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 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
NASA NTRS1973

Application of digital computer APU modeling techniques to control system design.

Study of the required controls for a H2-O2 auxiliary power unit (APU) technology program for the Space Shuttle. A steady-state system digital computer program was prepared and used to optimize initial system design. Analytical models of each system component were included. The program was used to solve a nineteen-dimensional problem, and then time-dependent differential equations were added to the computer program to simulate transient APU system and control. Some system parameters were considered quasi-steady-state, and others were treated as differential variables. The dynamic control analysis proceeded from initial ideal control modeling (which considered one control function and assumed the others to be ideal), stepwise through the system (adding control functions), until all of the control functions and their interactions were considered. In this way, the adequacy of the final control design over the required wide range of APU operating conditions was established.

Bailey, D. A.↗
DOE OSTI2023

Simultaneous Measurements of Noncommuting Observables: Positive Transformations and Instrumental Lie Groups

We formulate a general program for describing and analyzing continuous, differential weak, simultaneous measurements of noncommuting observables, which focuses on describing the measuring instrument autonomously, without states. The Kraus operators of such measuring processes are time-ordered products of fundamental differential positive transformations, which generate nonunitary transformation groups that we call instrumental Lie groups. The temporal evolution of the instrument is equivalent to the diffusion of a Kraus-operator distribution function, defined relative to the invariant measure of the instrumental Lie group. This diffusion can be analyzed using Wiener path integration, stochastic differential equations, or a Fokker-Planck-Kolmogorov equation. This way of considering instrument evolution we call the Instrument Manifold Program. We relate the Instrument Manifold Program to state-based stochastic master equations. We then explain how the Instrument Manifold Program can be used to describe instrument evolution in terms of a universal cover that we call the universal instrumental Lie group, which is independent not just of states, but also of Hilbert space. The universal instrument is generically infinite dimensional, in which case the instrument’s evolution is chaotic. Special simultaneous measurements have a finite-dimensional universal instrument, in which case the instrument is considered principal, and it can be analyzed within the differential geometry of the universal instrumental Lie group. Principal instruments belong at the foundation of quantum mechanics. We consider the three most fundamental examples: measurement of a single observable, position and momentum, and the three components of angular momentum. As these measurements are performed continuously, they converge to strong simultaneous measurements. For a single observable, this results in the standard decay of coherence between inequivalent irreducible representations. For the latter two cases, it leads to a collapse within each irreducible representation onto the classical or spherical phase space, with the phase space located at the boundary of these instrumental Lie groups.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1987

Optimal cure cycle design of a resin-fiber composite laminate

A unified computed aided design method was studied for the cure cycle design that incorporates an optimal design technique with the analytical model of a composite cure process. The preliminary results of using this proposed method for optimal cure cycle design are reported and discussed. The cure process of interest is the compression molding of a polyester which is described by a diffusion reaction system. The finite element method is employed to convert the initial boundary value problem into a set of first order differential equations which are solved simultaneously by the DE program. The equations for thermal design sensitivities are derived by using the direct differentiation method and are solved by the DE program. A recursive quadratic programming algorithm with an active set strategy called a linearization method is used to optimally design the cure cycle, subjected to the given design performance requirements. The difficulty of casting the cure cycle design process into a proper mathematical form is recognized. Various optimal design problems are formulated to address theses aspects. The optimal solutions of these formulations are compared and discussed.

Hou, Jean W.↗
NASA NTRS1995

Numerical solution of differential equations by artificial neural networks

Conventionally programmed digital computers can process numbers with great speed and precision, but do not easily recognize patterns or imprecise or contradictory data. Instead of being programmed in the conventional sense, artificial neural networks (ANN's) are capable of self-learning through exposure to repeated examples. However, the training of an ANN can be a time consuming and unpredictable process. A general method is being developed by the author to mate the adaptability of the ANN with the speed and precision of the digital computer. This method has been successful in building feedforward networks that can approximate functions and their partial derivatives from examples in a single iteration. The general method also allows the formation of feedforward networks that can approximate the solution to nonlinear ordinary and partial differential equations to desired accuracy without the need of examples. It is believed that continued research will produce artificial neural networks that can be used with confidence in practical scientific computing and engineering applications.

Meade, Andrew J., Jr.↗
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.↗
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 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↗
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 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]↗