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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 937 records · Page 52

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DOE OSTI2024

Reducing Operator Complexity of Galerkin Coarse-grid Operators with Machine Learning

Here, we propose a data-driven and machine-learning-based approach to compute non-Galerkin coarse-grid operators in multigrid (MG) methods, addressing the well-known issue of increasing operator complexity. Guided by the MG theory on spectrally equivalent coarse-grid operators, we have developed novel machine learning algorithms that utilize neural networks combined with smooth test vectors from multigrid eigenvalue problems. The proposed method demonstrates promise in reducing the complexity of coarse-grid operators while maintaining overall MG convergence for solving parametric partial differential equation problems. Numerical experiments on anisotropic rotated Laplacian and linear elasticity problems are provided to showcase the performance and comparison with existing methods for computing non-Galerkin coarse-grid operators.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1981

Using Landsat MSS data with soils information to identify wetland habitats

A previous study showed that certain fresh water wetland vegetation types can be spectrally separated when a maximum likelihood classification procedure is applied to Landsat spectral data. However, wetland and upland types which have similar vegetative life forms (e.g., upland hardwoods and hardwood swamps) are often confused because of spectral similarity. Therefore, the current investigation attempts to differentiate similar wetland and upland types by combining Landsat multispectral scanner (MSS) data with soils information. The Pigeon River area in northern Indiana used in the earlier study was also employed in this investigation. A layered classification algorithm which combined soils and spectral data was used to generate a wetland classification. The results of the spectral/soils wetland classification are compared to the previous classification that had been based on spectral data alone. The results indicate wetland habitat mapping can be improved by combining soils and other ancillary data with Landsat spectral data.

Ernst, C. L.↗

NASA NTRS1982

A minimal residual method for transonic potential flows

For transonic flow calculations, a combination of the successive line over-relaxation (SLOR) and the preconditioned conjugate gradient (CG) method has been suggested by Wong and Hafez (1981). This paper studies the method of minimal residual (MR) which avoids a combined iteration. This method is closely related to the CG method, may be regarded as a first-order gradient method, and is applicable to symmetric and nonsymmetric matrices. The problem is formulated as a nonlinear mixed elliptic-hyperbolic partial differential equation which includes an artificial viscosity and a switching function which is zero in subsonic regions and nonzero in supersonic regions. Alternatives to the SLOR method which provide faster convergence rates are introduced. The preconditioned MR algorithm is developed, and transonic potential flows around NACA 0012 airfoil are calculated for different Mach numbers and angles of attack. Preliminary results are presented, demonstrating that the MR algorithm requires no parameter estimation and rapidly converges for subsonic flows.

Wong, Y. S.↗

NASA NTRS1984

Acoustooptic linear algebra processors - Architectures, algorithms, and applications

Architectures, algorithms, and applications for systolic processors are described with attention to the realization of parallel algorithms on various optical systolic array processors. Systolic processors for matrices with special structure and matrices of general structure, and the realization of matrix-vector, matrix-matrix, and triple-matrix products and such architectures are described. Parallel algorithms for direct and indirect solutions to systems of linear algebraic equations and their implementation on optical systolic processors are detailed with attention to the pipelining and flow of data and operations. Parallel algorithms and their optical realization for LU and QR matrix decomposition are specifically detailed. These represent the fundamental operations necessary in the implementation of least squares, eigenvalue, and SVD solutions. Specific applications (e.g., the solution of partial differential equations, adaptive noise cancellation, and optimal control) are described to typify the use of matrix processors in modern advanced signal processing.

Casasent, D.↗

NASA NTRS1991

On the anomaly of velocity-pressure decoupling in collocated mesh solutions

The use of various pressure correction algorithms originally developed for fully staggered meshes can yield a velocity-pressure decoupled solution for collocated meshes. The mechanism that causes velocity-pressure decoupling is identified. It is shown that the use of a partial differential equation for the incremental pressure eliminates such a mechanism and yields a velocity-pressure coupled solution. Example flows considered are a three dimensional lid-driven cavity flow and a laminar flow through a 90 deg bend square duct. Numerical results obtained using the collocated mesh are in good agreement with the measured data and other numerical results.

Kim, Sang-Wook↗

NASA NTRS2006

Thermal Model of a Current-Carrying Wire in a Vacuum

A computer program implements a thermal model of an insulated wire carrying electric current and surrounded by a vacuum. The model includes the effects of Joule heating, conduction of heat along the wire, and radiation of heat from the outer surface of the insulation on the wire. The model takes account of the temperature dependences of the thermal and electrical properties of the wire, the emissivity of the insulation, and the possibility that not only can temperature vary along the wire but, in addition, the ends of the wire can be thermally grounded at different temperatures. The resulting second-order differential equation for the steady-state temperature as a function of position along the wire is highly nonlinear. The wire is discretized along its length, and the equation is solved numerically by use of an iterative algorithm that utilizes a multidimensional version of the Newton-Raphson method.

Border, James↗

NASA NTRS2008

Mission and Navigation Design for the 2009 Mars Science Laboratory Mission

NASA s Mars Science Laboratory mission will launch the next mobile science laboratory to Mars in the fall of 2009 with arrival at Mars occurring in the summer of 2010. A heat shield, parachute, and rocket-powered descent stage, including a sky crane, will be used to land the rover safely on the surface of Mars. The direction of the atmospheric entry vehicle lift vector will be controlled by a hypersonic entry guidance algorithm to compensate for entry trajectory errors and counteract atmospheric and aerodynamic dispersions. The key challenges for mission design are (1) develop a launch/arrival strategy that provides communications coverage during the Entry, Descent, and Landing phase either from an X-band direct-to-Earth link or from a Ultra High Frequency link to the Mars Reconnaissance Orbiter for landing latitudes between 30 deg North and 30 deg South, while satisfying mission constraints on Earth departure energy and Mars atmospheric entry speed, and (2) generate Earth-departure targets for the Atlas V-541 launch vehicle for the specified launch/arrival strategy. The launch/arrival strategy employs a 30-day baseline launch period and a 27-day extended launch period with varying arrival dates at Mars. The key challenges for navigation design are (1) deliver the spacecraft to the atmospheric entry interface point (Mars radius of 3522.2 km) with an inertial entry flight path angle error of +/- 0.20 deg (3 sigma), (2) provide knowledge of the entry state vector accurate to +/- 2.8 km (3 sigma) in position and +/- 2.0 m/s (3 sigma) in velocity for initializing the entry guidance algorithm, and (3) ensure a 99% probability of successful delivery at Mars with respect to available cruise stage propellant. Orbit determination is accomplished via ground processing of multiple complimentary radiometric data types: Doppler, range, and Delta-Differential One-way Ranging (a Very Long Baseline Interferometry measurement). The navigation strategy makes use of up to five interplanetary trajectory correction maneuvers to achieve entry targeting requirements. The requirements for cruise propellant usage and atmospheric entry targeting and knowledge are met with ample margins.

Mission design↗

DOE OSTI2022

Dynamic Parameter Estimation with Physics-based Neural Ordinary Differential Equations

Accurate estimation of dynamic parameters of gen-erators is crucial to building a reliable model for dynamical studies and reliable operation of the power system. This paper develops a physics-based neural ordinary differential equations (ODE) approach to learn the parameters of generator dynamic model using phasor measurement units (PMU) data. We design a physics-based neural network to represent the swing equations of the power system dynamics. A loss function is defined as the difference between dynamic simulation results from the physics-based neural networks and pseudo PMU measurements. The parameters of generator dynamic model are iteratively updated using the neural ODEs and the adjoint method. By exploiting the mini-batch scheme in neural ODE training, the parameter estimation performance is significantly improved. Numerical study results on a 3-machine 9-bus system show that the proposed algorithm outperforms state-of-the-art baseline method in both computation time and dynamic parameter estimation accuracy.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2023

Load-Displacement Relation and Gap Distribution Between Rough Surfaces: Partial Differential Equations Approach

We develop a theoretical model to predict the load-displacement relation and probability density function for gaps between contacting rough surfaces. We derive partial differential equations from the previous model (Joe et al., 2018), and extend them to the non-adhesive contact problem. The predictions of the present theory are compared with numerical results using the Green's function molecular dynamics algorithm, and a good agreement is obtained.

adhesion↗

DOE OSTI2024

Determining the effects of U/Pu ratio on subsolidus phase transitions in U-Pu-Zr metallic fuel alloys

Here, ternary alloys consisting primarily of uranium, plutonium, and zirconium (U-Pu-Zr) are among the leading candidate fuel systems considered for fast spectrum nuclear reactors. Despite historical operation data from the testing of U-Pu-Zr rods in the Experimental Breeder Reactor-II, considerable uncertainty about the evolution of phases and microstructure across the ternary composition space exists. Due to sluggish kinetics and other difficulties in handling metal actinide specimens, quantitative measurements of phase-transitions in U-Pu-Zr alloys remain sparse in scientific literature, with most investigators reporting either phase-transition temperatures or phase identification data, but not both from the same specimens. The purpose of this paper is to critically compare experimental and calculated phase transition data and correlate with the microstructure and phase characterization data of as-cast and annealed U-Pu-Zr alloys. Phase transition peaks were measured using differential scanning calorimetry in the subsolidus regions (723-948 K) of three ternary U-Pu-Zr alloys with the same zirconium concentration but various U/Pu ratios. Overlapping peaks were deconvoluted using a Frazier-Suzuki peak fitting algorithm, and the critical peak temperatures and enthalpies were calculated. In general, increasing concentrations of Pu were associated with enhanced thermal stability of the body-centered cubic γ phase upon both heating and cooling. Experimental phase transition temperatures in this study tended to agree well with the predictions of the established ternary phase diagrams and other reported phase transition temperatures in literature. Additionally, the TAF-ID thermodynamic database was used to calculate a U-Pu-40 at.% Zr pseudobinary diagram as well as ternary diagrams from 773 to 973 K. The equilibrium phase transition temperatures tended to be considerably lower than measured peak temperatures upon both heating and cooling. Recommendations for improving the quality of data in future U-Pu-Zr characterization studies are also discussed.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2021

Inference of neutrino flavor evolution through data assimilation and neural differential equations

The evolution of neutrino flavor in dense environments such as core-collapse supernovae and binary compact object mergers constitutes an important and unsolved problem. Its solution has potential implications for the dynamics and heavy-element nucleosynthesis in these environments. In this paper, we build upon recent work to explore inference-based techniques for the estimation of model parameters and neutrino flavor evolution histories. Here, we combine data assimilation, ordinary differential equation solvers, and neural networks to craft an inference approach tailored for nonlinear dynamical systems. Using this architecture, and a simple two-neutrino-beam, two-flavor model, we compare the performances of nine different optimization algorithms and expand upon previous assessments of the efficacy of inference for tackling problems in flavor evolution. We find that employing this new architecture, together with evolutionary optimization algorithms, accurately captures flavor histories in the small-scale model and allows us to quickly explore both model parameters and initial flavor content. In future work we plan to extend these inference techniques to large numbers of neutrinos.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Parametric Modeling and Economic Analysis of a 2MW th 3-Stream sCO 2 Heat Exchanger

Here, this paper presents the design and cost optimization of a novel 2MW th 3-stream sCO2 plate-fin heat exchanger. This heat exchanger design is unique in that it uses reduced metal oxide particle-to-sCO2 heat exchanger for cost-effective energy storage applications. The design uses low velocity, laminar air as the re-oxidizing reactant to transfer the heat of the re-oxidizing reaction to a sCO2 power loop. The design of the heat exchanger is based on a 2-D, 3-fluid plate/fin heat transfer model. The model parameterizes the size, shape, and number of passages of the heat exchanger to calculate the temperature profile, pressure drop, and fluid velocities of all three fluids. Global heat exchanger parameters such as the effectiveness and total heat transferred to the sCO2 are then calculated for overall performance. Due to the value and increased use of sCO2 heat exchangers in power cycles, a cost model of the system based on the unique high temperature/high pressure operating conditions was created using quotes from reference projects and market analysis. These quoted air-to-sCO2 heat exchangers are then processed using multiple weighting factors pertinent to heat exchanger design, including heat exchanger type, maximum temperature, differential pressures, fluids, duty, and more. These factors are then used in an exponential function in order to generate a parameterized cost curve. The design and cost of the heat exchanger are then optimized using the SMPSO genetic algorithm in Python. The optimization objectives for the system are to maximize the overall system effectiveness, including an air recuperator for preheating, and to minimize unit costs. Additional constraints are added to the system for the sCO2 and air pressure drops, air velocity to reduce particle entrainment, and the length and volume of the heat exchanger.

Cost Model↗

NASA NTRS1982

Incompressible Navier-Stokes and parabolized Navier-Stokes solution procedures and computational techniques

Recent developments with finite-difference techniques are emphasized. The quotation marks reflect the fact that any finite discretization procedure can be included in this category. Many so-called finite element collocation and galerkin methods can be reproduced by appropriate forms of the differential equations and discretization formulas. Many of the difficulties encountered in early Navier-Stokes calculations were inherent not only in the choice of the different equations (accuracy), but also in the method of solution or choice of algorithm (convergence and stability, in the manner in which the dependent variables or discretized equations are related (coupling), in the manner that boundary conditions are applied, in the manner that the coordinate mesh is specified (grid generation), and finally, in recognizing that for many high Reynolds number flows not all contributions to the Navier-Stokes equations are necessarily of equal importance (parabolization, preferred direction, pressure interaction, asymptotic and mathematical character). It is these elements that are reviewed. Several Navier-Stokes and parabolized Navier-Stokes formulations are also presented.

Rubin, S. G.↗

NASA NTRS1986

Reduction of the effects of the communication delays in scientific algorithms on message passing MIMD architectures

The efficient implementation of algorithms on multiprocessor machines requires that the effects of communication delays be minimized. The effects of these delays on the performance of a model problem on a hypercube multiprocessor architecture is investigated and methods are developed for increasing algorithm efficiency. The model problem under investigation is the solution by red-black Successive Over Relaxation YOUN71 of the heat equation; most of the techniques described here also apply equally well to the solution of elliptic partial differential equations by red-black or multicolor SOR methods. Methods for reducing communication traffic and overhead on a multiprocessor are identified and results of testing these methods on the Intel iPSC Hypercube reported. Methods for partitioning a problem's domain across processors, for reducing communication traffic during a global convergence check, for reducing the number of global convergence checks employed during an iteration, and for concurrently iterating on multiple time-steps in a time-dependent problem. Empirical results show that use of these models can markedly reduce a numewrical problem's execution time.

Saltz, J. H.↗

NASA NTRS1986

Mathematical model partitioning and packing for parallel computer calculation

This paper deals with the development of multiprocessor simulations from a serial set of ordinary differential equations describing a physical system. The identification of computational parallelism within the model equations is discussed. A technique is presented for identifying this parallelism and for partitioning the equations for parallel solution on a multiprocessor. Next, an algorithm which packs the equations into a minimum number of processors is described. The results of applying the packing algorithm to a turboshaft engine model are presented.

Arpasi, Dale J.↗

NASA NTRS1988

A computational procedure for large rotational motions in multibody dynamics

A computational procedure suitable for the solution of equations of motion for multibody systems is presented. The present procedure adopts a differential partitioning of the translational motions and the rotational motions. The translational equations of motion are then treated by either a conventional explicit or implicit direct integration method. A principal feature of this procedure is a nonlinearly implicit algorithm for updating rotations via the Euler four-parameter representation. This procedure is applied to the rolling of a sphere through a specific trajectory, which shows that it yields robust solutions.

Park, K. C.↗

NASA NTRS2018

G-band FMCW Radar for Humidity Profiling Inside Boundary Layer Clouds

We are developing a G-band FMCW radar for remote sensing of vertical water vapor proﬁles and total column water vapor. The radar utilizes the frequency-dependent absorption near the 183 GHz water absorption line to obtain a differential signal from which we can derive range-resolved humidity measurements. This proof-of-concept instrument will eventually be tested from an airborne platform. In this report, we discuss recent measurements and a humidity proﬁle retrieval algorithm based on an absorption line shape ﬁtting model

Monje, Raquel↗

DOE OSTI2021

Spatial Mapping of Electrostatic Fields in 2D Heterostructures

In situ electron microscopy is an effective tool for understanding the mechanisms driving novel phenomena in 2D structures. However, due to practical challenges, it is difficult to address these technologically relevant 2D heterostructures with electron microscopy. Here, we use the differential phase contrast (DPC) imaging technique to build a methodology for probing local electrostatic fields during electrical operation with nanoscale spatial resolution in such materials. We find that, by combining a traditional DPC setup with a high-pass filter, we can largely eliminate electric fluctuations emanating from short-range atomic potentials. Using a method based on this filtering algorithm, a priori electric field expectations can be directly compared with experimentally derived values to readily identify inhomogeneities and potentially problematic regions. Furthermore, we use this platform to analyze the electric field and charge density distribution across layers of hBN and MoS 2 .

79 ASTRONOMY AND ASTROPHYSICS↗