Search NASA⌕ Search

SEARCH · Search NASA

Results for “differentiable programming”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
NASA NTRS1974

COMOC: Three dimensional boundary region variant, programmer's manual

The three-dimensional boundary region variant of the COMOC computer program system solves the partial differential equation system governing certain three-dimensional flows of a viscous, heat conducting, multiple-species, compressible fluid including combustion. The solution is established in physical variables, using a finite element algorithm for the boundary value portion of the problem description in combination with an explicit marching technique for the initial value character. The computational lattice may be arbitrarily nonregular, and boundary condition constraints are readily applied. The theoretical foundation of the algorithm, a detailed description on the construction and operation of the program, and instructions on utilization of the many features of the code are presented.

Orzechowski, J. A.↗
DOE OSTI2019

Automatic Differentiation for Adjoint Stencil Loops

Stencil loops are a common motif in computations including convolutional neural networks, structured-mesh solvers for partial differential equations, and image processing. Stencil loops are easy to parallelise, and their fast execution is aided by compilers, libraries, and domain-specific languages. Reverse-mode automatic differentiation, also known as algorithmic differentiation, autodiff, adjoint differentiation, or back-propagation, is sometimes used to obtain gradients of programs that contain stencil loops. Unfortunately, conventional automatic differentiation results in a memory access pattern that is not stencil-like and not easily parallelisable. In this paper we present a novel combination of automatic differentiation and loop transformations that preserves the structure and memory access pattern of stencil loops, while computing fully consistent derivatives. The generated loops can be parallelised and optimised for performance in the same way and using the same tools as the original computation. We have implemented this new technique in the Python tool PerforAD, which we release with this paper along with test cases derived from seismic imaging and computational fluid dynamics applications.

Automatic Differentiation↗
NASA NTRS1981

A program to evaluate a control system based on feedback of aerodynamic pressure differentials. Part 2: Data report for phase 1 wind tunnel test

Wind tunnel test data are presented. The purpose of the test was to determine the sensor location for sensitivity to flap deflection and to determine the range required of the sensor. The calculations followed to correct the raw pressure measurements, the corrected measurements, which represent the static pressures along the airfoil surface, and the static pressures tabulated and in coefficient form are described. However, the chordwise locations of the upper and lower surface taps do not coincide. An interpolation routine is performed to find the lower surface pressure coefficients at the upper surface tap locations. The difference, C sub P(lower) - C sub P(upper), is calculated and listed and the data are reorganized with respect to each tap location. A numerical regression performed to quantify the slopes of the graphs allows more accurate comparison of sensitivity and linearity.

Hrabak, R. R.↗
NASA NTRS1981

A program to evaluate a control system based on feedback of aerodynamic pressure differentials

The use of aerodynamic pressure differentials to position a control surface is evaluated. The system is a differential pressure command loop, analogous to a position command loop, where the surface is commanded to move until a desired differential pressure across the surface is achieved. This type of control is more direct and accurate because it is the differential pressure which causes the control forces and moments. A frequency response test was performed in a low speed wind tunnel to measure the performance of the system. Both pressure and position feedback were tested. The pressure feedback performed as well as position feedback implying that the actuator, with a break frequency on the order of 10 Rad/sec, was the limiting component. Theoretical considerations indicate that aerodynamic lags will not appear below frequencies of 50 Rad/sec, or higher.

Levy, D. W.↗
DOE OSTI2014

A Cutting Surface Algorithm for Semi-Infinite Convex Programming with an Application to Moment Robust Optimization

In this paper, we present and analyze a central cutting surface algorithm for general semi-infinite convex optimization problems and use it to develop a novel algorithm for distributionally robust optimization problems in which the uncertainty set consists of probability distributions with given bounds on their moments. Moments of arbitrary order, as well as nonpolynomial moments, can be included in the formulation. We show that this gives rise to a hierarchy of optimization problems with decreasing levels of risk-aversion, with classic robust optimization at one end of the spectrum and stochastic programming at the other. Although our primary motivation is to solve distributionally robust optimization problems with moment uncertainty, the cutting surface method for general semi-infinite convex programs is also of independent interest. The proposed method is applicable to problems with nondifferentiable semi-infinite constraints indexed by an infinite dimensional index set. Examples comparing the cutting surface algorithm to the central cutting plane algorithm of Kortanek and No demonstrate the potential of our algorithm even in the solution of traditional semi-infinite convex programming problems, whose constraints are differentiable, and are indexed by an index set of low dimension. After the rate of convergence analysis of the cutting surface algorithm, we extend the authors' moment matching scenario generation algorithm to a probabilistic algorithm that finds optimal probability distributions subject to moment constraints. The combination of this distribution optimization method and the central cutting surface algorithm yields a solution to a family of distributionally robust optimization problems that are considerably more general than the ones proposed to date.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Building Toward a Small Wind Turbine Site Assessor Credential (Presentation)

Proper site assessment is integral to the development of a successful small wind project. Without a small wind site assessor certification program, consumers, including state incentive program managers, lack a benchmark for differentiating between qualified and nonqualified site assessors. A small wind site assessor best practice manual is being developed as a resource for consumers until a credential program becomes available. This presentation describes the purpose, proposed content, and the National Renewable Energy Laboratory's approach to the development of such a manual.

17 WIND ENERGY↗
DOE OSTI2023

A Fast Temporal Decomposition Procedure for Long-Horizon Nonlinear Dynamic Programming

We propose a fast temporal decomposition procedure for solving long-horizon nonlinear dynamic programs. The core of the procedure is sequential quadratic programming (SQP) that utilizes a differentiable exact augmented Lagrangian as the merit function. Within each SQP iteration, we approximately solve the Newton system using an overlapping temporal decomposition strategy. We show that the approximate search direction is still a descent direction of the augmented Lagrangian provided the overlap size and penalty parameters are suitably chosen, which allows us to establish the global convergence. Moreover, we show that a unit step size is accepted locally for the approximate search direction and further establish a uniform, local linear convergence over stages. This local convergence rate matches the rate of the recent Schwarz scheme (Na et al. 2022). However, the Schwarz scheme has to solve nonlinear subproblems to optimality in each iteration, whereas we only perform a single Newton step instead. Numerical experiments validate our theories and demonstrate the superiority of our method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Inconsistent Investment and Consumption Problems

In a traditional Black–Scholes market we develop a verification theorem for a general class of investment and consumption problems where the standard dynamic programming principle does not hold. The theorem is an extension of the standard Hamilton–Jacobi–Bellman equation in the form of a system of non-linear differential equations. We derive the optimal investment and consumption strategy for a mean-variance investor without pre-commitment endowed with labor income. In the case of constant risk aversion it turns out that the optimal amount of money to invest in stocks is independent of wealth. The optimal consumption strategy is given as a deterministic bang-bang strategy. In order to have a more realistic model we allow the risk aversion to be time and state dependent. Of special interest is the case were the risk aversion is inversely proportional to present wealth plus the financial value of future labor income net of consumption. Using the verification theorem we give a detailed analysis of this problem. It turns out that the optimal amount of money to invest in stocks is given by a linear function of wealth plus the financial value of future labor income net of consumption. The optimal consumption strategy is again given as a deterministic bang-bang strategy. We also calculate, for a general time and state dependent risk aversion function, the optimal investment and consumption strategy for a mean-standard deviation investor without pre-commitment. In that case, it turns out that it is optimal to take no risk at all.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1989

The 3DGRAPE book: Theory, users' manual, examples

A users' manual for a new three-dimensional grid generator called 3DGRAPE is presented. The program, written in FORTRAN, is capable of making zonal (blocked) computational grids in or about almost any shape. Grids are generated by the solution of Poisson's differential equations in three dimensions. The program automatically finds its own values for inhomogeneous terms which give near-orthogonality and controlled grid cell height at boundaries. Grids generated by 3DGRAPE have been applied to both viscous and inviscid aerodynamic problems, and to problems in other fluid-dynamic areas. The smoothness for which elliptic methods are known is seen here, including smoothness across zonal boundaries. An introduction giving the history, motivation, capabilities, and philosophy of 3DGRAPE is presented first. Then follows a chapter on the program itself. The input is then described in detail. A chapter on reading the output and debugging follows. Three examples are then described, including sample input data and plots of output. Last is a chapter on the theoretical development of the method.

Sorenson, Reese L.↗
DOE OSTI2015

Cobalt–iron nano catalysts supported on TiO{sub 2}–SiO{sub 2}: Characterization and catalytic performance in Fischer–Tropsch synthesis

Graphical abstract: The Co–Fe/TiO{sub 2}–SiO{sub 2} catalysts were prepared. The prepared catalysts were tested for light olefins and C{sub 5}–C{sub 12} production. The best operational conditions are 250 °C, H{sub 2}/CO = 1/1 under 5 bar pressure. - Highlights: • The TiO{sub 2}–SiO{sub 2} supported cobalt–iron catalysts were prepared via sol–gel method. • The best operational conditions were 250 °C, GHSV = 2000 h{sup −1}, H{sub 2}/CO = 1/1 and 5 bar. • The (Co/Fe)/TiO{sub 2}–SiO{sub 2} is efficient catalyst for light olefins and C{sub 5}–C{sub 12} production. - Abstract: A series of Co–Fe catalysts supported on TiO{sub 2}–SiO{sub 2} were prepared by the sol–gel method. This research investigated the effects of (Co/Fe) wt.%, the solution pH, different Co/Fe molar ratio, calcination conditions and different promoters on the catalytic performance of cobalt–iron catalysts for the Fisher–Tropsch synthesis (FTS). It was found that the catalyst containing 35 wt.% (Co–Fe)/TiO{sub 2}–SiO{sub 2} (Co/Fe molar ratio is 80/20) promoted with 1.5 wt.% Cu and calcined in air atmosphere at 600 °C for 7 h with a heating rate of 3 °C min{sup −1} is an optimal nano catalyst for converting synthesis gas to light olefins and C{sub 5}–C{sub 12} hydrocarbons. The effects of operational conditions such as the H{sub 2}/CO ratio, gas hourly space velocity (GHSV), different reaction temperature, and reaction pressure were investigated. The results showed that the best operational conditions for optimal nano catalyst are 250 °C, GHSV = 2000 h{sup −1}, H{sub 2}/CO molar ratio 1/1 under 5 bar total pressure. Catalysts and precursors were characterized by, X-ray diffraction (XRD), scanning electron microcopy (SEM), thermal gravimetric analysis (TGA), differential scanning calorimetry (DSC), temperature program reduction (TPR) and N{sub 2} adsorption–desorption measurements.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Simple, efficient and open-source CRISPR/Cas9 strategy for multi-site genome editing in Populus tremula × alba

Although the CRISPR/Cas9 system has been successfully used for crop breeding, its application remains limited in forest trees. Here, we describe an efficient gene editing strategy for hybrid poplar, (Populus tremula × alba INRA clone 717-1B4) based on the Golden Gate MoClo cloning. To test the system efficiency for generating single gene mutants, two single guide RNAs (sgRNAs) were designed and incorporated into the MoClo Tool Kit level 2 binary vector with the Cas9 expression cassette to mutate the SHORT ROOT (SHR) gene. Moreover, we also tested its efficiency for introducing mutations in two genes simultaneously by expressing one sgRNA targeting a single site of the YUC4 gene and the other sgRNA targeting the PLT1 gene. For a robust evaluation of the approach, we repeated the strategy to target the LBD12 and LBD4 genes simultaneously, using an independent construct. We generated hairy roots by Agrobacterium rhizogenes-mediated leaf transformation. Sequencing results confirmed the CRISPR/Cas9-mediated mutation in the targeted sites of PtaSHR. Biallelic and homozygous knockout mutations were detected. A deletion spanning both target sites and small insertions/deletions were the most common mutations. Out of the 22 SHR alleles sequenced, 21 were mutated. The phenotype’s characterization showed that transgenic roots with biallelic mutations for the SHR gene lacked a defined endodermal single cell layer, suggesting a conserved gene function similar to its homolog in Arabidopsis Arabidopsis thaliana (L.) Heynh. Sequencing results also revealed the high efficiency of the system for generating double mutants. Biallelic mutations for both genes in the yuc4/plt1 and lbd12/lbd4 roots were detected in three (yuc4/plt1) and two (lbd12/lbd4) out of four transgenic roots evaluated. A small deletion or a single nucleotide insertion at the single target site was the most common mutations. This CRISPR/Cas9 strategy arises as a rapid, simple and standardized gene-editing tool to evaluate the gene role in essential developmental programs such as radial cell differentiation of poplar roots.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS1972

Optimized solution of Kepler's equation

A detailed description is presented of KEPLER, an IBM 360 computer program used for the solution of Kepler's equation for eccentric anomaly. The program KEPLER employs a second-order Newton-Raphson differential correction process, and it is faster than previously developed programs by an order of magnitude.

Kohout, J. M.↗
NASA NTRS1984

Recent advances in methods for numerical solution of O.D.E. initial value problems

In the mathematical modeling of physical systems, it is often necessary to solve an initial value problem (IVP), consisting of a system of ordinary differential equations (ODE). A typical program produces approximate solutions at certain mesh points. Almost all existing codes try to control the local truncation error, while the user is really interested in controlling the true or global error. The present investigation provides a review of recent advances regarding the solution of the IVP, giving particular attention to stiff systems. Stiff phenomena are customarily defined in terms of the eigenvalues of the Jacobian. There are, however, some difficulties connected with this approach. It is pointed out that an estimate of the Lipschitz constant proves to be a very practical way to determine the stiffness of a problem.

Bui, T. D.↗
NASA NTRS2003

The zinc finger transcription factor Gfi1, implicated in lymphomagenesis, is required for inner ear hair cell differentiation and survival

Gfi1 was first identified as causing interleukin 2-independent growth in T cells and lymphomagenesis in mice. Much work has shown that Gfi1 and Gfi1b, a second mouse homolog, play pivotal roles in blood cell lineage differentiation. However, neither Gfi1 nor Gfi1b has been implicated in nervous system development, even though their invertebrate homologues, senseless in Drosophila and pag-3 in C. elegans are expressed and required in the nervous system. We show that Gfi1 mRNA is expressed in many areas that give rise to neuronal cells during embryonic development in mouse, and that Gfi1 protein has a more restricted expression pattern. By E12.5 Gfi1 mRNA is expressed in both the CNS and PNS as well as in many sensory epithelia including the developing inner ear epithelia. At later developmental stages, Gfi1 expression in the ear is refined to the hair cells and neurons throughout the inner ear. Gfi1 protein is expressed in a more restricted pattern in specialized sensory cells of the PNS, including the eye, presumptive Merkel cells, the lung and hair cells of the inner ear. Gfi1 mutant mice display behavioral defects that are consistent with inner ear anomalies, as they are ataxic, circle, display head tilting behavior and do not respond to noise. They have a unique inner ear phenotype in that the vestibular and cochlear hair cells are differentially affected. Although Gfi1-deficient mice initially specify inner ear hair cells, these hair cells are disorganized in both the vestibule and cochlea. The outer hair cells of the cochlea are improperly innervated and express neuronal markers that are not normally expressed in these cells. Furthermore, Gfi1 mutant mice lose all cochlear hair cells just prior to and soon after birth through apoptosis. Finally, by five months of age there is also a dramatic reduction in the number of cochlear neurons. Hence, Gfi1 is expressed in the developing nervous system, is required for inner ear hair cell differentiation, and its loss causes programmed cell death.

NASA Discipline Developmental Biology↗
NASA NTRS2004

Further Improvement in 3DGRAPE

3DGRAPE/AL:V2 denotes version 2 of the Three-Dimensional Grids About Anything by Poisson's Equation with Upgrades from Ames and Langley computer program. The preceding version, 3DGRAPE/AL, was described in Improved 3DGRAPE (ARC-14069) NASA Tech Briefs, Vol. 21, No. 5 (May 1997), page 66. These programs are so named because they generate volume grids by iteratively solving Poisson's Equation in three dimensions. The grids generated by the various versions of 3DGRAPE have been used in computational fluid dynamics (CFD). The main novel feature of 3DGRAPE/AL:V2 is the incorporation of an optional scheme in which anisotropic Lagrange-based trans-finite interpolation (ALBTFI) is coupled with exponential decay functions to compute and blend interior source terms. In the input to 3DGRAPE/AL:V2 the user can specify whether or not to invoke ALBTFI in combination with exponential-decay controls, angles, and cell size for controlling the character of grid lines. Of the known programs that solve elliptic partial differential equations for generating grids, 3DGRAPE/AL:V2 is the only code that offers a combination of speed and versatility with most options for controlling the densities and other characteristics of grids for CFD.

Alter, Stephen↗
DOE OSTI2025

Unified differentiable digital twin for the IOTA/FAST facility

As the design complexity of modern accelerators grows, there is more interest in using advanced simulations that have fast execution time or produce insights about accelerator state. One notable example of additional information are gradients of physical observables with respect to design parameters produced by differentiable simulations. The IOTA/FAST facility has recently begun a program to implement and experimentally validate a unified start-to-end differentiable digital twin to serve as a virtual accelerator test stand, allowing for rapid prototyping of new software and experiments with minimal beam time costs. In this contribution we will discuss our plans and progress. Specifically, we will cover the selection and benchmarking of both physics and ML codes, the development of generic interfaces between device models and surrogate or physics-based sections, and the export of the parameters through either a deterministic event loop or a fully asynchronous EPICS soft input/output controller. We will also discuss challenges in model calibration and uncertainty quantification, as well as future plans to support larger proton accelerators like PIPII and Booster.

Kuklev, Nikita [Fermilab]↗