Search NASA⌕ Search

SEARCH · Search NASA

Results for “Symbolic computing”

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 289 records · Page 16

Program Verification for Extreme-Scale Applications (Final Scientific/Technical Report)

The project seeks to develop tools and techniques to help software developers verify the correctness and accuracy of their code. The target domain is scientific software of the kind widely used and developed in the Department of Energy research community, with a particular focus on "extreme scale" programs - those that are expected to involve possibly millions of parallel threads of execution. The report covers the University of Delaware contribution to the collaborative project. The project had a number of successful outcomes, especially regarding the development and extension of the CIVL software verification framework. CIVL is a verification tool for C or Fortran programs that use MPI, OpenMP, CUDA, and/or Pthreads for parallelization. CIVL went through vast improvements and extensions, and was successfully applied to a number of challenging codes. It found a subtle bug in the Devito PDE framework. It was able to verify the functional correctness of a conjugate gradient solver using a novel probabilistic technique with vanishingly small chance of error. CIVL was used very successfully in verification competitions, and the CIVL solutions to the competition challenges were presented and published. CIVL was also used successfully by other researchers on a computational chemistry kernel.

97 MATHEMATICS AND COMPUTING↗

Analysis of the Hessian for aeroelastic optimization

The symbol of the Hessian for an aeroelastic optimization model problem is analyzed. The flow is modeled by the small-disturbance full potential equation and the structure is modeled by an isotropic (von Karman) plate equation. The cost function consists of both aerodynamic and structural terms. In the new analysis the symbol of the cost function Hessian near the minimum is computed. The result indicates that under some conditions, which are likely fulfilled in most applications, the system is decoupled for the non-smooth components. The result also shows that the structure part in the Hessian is well-conditioned while the aerodynamic part is ill-conditioned. Applications of the result to optimization strategies are discussed.

Arian, Eyal↗

AI's Philosophical Underpinnings: A Thinking Person's Walk through the Twists and Turns of Artificial Intelligence's Meandering Path

Few human endeavors can be viewed both as extremely successful and unsuccessful at the same time. This is typically the case when goals have not been well defined or have been shifting in time. This has certainly been true of Artificial Intelligence (AI). The nature of intelligence has been the object of much thought and speculation throughout the history of philosophy. It is in the nature of philosophy that real headway is sometimes made only when appropriate tools become available. Similarly the computer, coupled with the ability to program (at least in principle) any function, appeared to be the tool that could tackle the notion of intelligence. To suit the tool, the problem of the nature of intelligence was soon sidestepped in favor of this notion: If a probing conversation with a computer could not be distinguished from a conversation with a human, then AI had been achieved. This notion became known as the Turing test, after the mathematician Alan Turing who proposed it in 1950. Conceptually rich and interesting, these early efforts gave rise to a large portion of the field's framework. Key to AI, rather than the 'number crunching' typical of computers until then, was viewed as the ability to manipulate symbols and make logical inferences. To facilitate these tasks, AI languages such as LISP and Prolog were invented and used widely in the field. One idea that emerged and enabled some success with real world problems was the notion that 'most intelligence' really resided in knowledge. A phrase attributed to Feigenbaum, one of the pioneers, was 'knowledge is the power.' With this premise, the problem is shifted from 'how do we solve problems' to 'how do we represent knowledge.' A good knowledge representation scheme could allow one to draw conclusions from given premises. Such schemes took forms such as rules,frames and scripts. It allowed the building of what became known as expert systems or knowledge based systems (KBS).

Colombano, Silvano↗

Frame Synchronization Without Attached Sync Markers

We describe a method to synchronize codeword frames without making use of attached synchronization markers (ASMs). Instead, the synchronizer identifies the code structure present in the received symbols, by operating the decoder for a handful of iterations at each possible symbol offset and forming an appropriate metric. This method is computationally more complex and doesn't perform as well as frame synchronizers that utilize an ASM; nevertheless, the new synchronizer acquires frame synchronization in about two seconds when using a 600 kbps software decoder, and would take about 15 milliseconds on prototype hardware. It also eliminates the need for the ASMs, which is an attractive feature for short uplink codes whose coding gain would be diminished by the overheard of ASM bits. The lack of ASMs also would simplify clock distribution for the AR4JA low-density parity-check (LDPC) codes and adds a small amount to the coding gain as well (up to 0.2 dB).

Hamkins, Jon↗

Modelling protein functional domains in signal transduction using Maude

Modelling of protein-protein interactions in signal transduction is receiving increased attention in computational biology. This paper describes recent research in the application of Maude, a symbolic language founded on rewriting logic, to the modelling of functional domains within signalling proteins. Protein functional domains (PFDs) are a critical focus of modern signal transduction research. In general, Maude models can simulate biological signalling networks and produce specific testable hypotheses at various levels of abstraction. Developing symbolic models of signalling proteins containing functional domains is important because of the potential to generate analyses of complex signalling networks based on structure-function relationships.

Signal Transduction↗

An Interactive Software for Conceptual Wing Flutter Analysis and Parametric Study

An interactive computer program was developed for wing flutter analysis in the conceptual design stage. The objective was to estimate the flutter instability boundary of a flexible cantilever wing, when well-defined structural and aerodynamic data are not available, and then study the effect of change in Mach number, dynamic pressure, torsional frequency, sweep, mass ratio, aspect ratio, taper ratio, center of gravity, and pitch inertia, to guide the development of the concept. The software was developed for Macintosh or IBM compatible personal computers, on MathCad application software with integrated documentation, graphics, data base and symbolic mathematics. The analysis method was based on non-dimensional parametric plots of two primary flutter parameters, namely Regier number and Flutter number, with normalization factors based on torsional stiffness, sweep, mass ratio, taper ratio, aspect ratio, center of gravity location and pitch inertia radius of gyration. The parametric plots were compiled in a Vought Corporation report from a vast data base of past experiments and wind-tunnel tests. The computer program was utilized for flutter analysis of the outer wing of a Blended-Wing-Body concept, proposed by McDonnell Douglas Corp. Using a set of assumed data, preliminary flutter boundary and flutter dynamic pressure variation with altitude, Mach number and torsional stiffness were determined.

Mukhopadhyay, Vivek↗

A Flexible and Non-instrusive Approach for Computing Complex Structural Coverage Metrics

Software analysis tools and techniques often leverage structural code coverage information to reason about the dynamic behavior of software. Existing techniques instrument the code with the required structural obligations and then monitor the execution of the compiled code to report coverage. Instrumentation based approaches often incur considerable runtime overhead for complex structural coverage metrics such as Modified Condition/Decision (MC/DC). Code instrumentation, in general, has to be approached with great care to ensure it does not modify the behavior of the original code. Furthermore, instrumented code cannot be used in conjunction with other analyses that reason about the structure and semantics of the code under test. In this work, we introduce a non-intrusive preprocessing approach for computing structural coverage information. It uses a static partial evaluation of the decisions in the source code and a source-to-bytecode mapping to generate the information necessary to efficiently track structural coverage metrics during execution. Our technique is flexible; the results of the preprocessing can be used by a variety of coverage-driven software analysis tasks, including automated analyses that are not possible for instrumented code. Experimental results in the context of symbolic execution show the efficiency and flexibility of our nonintrusive approach for computing code coverage information

DO-178C↗

Closed-form solution of decomposable stochastic models

Markov and semi-Markov processes are increasingly being used in the modeling of complex reconfigurable systems (fault tolerant computers). The estimation of the reliability (or some measure of performance) of the system reduces to solving the process for its state probabilities. Such a model may exhibit numerous states and complicated transition distributions, contributing to an expensive and numerically delicate solution procedure. Thus, when a system exhibits a decomposition property, either structurally (autonomous subsystems), or behaviorally (component failure versus reconfiguration), it is desirable to exploit this decomposition in the reliability calculation. In interesting cases there can be failure states which arise from non-failure states of the subsystems. Equations are presented which allow the computation of failure probabilities of the total (combined) model without requiring a complete solution of the combined model. This material is presented within the context of closed-form functional representation of probabilities as utilized in the Symbolic Hierarchical Automated Reliability and Performance Evaluator (SHARPE) tool. The techniques adopted enable one to compute such probability functions for a much wider class of systems at a reduced computational cost. Several examples show how the method is used, especially in enhancing the versatility of the SHARPE tool.

Sjogren, Jon A.↗

Solving differential‐algebraic equations in power system dynamic analysis with quantum computing

Abstract Power system dynamics are generally modeled by high dimensional non‐linear differential‐algebraic equations (DAEs) given a large number of components forming the network. These DAEs' complexity can grow exponentially due to the increasing penetration of distributed energy resources, whereas their computation time becomes sensitive due to the increasing interconnection of the power grid with other energy systems. This paper demonstrates the use of quantum computing algorithms to solve DAEs for power system dynamic analysis. We leverage a symbolic programming framework to equivalently convert the power system's DAEs into ordinary differential equations (ODEs) using index reduction methods and then encode their data into qubits using amplitude encoding. The system non‐linearity is captured by Hamiltonian simulation with truncated Taylor expansion so that state variables can be updated by a quantum linear equation solver. Our results show that quantum computing can solve the power system's DAEs accurately with a computational complexity polynomial in the logarithm of the system dimension. We also illustrate the use of recent advanced tools in scientific machine learning for implementing complex computing concepts, that is, Taylor expansion, DAEs/ODEs transformation, and quantum computing solver with abstract representation for power engineering applications.

computational complexity↗

Effects of low sampling rate in the digital data-transition tracking loop

This article describes the performance of the all-digital data-transition tracking loop (DTTL) with coherent and noncoherent sampling using nonlinear theory. The effects of few samples per symbol and of noncommensurate sampling and symbol rates are addressed and analyzed. Their impact on the probability density and variance of the phase error are quantified through computer simulations. It is shown that the performance of the all-digital DTTL approaches its analog counterpart when the sampling and symbol rates are noncommensurate (i.e., the number of samples per symbol is an irrational number). The loop signal-to-noise ratio (SNR) (inverse of phase error variance) degrades when the number of samples per symbol is an odd integer but degrades even further for even integers.

Mileant, A.↗

The performance of trellis-coded MDPSK with multiple symbol detection

The idea of using a multiple (more than two) symbol observation interval to improve error probability performance is applied to differential detection of trellis-coded multiple phase-shift keying (MPSK) over an additive white Gaussian noise (AWGN) channel. An equivalent Euclidean distance measure per trellis branch is determined for this detection scheme. This is used to define an augmented (larger multiplicity) trellis code whose distance measure is the conventional squared Euclidean distance typical of conventional trellis-coded modulation on the AWGN. Such an augmented multiple trellis code is a convenient mathematical tool for simplifying the analysis. Results are obtained by a combination of analysis (upper Chernoff bounds and asymptotic large-SNR approximations) and computer simulation. It is shown that only a slight increase (e.g., one symbol) in the length of the observation interval will provide a significant improvement in bit error probability performance.

Divsalar, Dariush↗

Closed-form solution of decomposable stochastic models

Equations to compute failure probabilities of the total (combined) model without a complete solution of the combined model are presented. A closed-form analytical approach to presentation of probabilities is used on the bases of the Symbolic Hierarchical Automated Reliability and Performance Evaluator tool. The techniques under consideration make it possible to compute the probability function for a much wider class of systems at a reduced computational cost.

Sjogren, Jon A.↗

Complexity-calibrated benchmarks for machine learning reveal when prediction algorithms succeed and mislead

Abstract Recurrent neural networks are used to forecast time series in finance, climate, language, and from many other domains. Reservoir computers are a particularly easily trainable form of recurrent neural network. Recently, a “next-generation” reservoir computer was introduced in which the memory trace involves only a finite number of previous symbols. We explore the inherent limitations of finite-past memory traces in this intriguing proposal. A lower bound from Fano’s inequality shows that, on highly non-Markovian processes generated by large probabilistic state machines, next-generation reservoir computers with reasonably long memory traces have an error probability that is at least $$\sim 60\%$$ ∼ 60 % higher than the minimal attainable error probability in predicting the next observation. More generally, it appears that popular recurrent neural networks fall far short of optimally predicting such complex processes. These results highlight the need for a new generation of optimized recurrent neural network architectures. Alongside this finding, we present concentration-of-measure results for randomly-generated but complex processes. One conclusion is that large probabilistic state machines—specifically, large $$\epsilon$$ ϵ -machines—are key to generating challenging and structurally-unbiased stimuli for ground-truthing recurrent neural network architectures.

97 MATHEMATICS AND COMPUTING↗

The waiting time problem in a model hominin population

Functional information is normally communicated using specific, context-dependent strings of symbolic characters. This is true within the human realm (texts and computer programs), and also within the biological realm (nucleic acids and proteins). In biology, strings of nucleotides encode much of the information within living cells. How do such information-bearing nucleotide strings arise and become established? This paper uses comprehensive numerical simulation to understand what types of nucleotide strings can realistically be established via the mutation/selection process, given a reasonable timeframe. The program Mendel’s Accountant realistically simulates the mutation/selection process, and was modified so that a starting string of nucleotides could be specified, and a corresponding target string of nucleotides could be specified. We simulated a classic pre-human hominin population of at least 10,000 individuals, with a generation time of 20 years, and with very strong selection (50 % selective elimination). Random point mutations were generated within the starting string. Whenever an instance of the target string arose, all individuals carrying the target string were assigned a specified reproductive advantage. When natural selection had successfully amplified an instance of the target string to the point of fixation, the experiment was halted, and the waiting time statistics were tabulated. Using this methodology we tested the effect of mutation rate, string length, fitness benefit, and population size on waiting time to fixation. Biologically realistic numerical simulations revealed that a population of this type required inordinately long waiting times to establish even the shortest nucleotide strings. To establish a string of two nucleotides required on average 84 million years. To establish a string of five nucleotides required on average 2 billion years. We found that waiting times were reduced by higher mutation rates, stronger fitness benefits, and larger population sizes. However, even using the most generous feasible parameters settings, the waiting time required to establish any specific nucleotide string within this type of population was consistently prohibitive. We show that the waiting time problem is a significant constraint on the macroevolution of the classic hominin population. Routine establishment of specific beneficial strings of two or more nucleotides becomes very problematic.

54 ENVIRONMENTAL SCIENCES↗

Computer program for Stirling engine performance calculations

The thermodynamic characteristics of the Stirling engine were analyzed and modeled on a computer to support its development as a possible alternative to the automobile spark ignition engine. The computer model is documented. The documentation includes a user's manual, symbols list, a test case, comparison of model predictions with test results, and a description of the analytical equations used in the model.

Tew, R. C., Jr.↗

Working Notes from the 1992 AAAI Spring Symposium on Practical Approaches to Scheduling and Planning

The symposium presented issues involved in the development of scheduling systems that can deal with resource and time limitations. To qualify, a system must be implemented and tested to some degree on non-trivial problems (ideally, on real-world problems). However, a system need not be fully deployed to qualify. Systems that schedule actions in terms of metric time constraints typically represent and reason about an external numeric clock or calendar and can be contrasted with those systems that represent time purely symbolically. The following topics are discussed: integrating planning and scheduling; integrating symbolic goals and numerical utilities; managing uncertainty; incremental rescheduling; managing limited computation time; anytime scheduling and planning algorithms, systems; dependency analysis and schedule reuse; management of schedule and plan execution; and incorporation of discrete event techniques.

Drummond, Mark↗

Automatic Differentiation in MetaPhysicL and Its Applications in MOOSE

Efficient solution via Newton’s method of nonlinear systems of equations requires an accurate representation of the Jacobian, corresponding to the derivatives of the component residual equations with respect to the degrees of freedom. In practice these systems of equations often arise from spatial discretization of partial differential equations used to model physical phenomena. These equations may involve domain motion or material equations that are complex functions of the systems’ degrees of freedom. Computing the Jacobian by hand in these situations is arduous and prone to error. Finite difference approximations of the Jacobian or its action are prone to truncation error, especially in multiphysics settings. Symbolic differentiation packages may be used, but often result in an excessive number of terms in realistic model scenarios. An alternative to symbolic and numerical differentiation is automatic differentiation (AD), which propagates derivatives with every elementary operation of a computer program, corresponding to continual application of the chain rule. Automatic differentiation offers the guarantee of an exact Jacobian at a relatively small overhead cost. In this work, we outline the adoption of AD in the Multiphysics Object Oriented Simulation Environment (MOOSE) via the MetaPhysicL package. We describe the application of MOOSE’s AD capability to several sets of physics that were previously infeasible to model via hand-coded or Jacobian-free simulation techniques, including arbitrary Lagrangian-Eulerian and level-set simulations of laser melt pools, phase-field simulations with free energies provided through neural networks, and metallic nuclear fuel simulations that require inner Newton loop calculation of nonlinear material properties.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗