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 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

State elimination for mixed‐integer optimal control of partial differential equations by semigroup theory

Abstract Mixed‐integer optimal control problems governed by partial differential equations (MIPDECOs) are powerful modeling tools but also challenging in terms of theory and computation. We propose a highly efficient state elimination approach for MIPDECOs that are governed by partial differential equations that have the structure of an abstract ordinary differential equation in function space. This allows us to avoid repeated calculations of the states for all time steps, and our approach is applied only once before starting the optimization. The presentation of theoretical results is complemented by numerical experiments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Applying Quantum Computing to Simulate Power System Dynamics

Power system dynamics are generally modeled by high dimensional nonlinear differential-algebraic equations due to a large number of generators, loads, and transmission lines. Thus, its computational complexity grows exponentially with the system size. This paper demonstrates the potential use of quantum computing algorithms to model the power system dynamics. Leveraging a symbolic programming framework, we equivalently convert the power system dynamics’ differential algebraic equations (DAEs) into ordinary differential equations (ODEs), where the data of the state vector can be encoded into quantum computers via amplitude encoding. The system's nonlinearity is captured by Taylor polynomial expansion, the quantum state tensor, and Hamiltonian simulation, whereas state variables can be updated by a quantum linear equation solver. Our results show that quantum computing can simulate the dynamics of the power system with high accuracy, whereas its complexity is polynomial in the logarithm of the system dimension. Our work also illustrates the use of scientific machine learning tools for implementing scientific computing concepts, e.g., Taylor expansion, DAEs/ODEs transform, and quantum computing solver, in the field of power engineering.

Tran, Huynh↗
NASA NTRS1972

A theory of supercritical wing sections, with computer programs and examples.

Mathematical methods for the design of supercritical wings, which depend on the numerical solution of the partial differential equations of two-dimensional gas dynamics, are developed. The main contribution is a computer program for the design of shockless transonic airfoils using the hodograph transformation and analytic continuation into the complex domain. The mathematical theory is described, and a manual for users of the programs is provided. Numerical examples are given and computational results are discussed, and the computer programs themselves are listed. The analysis routine can be used to ascertain whether the profiles behave well at off-design conditions, or to smooth coordinates and obtain a desirable shape more quickly when perfectly shockless flow is not essential.

Bauer, F.↗
NASA NTRS1976

A hybrid computer program for rapidly solving flowing or static chemical kinetic problems involving many chemical species

A hybrid chemical kinetic computer program was assembled which provides a rapid solution to problems involving flowing or static, chemically reacting, gas mixtures. The computer program uses existing subroutines for problem setup, initialization, and preliminary calculations and incorporates a stiff ordinary differential equation solution technique. A number of check cases were recomputed with the hybrid program and the results were almost identical to those previously obtained. The computational time saving was demonstrated with a propane-oxygen-argon shock tube combustion problem involving 31 chemical species and 64 reactions. Information is presented to enable potential users to prepare an input data deck for the calculation of a problem.

Mclain, A. G.↗
NASA NTRS1972

SCIP2 flight instrumentation specification for parameter identification: User's guide

SCIP2 which is a digital computer program that can be used to investigate the effects of instrumentation errors on the accuracy of aircraft stability and control derivatives identified from flight test data is presented. The program is based on the assumptions that the aircraft differential equations of motion are linear and consist of small perturbations about a quasisteady flight condition. It is also assumed that a Newton-Raphson optimization technique is used for identifying the estimates of the parameters. A summary of the equations which are coded in the program are included.

Taniguchi, N.↗
DOE OSTI2011

GPU accelerated simulations of 3D deterministic particle transport using discrete ordinates method

Graphics Processing Unit (GPU), originally developed for real-time, high-definition 3D graphics in computer games, now provides great faculty in solving scientific applications. The basis of particle transport simulation is the time-dependent, multi-group, inhomogeneous Boltzmann transport equation. The numerical solution to the Boltzmann equation involves the discrete ordinates (S{sub n}) method and the procedure of source iteration. In this paper, we present a GPU accelerated simulation of one energy group time-independent deterministic discrete ordinates particle transport in 3D Cartesian geometry (Sweep3D). The performance of the GPU simulations are reported with the simulations of vacuum boundary condition. The discussion of the relative advantages and disadvantages of the GPU implementation, the simulation on multi GPUs, the programming effort and code portability are also reported. The results show that the overall performance speedup of one NVIDIA Tesla M2050 GPU ranges from 2.56 compared with one Intel Xeon X5670 chip to 8.14 compared with one Intel Core Q6600 chip for no flux fixup. The simulation with flux fixup on one M2050 is 1.23 times faster than on one X5670.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1964

Analytical Solutions for Non-Linear Differential Equations with the Help of a Digital Computer

A technique was developed with the help of a digital computer for analytic (algebraic) solutions of autonomous and nonautonomous equations. Two operational transform techniques have been programmed for the solution of these equations. Only relatively simple nonlinear differential equations have been considered. In the cases considered it has been possible to assimilate the secular terms into the solutions. For cases where f(t) is not a bounded function, a direct series solution is developed which can be shown to be an analytic function. All solutions have been checked against results obtained by numerical integration for given initial conditions and constants. It is evident that certain nonlinear differential equations can be solved with the help of a digital computer.

Cromwell, P. C.↗
DOE OSTI2018

A novel role for PTK2B in cultured beige adipocyte differentiation

Highlights: • PTK2B protein levels are higher during cultured beige versus white adipogenesis. • Ptk2b knock-out SVF cells have poor white adipocyte differentiation. • Ptk2b knock-out beige adipocytes have elevated lipid accumulation. • Ptk2b knock-out beige adipocytes have a greatly diminished thermogenic gene program. • Ptk2b knock-out beige adipocytes have altered mitochondrial respiration. Adipocyte differentiation is a tightly regulated process which requires the sequential and organized expression of numerous genes and proteins. Phosphorylation of cytoplasmic proteins and key transcription factors represents a critical regulatory mechanism of the process leading to adipocyte maturation and modulation of associated metabolic pathways. Despite the recognition of the importance of protein phosphorylation in adipocyte biology, relatively little is known about the role of specific kinases in thermogenic (brown or beige) adipocyte differentiation and function. In this study, we demonstrate that the non-receptor protein tyrosine kinase 2 beta (PTK2B) plays a critical role in murine beige adipocyte differentiation. We observed that PTK2B protein expression is associated with beige adipocyte differentiation in cultured, immortalized, inguinal stromal vascular fraction cells. CRISPR/Cas9-mediated knock-out of Ptk2b results in non-differentiating white adipocytes, and differentiated beige adipocytes with significantly reduced thermogenic gene and protein expression, enlarged lipid droplet size, and altered mitochondrial respiration. Together, our data in a cell culture system provides evidence for a role of PTK2B in the differentiation of murine beige adipocytes.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2011

Relativistic distorted-wave analysis of quasielastic proton-nucleus scattering

A relativistic distorted-wave impulse approximation formalism is presented for the calculation of quasielastic proton-nucleus scattering. It is shown that the double differential cross section may be written as a contraction between the hadronic tensor (describing the projectile and ejectile) and the polarization tensor (describing the nuclear target) and that this mathematical structure also holds for the case where distortions are included. The eikonal approximation is used to introduce distortions in the wave functions, and the nuclear response is described using a Fermi gas model. The highly oscillatory nine-dimensional integrand contained in the expression for the double differential cross section is computed using a novel technique based on combining traditional Gaussian integration methods with the powerful fitting functions in the matlab programming language. This work has successfully calculated the distorted-wave quasielastic differential cross section for proton-nucleus scattering within a fully relativistic framework. It is found that the distortions lead to a reduction in the double differential cross section and have a negligible effect on the computed spin observables.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2016

Optimal Multistage Algorithm for Adjoint Computation

We reexamine the work of Stumm and Walther on multistage algorithms for adjoint computation. We provide an optimal algorithm for this problem when there are two levels of checkpoints, in memory and on disk. Previously, optimal algorithms for adjoint computations were known only for a single level of checkpoints with no writing and reading costs; a well-known example is the binomial checkpointing algorithm of Griewank and Walther. Stumm and Walther extended that binomial checkpointing algorithm to the case of two levels of checkpoints, but they did not provide any optimality results. We bridge the gap by designing the first optimal algorithm in this context. We experimentally compare our optimal algorithm with that of Stumm and Walther to assess the difference in performance.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

An important class of intron retention events in human erythroblasts is regulated by cryptic exons proposed to function as splicing decoys

During terminal erythropoiesis, the splicing machinery in differentiating erythroblasts executes a robust intron retention (IR) program that impacts expression of hundreds of genes. We studied IR mechanisms in the SF3B1 splicing factor gene, which expresses ~50% of its transcripts in late erythroblasts as a nuclear isoform that retains intron 4. RNA-seq analysis of nonsense-mediated decay (NMD)-inhibited cells revealed previously undescribed splice junctions, rare or not detected in normal cells, that connect constitutive exons 4 and 5 to highly conserved cryptic cassette exons within the intron. Minigene splicing reporter assays showed that these cassettes promote IR. Genome-wide analysis of splice junction reads demonstrated that cryptic noncoding cassettes are much more common in large (>1 kb) retained introns than they are in small retained introns or in nonretained introns. Functional assays showed that heterologous cassettes can promote retention of intron 4 in the SF3B1 splicing reporter. Although many of these cryptic exons were spliced inefficiently, they exhibited substantial binding of U2AF1 and U2AF2 adjacent to their splice acceptor sites. We propose that these exons function as decoys that engage the intron-terminal splice sites, thereby blocking cross-intron interactions required for excision. Developmental regulation of decoy function underlies a major component of the erythroblast IR program.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2026

Status of 1eNp0π Charged-Current Electron Neutrino Cross Section on Argon in the NuMI Beam at ICARUS

The Short-Baseline Neutrino (SBN) Program is designed to probe short-baseline neutrino anomalies, including the LSND electron neutrino excess and the MiniBooNE low-energy excess. Essential to interpreting these anomalies and to the success of future experiments like DUNE, is the precise measurement of neutrino-argon interaction cross sections. The program utilizes two liquid argon time projection chamber (LArTPC) detectors: the Short-Baseline Near Detector (SBND) located 110 meters downstream from the Booster Neutrino Beam (BNB) target, and the ICARUS detector positioned 600 meters downstream. Additionally, the ICARUS detector lies off-axis to the NuMI beamline, providing a unique, high-statistics flux of electron neutrinos and sensitivity to energies that overlap with the DUNE spectrum. To analyze the data from these detectors, we have begun employing a machine-learning-based reconstruction algorithm referred to as “Scalable Particle Imaging with Neural Embeddings” (SPINE). SPINE has shown improvement in the ability to reconstruct the properties of final state particles in the detector, like the particle ID and momentum, with the potential to enhance the quality of measurements achievable within the SBN Program e.g., the resolution on kinematics used in differential cross section extraction. This poster presents progress toward measuring the electron neutrino argon interaction cross section in the 1eNp0π topology using the NuMI beam, highlighting the impact of SPINE through the ability to select signal events across a wide kinematic range without sacrificing background rejection power.

Carber, Dan [Colorado State U.] (ORCID:00090006451↗
DOE OSTI2023

The Dark Energy Survey Supernova Program: Corrections on Photometry Due to Wavelength-dependent Atmospheric Effects

Abstract Wavelength-dependent atmospheric effects impact photometric supernova flux measurements for ground-based observations. We present corrections on supernova flux measurements from the Dark Energy Survey Supernova Program’s 5YR sample (DES-SN5YR) for differential chromatic refraction (DCR) and wavelength-dependent seeing, and we show their impact on the cosmological parameters w and Ω m . We use g − i colors of Type Ia supernovae to quantify astrometric offsets caused by DCR and simulate point-spread functions (PSFs) using the GalSIM package to predict the shapes of the PSFs with DCR and wavelength-dependent seeing. We calculate the magnitude corrections and apply them to the magnitudes computed by the DES-SN5YR photometric pipeline. We find that for the DES-SN5YR analysis, not accounting for the astrometric offsets and changes in the PSF shape cause an average bias of +0.2 mmag and −0.3 mmag, respectively, with standard deviations of 0.7 mmag and 2.7 mmag across all DES observing bands ( griz ) throughout all redshifts. When the DCR and seeing effects are not accounted for, we find that w and Ω m are lower by less than 0.004 ± 0.02 and 0.001 ± 0.01, respectively, with 0.02 and 0.01 being the 1 σ statistical uncertainties. Although we find that these biases do not limit the constraints of the DES-SN5YR sample, future surveys with much higher statistics, lower systematics, and especially those that observe in the u band will require these corrections as wavelength-dependent atmospheric effects are larger at shorter wavelengths. We also discuss limitations of our method and how they can be better accounted for in future surveys.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1974

Contribution to the theory of tidal oscillations of an elastic earth. External tidal potential

The differential equations of the tidal oscillations of the earth were established under the assumption that the interior of the earth is laterally inhomogeneous. The theory was developed using vectorial and dyadic symbolism to shorten the exposition and to reduce the differential equations to a symmetric form convenient for programming and for numerical integration. The formation of tidal buldges on the surfaces of discontinuity and the changes in the internal density produce small periodic variations in the exterior geopotential which are reflected in the motion of artificial satellites. The analoques of Love elastic parameters in the expansion of exterior tidal potential reflect the asymmetric and inhomogeneous structure of the interior of the earth.

Musen, P.↗
NASA NTRS1975

A survey of NASTRAN improvements since level 15.5

Several improvements and capabilities were developed and installed in intermediate levels and are being analyzed and evaluated. A survey of current improvements to the program is presented which includes static analysis with differential stiffness rigid format, normal modes with differential stiffness rigid format, the TRIAAX and TRAPAX elements, the CNGRNT feature, fully stressed design, element strain energy and grid point force balance, and complex modal displacement plots.

Mcdonough, J. R.↗