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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 NTRS1976

The fast decoding of Reed-Solomon codes using number theoretic transforms

It is shown that Reed-Solomon (RS) codes can be encoded and decoded by using a fast Fourier transform (FFT) algorithm over finite fields. The arithmetic utilized to perform these transforms requires only integer additions, circular shifts and a minimum number of integer multiplications. The computing time of this transform encoder-decoder for RS codes is less than the time of the standard method for RS codes. More generally, the field GF(q) is also considered, where q is a prime of the form K x 2 to the nth power + 1 and K and n are integers. GF(q) can be used to decode very long RS codes by an efficient FFT algorithm with an improvement in the number of symbols. It is shown that a radix-8 FFT algorithm over GF(q squared) can be utilized to encode and decode very long RS codes with a large number of symbols. For eight symbols in GF(q squared), this transform over GF(q squared) can be made simpler than any other known number theoretic transform with a similar capability. Of special interest is the decoding of a 16-tuple RS code with four errors.

Reed, I. S.↗

NASA NTRS1978

The N-BOD2 user's and programmer's manual

A general purpose digital computer program was developed and designed to aid in the analysis of spacecraft attitude dynamics. The program provides the analyst with the capability of automatically deriving and numerically solving the equations of motion of any system that can be modeled as a topological tree of coupled rigid bodies, flexible bodies, point masses, and symmetrical momentum wheels. Two modes of output are available. The composite system equations of motion may be outputted on a line printer in a symbolic form that may be easily translated into common vector-dyadic notation, or the composite system equations of motion may be solved numerically and any desirable set of system state variables outputted as a function of time.

Frisch, H. P.↗

DOE OSTI2026

Symbol alphabets in QCD and flag cluster algebras

The full 245-letter symbol alphabet for all planar massless two-loop six-point Feynman integrals was recently determined in arXiv:2412.19884 and arXiv:2501.01847. In a parallel mathematical development, it was shown in arXiv:2408.14956 that there is an embedding of the cluster algebra associated to the partial flag variety $\mathcal{Fl}$ $2,n-2;n$ , which describes the kinematics of n massless particles, into that of the Grassmannian Gr(n–2, 2n–4). In this paper we connect these developments by showing that most of the rational symbol letters can be expressed in terms of flag cluster variables, and that all of the algebraic symbol letters arise from infinite mutation sequences.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1985

STAR (Simple Tool for Automated Reasoning): Tutorial guide and reference manual

STAR is an interactive, interpreted programming language for the development and operation of Artificial Intelligence application systems. The language is intended for use primarily in the development of software application systems which rely on a combination of symbolic processing, central to the vast majority of AI algorithms, with routines and data structures defined in compiled languages such as C, FORTRAN and PASCAL. References to routines and data structures defined in compiled languages are intermixed with symbolic structures in STAR, resulting in a hybrid operating environment in which symbolic and non-symbolic processing and organization of data may interact to a high degree within the execution of particular application systems. The STAR language was developed in the course of a project involving AI techniques in the interpretation of imaging spectrometer data and is derived in part from a previous language called CLIP. The interpreter for STAR is implemented as a program defined in the language C and has been made available for distribution in source code form through NASA's Computer Software Management and Information Center (COSMIC). Contained within this report are the STAR Tutorial Guide, which introduces the language in a step-by-step manner, and the STAR Reference Manual, which provides a detailed summary of the features of STAR.

Borchardt, G. C.↗

DOE OSTI2022

HyKKT: a hybrid direct-iterative method for solving KKT linear systems

Here, we propose a solution strategy for the large indefinite linear systems arising in interior methods for nonlinear optimization. The method is suitable for implementation on hardware accelerators such as graphical processing units (GPUs). The current gold standard for sparse indefinite systems is the LBLT factorization where L is a lower triangular matrix and B is 1×1 or 2×2 block diagonal. However, this requires pivoting, which substantially increases communication cost and degrades performance on GPUs. Our approach solves a large indefinite system by solving multiple smaller positive definite systems, using an iterative solver on the Schur complement and an inner direct solve (via Cholesky factorization) within each iteration. Cholesky is stable without pivoting, thereby reducing communication and allowing reuse of the symbolic factorization. We demonstrate the practicality of our approach on large optimal power flow problems and show that it can efficiently utilize GPUs and outperform LBL T factorization of the full system.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1994

A novel computational method to simulate non-enzymatic self-replication

Non-enzymatic, template-directed synthesis of oligonucleotides has been extensively studied in the laboratory as a model to understand the kind of chemical processes that might have contributed to the origin of life on Earth. Several oligonucleotides have been shown to catalyze the synthesis of their complements from activated mononucleotides; however, a restricted number of them have been found to self-replicate. Recently we developed an efficient modified cellular automata method that supports the study of self-replicating oligonucleotides. With this method the oligonucleotide molecules are represented as active cells imbedded in a two-dimensional array of inactive cells symbolizing the environment. Random movements and probability-governed chemical reactions occurring in a cellular space can effectively simulate the experimental behavior observed in self-directed replication of oligonucleotides.

Navarro-Gonzalez, Rafael↗

NASA NTRS1992

High level cognitive information processing in neural networks

Two related research efforts were addressed: (1) high-level connectionist cognitive modeling; and (2) local neural circuit modeling. The goals of the first effort were to develop connectionist models of high-level cognitive processes such as problem solving or natural language understanding, and to understand the computational requirements of such models. The goals of the second effort were to develop biologically-realistic model of local neural circuits, and to understand the computational behavior of such models. In keeping with the nature of NASA's Innovative Research Program, all the work conducted under the grant was highly innovative. For instance, the following ideas, all summarized, are contributions to the study of connectionist/neural networks: (1) the temporal-winner-take-all, relative-position encoding, and pattern-similarity association techniques; (2) the importation of logical combinators into connection; (3) the use of analogy-based reasoning as a bridge across the gap between the traditional symbolic paradigm and the connectionist paradigm; and (4) the application of connectionism to the domain of belief representation/reasoning. The work on local neural circuit modeling also departs significantly from the work of related researchers. In particular, its concentration on low-level neural phenomena that could support high-level cognitive processing is unusual within the area of biological local circuit modeling, and also serves to expand the horizons of the artificial neural net field.

Barnden, John A.↗

DOE OSTI2018

An Interactive Visualization Tool for Large-Scale Building Stock Modeling

Recent advancements in data science and high-performance computing are making it easier to run millions of building simulations, but meaningful visualization of such large datasets remains a challenge. This paper presents a new tool developed to view the results of large-scale OpenStudio simulations of national, regional, or local building stocks. The tool processes millions of simulations to calculate measure savings, utility bills, carbon emissions, primary energy, and cost-effectiveness metrics at a high geographic resolution. Interactive visualizations of the building characteristics, consumption, and measure savings data include proportional symbol maps and histogram plots and can be filtered by any building characteristic.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2022

An Interactive Visualization Tool for Large-Scale Building Stock Modeling: Preprint

big data↗

NASA NTRS1994

Local performance optimization for a class of redundant eight-degree-of-freedom manipulators

Local performance optimization for joint limit avoidance and manipulability maximization (singularity avoidance) is obtained by using the Jacobian matrix pseudoinverse and by projecting the gradient of an objective function into the Jacobian null space. Real-time redundancy optimization control is achieved for an eight-joint redundant manipulator having a three-axis spherical shoulder, a single elbow joint, and a four-axis spherical wrist. Symbolic solutions are used for both full-Jacobian and wrist-partitioned pseudoinverses, partitioned null-space projection matrices, and all objective function gradients. A kinematic limitation of this class of manipulators and the limitation's effect on redundancy resolution are discussed. Results obtained with graphical simulation are presented to demonstrate the effectiveness of local redundant manipulator performance optimization. Actual hardware experiments performed to verify the simulated results are also discussed. A major result is that the partitioned solution is desirable because of low computation requirements. The partitioned solution is suboptimal compared with the full solution because translational and rotational terms are optimized separately; however, the results show that the difference is not significant. Singularity analysis reveals that no algorithmic singularities exist for the partitioned solution. The partitioned and full solutions share the same physical manipulator singular conditions. When compared with the full solution, the partitioned solution is shown to be ill-conditioned in smaller neighborhoods of the shared singularities.

Williams, Robert L., II↗

NASA NTRS1994

Toward Automatic Scalability Analysis of Message Passing Programs: A Case Study

Scalability analysis forms an important component of any performance debugging cycle, for massively parallel machines. However, tools that help in performing such analysis for parallel programs are non-existent. The primary reason for lack of such tools is the complexity involved in capturing program dynamics such as communication-computation overlap, communication latencies and memory hierarchy reference patterns. In this paper, we highlight some simple techniques that can be used to study scalability of explicit message-passing parallel programs that consider the above issues. We start from the high level source code and use a methodology for deducing communication characteristics and its impact on the total execution time of the program. The approach is validated with the help of a pipelined method for solving scalar tri-diagonal systems, using both simulations and symbolic cost models on the Intel hypercube.

Sarukkai, Sekhar R.↗

DOE OSTI2017

Rapid multiphase-field model development using a modular free energy based approach with automatic differentiation in MOOSE/MARMOT

In this paper, we present a novel rapid phase-field model development capability using a modular free energy based approach in the finite element based MOOSE framework. The phase-field equations are implemented in a general form as separate code form the model specific data such as the thermodynamic free energy density and mobility functions. This isolates researchers from complicated code and allows them to focus on implementing new material models. In addition, using a native symbolic differentiation algorithm, all required derivatives of the free energy density are automatically determined, removing sources for potential human error, and guaranteeing optimally preconditioned equation systems through fully populated Jacobian matrices. Free energy terms contributing to a phase-field model are abstracted into self contained objects that can be combined at will at simulation run time. Combining multiple chemical and mechanical free energy contributions allows the construction of coupled phase-field, mechanics, and multiphase models. Through just-in-time compilation, we greatly reduce the computational time required to evaluate the differentiated expressions. Lastly, we demonstrate the new capability on a variety of example simulations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

Kinetic Alfvén Turbulence: Electron and Ion Heating by Particle-in-cell Simulations

Three-dimensional particle-in-cell simulations of the forward cascade of decaying kinetic Alfvén turbulence have been carried out as an initial-value problem on a collisionless, homogeneous, magnetized, electron–ion plasma model with β{sub e}=β{sub i}=0.50 and m {sub i}/m {sub e} = 100, where subscripts e and i represent electrons and ions, respectively. Initial anisotropic narrowband spectra of relatively long-wavelength modes with approximately gyrotropic distributions in k{sub ⊥} undergo a forward cascade to broadband spectra of magnetic fluctuations at shorter wavelengths. Maximum electron and ion heating rates are computed as functions of the initial fluctuating magnetic field energy density ε{sub o} on the range 0.05<ε{sub o}<0.50. In contrast to dissipation by whistler turbulence, the maximum ion heating rate due to kinetic Alfvén turbulence is substantially greater than the maximum electron heating rate. Furthermore, ion heating as well as electron heating due to kinetic Alfvén turbulence scale approximately with ε {sub o}. Finally, electron heating leads to anisotropies of the type T{sub ∥e}>T{sub ⊥e}, where the parallel and perpendicular symbols refer to directions parallel and perpendicular, respectively, to the background magnetic field, whereas the heated ions remain relatively isotropic. This implies that, for the range of ε {sub o} values considered, the Landau wave–particle resonance is a likely heating mechanism for the electrons and may also contribute to ion heating.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2009

Error-Rate Bounds for Coded PPM on a Poisson Channel

Equations for computing tight bounds on error rates for coded pulse-position modulation (PPM) on a Poisson channel at high signal-to-noise ratio have been derived. These equations and elements of the underlying theory are expected to be especially useful in designing codes for PPM optical communication systems. The equations and the underlying theory apply, more specifically, to a case in which a) At the transmitter, a linear outer code is concatenated with an inner code that includes an accumulator and a bit-to-PPM-symbol mapping (see figure) [this concatenation is known in the art as "accumulate-PPM" (abbreviated "APPM")]; b) The transmitted signal propagates on a memoryless binary-input Poisson channel; and c) At the receiver, near-maximum-likelihood (ML) decoding is effected through an iterative process. Such a coding/modulation/decoding scheme is a variation on the concept of turbo codes, which have complex structures, such that an exact analytical expression for the performance of a particular code is intractable. However, techniques for accurately estimating the performances of turbo codes have been developed. The performance of a typical turbo code includes (1) a "waterfall" region consisting of a steep decrease of error rate with increasing signal-to-noise ratio (SNR) at low to moderate SNR, and (2) an "error floor" region with a less steep decrease of error rate with increasing SNR at moderate to high SNR. The techniques used heretofore for estimating performance in the waterfall region have differed from those used for estimating performance in the error-floor region. For coded PPM, prior to the present derivations, equations for accurate prediction of the performance of coded PPM at high SNR did not exist, so that it was necessary to resort to time-consuming simulations in order to make such predictions. The present derivation makes it unnecessary to perform such time-consuming simulations.

Moision, Bruce↗

DOE OSTI2018

Ternary Bismuthide SrPtBi 2 : Computation and Experiment in Synergism to Explore Solid-State Materials

A combination of theoretical calculation and the experimental synthesis to explore the new ternary compound is demonstrated in the Sr–Pt–Bi system. Because Pt–Bi is considered as a new critical charge-transfer pair for superconductivity, it inspired us to investigate the Sr–Pt–Bi system. With a thorough calculation of all the known stable/metastable compounds in the Sr–Pt–Bi system and crystal structure predictions, the thermodynamic stability of hypothetical stoichiometry, SrPtBi2, is determined. Following the high-temperature synthesis and crystallographic analysis, the first ternary bismuthide in Sr–Pt–Bi, SrPtBi2 was prepared, and the stoichiometry was confirmed experimentally. SrPtBi 2 crystallizes in the space group Pnma (S.G. 62, Pearson Symbol oP48), which matches well with theoretical prediction using an adaptive genetic algorithm. Using first-principles calculations, we demonstrate that the orthorhombic structure has lower formation energies than other 112 structure types, such as tetragonal BaMnBi 2 (CuSmP 2 ) and LaAuBi 2 (CuHfSi 2 ) structure types. The bonding analysis indicates that the Pt–Bi interactions play a critical role in structural stability. The physical property measurements show the metallic properties at the low temperature, which agrees with the electronic structure assessment.

36 MATERIALS SCIENCE↗

DOE OSTI2016

Feynman formulae and phase space Feynman path integrals for tau-quantization of some Lévy-Khintchine type Hamilton functions

Evolution semigroups generated by pseudo-differential operators are considered. These operators are obtained by different (parameterized by a number τ) procedures of quantization from a certain class of functions (or symbols) defined on the phase space. This class contains Hamilton functions of particles with variable mass in magnetic and potential fields and more general symbols given by the Lévy-Khintchine formula. The considered semigroups are represented as limits of n-fold iterated integrals when n tends to infinity. Such representations are called Feynman formulae. Some of these representations are constructed with the help of another pseudo-differential operator, obtained by the same procedure of quantization; such representations are called Hamiltonian Feynman formulae. Some representations are based on integral operators with elementary kernels; these are called Lagrangian Feynman formulae. Langrangian Feynman formulae provide approximations of evolution semigroups, suitable for direct computations and numerical modeling of the corresponding dynamics. Hamiltonian Feynman formulae allow to represent the considered semigroups by means of Feynman path integrals. In the article, a family of phase space Feynman pseudomeasures corresponding to different procedures of quantization is introduced. The considered evolution semigroups are represented as phase space Feynman path integrals with respect to these Feynman pseudomeasures, i.e., different quantizations correspond to Feynman path integrals with the same integrand but with respect to different pseudomeasures. This answers Berezin’s problem of distinguishing a procedure of quantization on the language of Feynman path integrals. Moreover, the obtained Lagrangian Feynman formulae allow also to calculate these phase space Feynman path integrals and to connect them with some functional integrals with respect to probability measures.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1973

Digital-computer program for design analysis of salient, wound pole alternators

A digital computer program for analyzing the electromagnetic design of salient, wound pole alternators is presented. The program, which is written in FORTRAN 4, calculates the open-circuit saturation curve, the field-current requirements at rated voltage for various loads and losses, efficiency, reactances, time constants, and weights. The methods used to calculate some of these items are presented or appropriate references are cited. Instructions for using the program and typical program input and output for an alternator design are given, and an alphabetical list of most FORTRAN symbols and the complete program listing with flow charts are included.

Repas, D. S.↗

DOE OSTI2026

Robust Explanations using Diverse Adversarially Trained Ensembles, Multi-Modal Contrastive Learning, and Attribution-based Confidence Metrics

The primary objective of this project is to strengthen the trustworthiness of AI systems by designing algorithms that make their internal decision-making processes more understandable to human users. This involves creating clear, interpretable explanations for AI decisions and developing metrics to assess these explanations' validity and reliability. Significant progress has been achieved through (i) developing symbolic explanations, (ii) generating meaningful interpretive insights, (iii) establishing accuracy and confidence metrics, and (iv) devising methods to evaluate the knowledge boundaries of AI models. To date, the research findings have been shared in peer-reviewed publications, with accompanying scientific and technical information (STI) detailed below.

97 MATHEMATICS AND COMPUTING↗