boundary value problems.

Kosloff, Dan↗

NASA NTRS1993

A modified Chebyshev pseudospectral method with an O(N exp -1) time step restriction

Kosloff, Dan↗

NASA NTRSDate not supplied

TPSAS-NF1676L-20108-DND

This presentation describes several enhancements planned for the version 4 aerosol subtyping and lidar ratio selection algorithms of the Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) instrument. The CALIOP subtyping algorithm determines the most likely aerosol type from CALIOP measurements (attenuated backscatter, estimated particulate depolarization ratios de, layer altitude), and surface type. The aerosol type, so determined, is associated with a lidar ratio (LR) from a discrete set of values. In the version 3 algorithms, there are 6 pairs of 532 and 1064 nm lidar ratios. Some of these lidar ratios will be updated in the version 4 algorithms. In particular, the dust and polluted dust will be adjusted to reflect the latest measurements and model studies of these types. The algorithms are being updated to eliminate the occasional confusion between smoke and clean marine aerosols seen in version 3 by modifications to the elevated layer flag definitions that are used to determine the presence of smoke aerosols over the ocean. In the subtyping algorithms pure dust is determined by high estimated particulate depolarization ratios [de > 0.20]. Mixtures of dust and other aerosol types are determined by intermediate values of the estimated depolarization ratio [0.075< de <0.2]. The version 3 algorithms are limited to mixtures of dust and smoke, the so-called polluted dust aerosol type. To differentiate between mixtures of dust and smoke, and dust and marine aerosols, a new aerosol type will be added in the version 4 data products. In the revised classification algorithms, polluted dust will still defined as dust + smoke/pollution but in the marine boundary layer instances of moderate depolarization will be typed as dusty marine aerosols with a lower lidar ratio [LR = 35 sr] than polluted dust [currently LR = 55 sr]. The dusty marine type introduced in version 4 is modeled as a mixture of dust + marine aerosol. In the v3 algorithms the frequency of dust and polluted dust aerosols at daytime is higher than at nighttime. We present possible reasons for this and present the v4 distributions resulting from both improved background slope corrections of the daytime depolarization ratios and changes to the daytime thresholds for the polluted dust and dusty marine types of version 4. To gauge the impact of the enhancements, we contrast the following between versions 3 and 4: aerosol type, parameter distributions of each type, layer heights of maximum frequency, and distributions of smoke in biomass burning regions. To illustrate specific impacts the presentation shows case studies of version 3 and version 4 vertical feature masks of the aerosol subtypes, where appropriate, for the above enhancements.

A Omar↗

DOE OSTI2021

Linear embedding of nonlinear dynamical systems and prospects for efficient quantum algorithms

The simulation of large nonlinear dynamical systems, including systems generated by discretization of hyperbolic partial differential equations, can be computationally demanding. Such systems are important in both fluid and kinetic computational plasma physics. This motivates exploring whether a future error-corrected quantum computer could perform these simulations more efficiently than any classical computer. In this work, we describe a method for mapping any finite nonlinear dynamical system to an infinite linear dynamical system (embedding) and detail three specific cases of this method that correspond to previously studied mappings. Then we explore an approach for approximating the resulting infinite linear system with finite linear systems (truncation). Using a number of qubits only logarithmic in the number of variables of the nonlinear system, a quantum computer could simulate truncated systems to approximate output quantities if the nonlinearity is sufficiently weak. Other aspects of the computational efficiency of the three detailed embedding strategies are also discussed.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Adaptive Data-Driven Deep-Learning Surrogate Model for Frontal Polymerization in Dicyclopentadiene

Frontal polymerization (FP) is a self-sustaining curing process that enables rapid and energy-efficient manufacturing of thermoset polymers and composites. Computational methods conventionally used to simulate the FP process are time-consuming, and repeating simulations are required for sensitivity analysis, uncertainty quantification, or optimization of the manufacturing process. Here, in this work, we develop an adaptive surrogate deep-learning model for FP of dicyclopentadiene (DCPD), which predicts the evolution of temperature and degree of cure orders of magnitude faster than the finite-element method (FEM). The adaptive algorithm provides a strategy to select training samples efficiently and save computational costs by reducing the redundancy of FEM-based training samples. The adaptive algorithm calculates the residual error of the FP governing equations using automatic differentiation of the deep neural network. A probability density function expressed in terms of the residual error is used to select training samples from the Sobol sequence space. The temperature and degree of cure evolution of each training sample are obtained by a 2D FEM simulation. The adaptive method is more efficient and has a better prediction accuracy than the random sampling method. With the well-trained surrogate neural network, the FP characteristics (front speed, shape, and temperature) can be extracted quickly from the predicted temperature and degree-of-cure fields.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1991

On-orbit demonstration of automated closure and capture using ESA-developed proximity operations technologies and an existing, serviceable NASA Explorer Platform spacecraft

The European Space Agency (ESA) has been working to develop an autonomous rendezvous and docking capability since 1984 to enable Hermes to automatically dock with Columbus. As a result, ESA with Matra, MBB, and other space companies have developed technologies that are also directly supportive of the current NASA initiative for Automated Rendezvous and Capture. Fairchild and Matra would like to discuss the results of the applicable ESA/Matra rendezvous and capture developments, and suggest how these capabilities could be used, together with an existing NASA Explorer Platform satellite, to minimize new development and accomplish a cost effective automatic closure and capture demonstration program. Several RV sensors have been developed at breadboard level for the Hermes/Columbus program by Matra, MBB, and SAAB. Detailed algorithms for automatic rendezvous, closure, and capture have been developed by ESA and CNES for application with Hermes to Columbus rendezvous and docking, and they currently are being verified with closed-loop software simulation. The algorithms have multiple closed-loop control modes and phases starting at long range using GPS navigation. Differential navigation is used for coast/continuous thrust homing, holdpoint acquisition, V-bar hopping, and station point acquisition. The proximity operation sensor is used for final closure and capture. A subset of these algorithms, comprising the proximity operations algorithms, could easily be extracted and tailored to a limited objective closure and capture flight demonstration.

Hohwiesner, Bill↗

DOE OSTI2025

Engineering Privacy at the Edge: A Practical Guide to Differential Privacy in System Architectures

The rapid expansion of distributed and edge computing platforms—spanning autonomous vehicles, IoT sensors, and healthcare monitors—has heightened concerns about data privacy. Differential Privacy (DP) offers a rigorous mathematical framework to protect sensitive information while retaining analytical utility. This tutorial introduces the foundations of DP for both numerical and categorical datasets and extends the discussion to correlation-aware techniques tailored for structured and high-dimensional data. Hands-on demonstrations will begin with the PETINA (Privacy prEservaTIoN Algorithms) package for numerical data and continue with MIC-DP (Maximum Information Correlated Differential Privacy) for tabular data. Designed for researchers and practitioners in secure systems, embedded architectures, and AI accelerators, the tutorial emphasizes practical and scalable methods for integrating DP into real-world system designs.

Kotevska, Olivera [ORNL] (ORCID:0000000316772243)↗

NASA NTRS2001

Low power, lightweight vapor sensing using arrays of conducting polymer composite chemically-sensitive resistors

Arrays of broadly responsive vapor detectors can be used to detect, identify, and quantify vapors and vapor mixtures. One implementation of this strategy involves the use of arrays of chemically-sensitive resistors made from conducting polymer composites. Sorption of an analyte into the polymer composite detector leads to swelling of the film material. The swelling is in turn transduced into a change in electrical resistance because the detector films consist of polymers filled with conducting particles such as carbon black. The differential sorption, and thus differential swelling, of an analyte into each polymer composite in the array produces a unique pattern for each different analyte of interest, Pattern recognition algorithms are then used to analyze the multivariate data arising from the responses of such a detector array. Chiral detector films can provide differential detection of the presence of certain chiral organic vapor analytes. Aspects of the spaceflight qualification and deployment of such a detector array, along with its performance for certain analytes of interest in manned life support applications, are reviewed and summarized in this article.

NASA Discipline Life Sciences Technologies↗

DOE OSTI2022

Differential methods for assessing sensitivity in biological models

Differential sensitivity analysis is indispensable in fitting parameters, understanding uncertainty, and forecasting the results of both thought and lab experiments. Although there are many methods currently available for performing differential sensitivity analysis of biological models, it can be difficult to determine which method is best suited for a particular model. In this paper, we explain a variety of differential sensitivity methods and assess their value in some typical biological models. First, we explain the mathematical basis for three numerical methods: adjoint sensitivity analysis, complex perturbation sensitivity analysis, and forward mode sensitivity analysis. We then carry out four instructive case studies. (a) The CARRGO model for tumor-immune interaction highlights the additional information that differential sensitivity analysis provides beyond traditional naive sensitivity methods, (b) the deterministic SIR model demonstrates the value of using second-order sensitivity in refining model predictions, (c) the stochastic SIR model shows how differential sensitivity can be attacked in stochastic modeling, and (d) a discrete birth-death-migration model illustrates how the complex perturbation method of differential sensitivity can be generalized to a broader range of biological models. Finally, we compare the speed, accuracy, and ease of use of these methods. We find that forward mode automatic differentiation has the quickest computational time, while the complex perturbation method is the simplest to implement and the most generalizable.

59 BASIC BIOLOGICAL SCIENCES↗

NASA NTRS2013

Fuzzy Reasoning to More Accurately Determine Void Areas on Optical Micrographs of Composite Structures

Accomplishing the best-performing composite matrix (resin) requires that not only the processing method but also the cure cycle generate low-void-content structures. If voids are present, the performance of the composite matrix will be significantly reduced. This is usually noticed by significant reductions in matrix-dominated properties, such as compression and shear strength. Voids in composite materials are areas that are absent of the composite components: matrix and fibers. The characteristics of the voids and their accurate estimation are critical to determine for high performance composite structures. One widely used method of performing void analysis on a composite structure sample is acquiring optical micrographs or Scanning Electron Microscope (SEM) images of lateral sides of the sample and retrieving the void areas within the micrographs/images using an image analysis technique. Segmentation for the retrieval and subsequent computation of void areas within the micrographs/images is challenging as the gray-scaled values of the void areas are close to the gray-scaled values of the matrix leading to the need of manually performing the segmentation based on the histogram of the micrographs/images to retrieve the void areas. The use of an algorithm developed by NASA and based on Fuzzy Reasoning (FR) proved to overcome the difficulty of suitably differentiate void and matrix image areas with similar gray-scaled values leading not only to a more accurate estimation of void areas on composite matrix micrographs but also to a faster void analysis process as the algorithm is fully autonomous.

Dominquez, Jesus A.↗

NASA NTRS1992

Spurious Solutions Of Nonlinear Differential Equations

Report utilizes nonlinear-dynamics approach to investigate possible sources of errors and slow convergence and non-convergence of steady-state numerical solutions when using time-dependent approach for problems containing nonlinear source terms. Emphasizes implications for development of algorithms in CFD and computational sciences in general. Main fundamental conclusion of study is that qualitative features of nonlinear differential equations cannot be adequately represented by finite-difference method and vice versa.

Yee, H. C.↗