Improving Symbolic Optimization Learning by Leveraging Language Models
Explore the source record for details and available documents.
Mathematics and Computing↗
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.
Automatic mathematical modeling for real time simulation system
A methodology for automatic mathematical modeling and generating simulation models is described. The models will be verified by running in a test environment using standard profiles with the results compared against known results. The major objective is to create a user friendly environment for engineers to design, maintain, and verify their model and also automatically convert the mathematical model into conventional code for conventional computation. A demonstration program was designed for modeling the Space Shuttle Main Engine Simulation. It is written in LISP and MACSYMA and runs on a Symbolic 3670 Lisp Machine. The program provides a very friendly and well organized environment for engineers to build a knowledge base for base equations and general information. It contains an initial set of component process elements for the Space Shuttle Main Engine Simulation and a questionnaire that allows the engineer to answer a set of questions to specify a particular model. The system is then able to automatically generate the model and FORTRAN code. The future goal which is under construction is to download the FORTRAN code to VAX/VMS system for conventional computation. The SSME mathematical model will be verified in a test environment and the solution compared with the real data profile. The use of artificial intelligence techniques has shown that the process of the simulation modeling can be simplified.
Wang, Caroline↗
Hedgehog bases for A n cluster polylogarithms and an application to six-point amplitudes
Multi-loop scattering amplitudes in N=4 Yang-Mills theory possess cluster algebra structure. In order to develop a computational framework which exploits this connection, we show how to construct bases of Goncharov polylogarithm functions, at any weight, whose symbol alphabet consists of cluster coordinates on the A n cluster algebra. As a result, using such a basis we present a new expression for the 2-loop 6-particle NMHV amplitude which makes some of its cluster structure manifest.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Plant Bioengineering Atlas: A Knowledge Graph of Genes, DNA Constructs, and Plant Traits.
Plant bioengineering has generated tens of thousands of genotype-to-phenotype relationships, but this knowledge remains fragmented across narrative literature and difficult to use computationally. Inconsistent descriptions of DNA constructs, host species, and traits, including variable species names, omitted regulatory elements, and inconsistent gene symbols, impede data reuse, comparative analysis, and design-build-test-learn cycles. Here, we present the Plant Bioengineering Atlas, a literature-mined, ontology-grounded knowledge base assembled using an artificial intelligence (AI)-aided extraction pipeline. A large language model parsed open-access primary research articles to generate structured, provenance-anchored records of engineered genes, modification types, promoter-gene-terminator constructs, host species, target traits, and reported phenotypes, with every record traceable to its source. The current release contains 14,358 curated records encompassing 6,998 distinct genes across 436 plant species from 6,452 papers published between 2000 and 2026. Corpus analysis reveals that experiments are concentrated in a small group of model and crop species, disease and pathogen resistance is the most frequently engineered trait class, and constitutive regulatory parts (particularly the CaMV 35S promoter and NOS terminator) remain pervasive. Two in five records omit one or both flanking regulatory elements (i.e., promoter and terminator), while only 23.4% describe cassettes in which both elements resolve to named part classes, exposing a systematic reproducibility gap. We organize these data into a knowledge graph linking genes, constructs, species, and traits; provide access through an interactive web portal; and propose an AI-compatible documentation standard for AI-ready reporting. The Plant Bioengineering Atlas provides a foundation for data-driven hypothesis generation and AI-aided plant biodesign.
, Genes, DNA Constructs↗
Indicator tensor manipulation on MACSYMA
A new computational tool for physical calculations is described. It is the first computer system capable of performing indicial tensor calculus (as opposed to component tensor calculus). It is now operational on the symbolic manipulation system MACSYMA. The capabilities of the system are outlined.
Bogen, R. A.↗
Rapid prototyping facility for flight research in artificial-intelligence-based flight systems concepts
The Dryden Flight Research Facility of the NASA Ames Research Facility of the NASA Ames Research Center is developing a rapid prototyping facility for flight research in flight systems concepts that are based on artificial intelligence (AI). The facility will include real-time high-fidelity aircraft simulators, conventional and symbolic processors, and a high-performance research aircraft specially modified to accept commands from the ground-based AI computers. This facility is being developed as part of the NASA-DARPA automated wingman program. This document discusses the need for flight research and for a national flight research facility for the rapid prototyping of AI-based avionics systems and the NASA response to those needs.
Duke, E. L.↗
A rapid prototyping facility for flight research in advanced systems concepts
The Dryden Flight Research Facility of the NASA Ames Research Facility of the NASA Ames Research Center is developing a rapid prototyping facility for flight research in flight systems concepts that are based on artificial intelligence (AI). The facility will include real-time high-fidelity aircraft simulators, conventional and symbolic processors, and a high-performance research aircraft specially modified to accept commands from the ground-based AI computers. This facility is being developed as part of the NASA-DARPA automated wingman program. This document discusses the need for flight research and for a national flight research facility for the rapid prototyping of AI-based avionics systems and the NASA response to those needs.
Duke, Eugene L.↗
Bayesian Model Selection for Reducing Bloat and Overfitting in Genetic Programming for Symbolic Regression
When performing symbolic regression using genetic programming, overfitting and bloat can negatively impact generalizability and interpretability of the resulting equations as well as increase computation times. A Bayesian fitness metric is introduced and its impact on bloat and overfitting during population evolution is studied and compared to common alternatives in the literature. The proposed approach was found to be more robust to noise and data sparsity in numerical experiments, guiding evolution to a level of complexity appropriate to the dataset. Further evolution of the population resulted not in overfitting or bloat, but rather in slight simplifications in model form. The ability to identify an equation of complexity appropriate to the scale of noise in the training data was also demonstrated. In general, the Bayesian model selection algorithm was shown to be an effective means of regularization which resulted in less bloat and overfitting when any amount of noise was present in the training data.
Uncertainty quantification↗
User's manual for EZPLOT version 5.5: A FORTRAN program for 2-dimensional graphic display of data
EZPLOT is a computer applications program that converts data resident on a file into a plot displayed on the screen of a graphics terminal. This program generates either time history or x-y plots in response to commands entered interactively from a terminal keyboard. Plot parameters consist of a single independent parameter and from one to eight dependent parameters. Various line patterns, symbol shapes, axis scales, text labels, and data modification techniques are available. This user's manual describes EZPLOT as it is implemented on the Ames Research Center, Dryden Research Facility ELXSI computer using DI-3000 graphics software tools.
Garbinski, Charles↗
The Block V Receiver fast acquisition algorithm for the Galileo S-band mission
A fast acquisition algorithm for the Galileo suppressed carrier, subcarrier, and data symbol signals under low data rate, signal-to-noise ratio (SNR) and high carrier phase-noise conditions has been developed. The algorithm employs a two-arm fast Fourier transform (FFT) method utilizing both the in-phase and quadrature-phase channels of the carrier. The use of both channels results in an improved SNR in the FFT acquisition, enabling the use of a shorter FFT period over which the carrier instability is expected to be less significant. The use of a two-arm FFT also enables subcarrier and symbol acquisition before carrier acquisition. With the subcarrier and symbol loops locked first, the carrier can be acquired from an even shorter FFT period. Two-arm tracking loops are employed to lock the subcarrier and symbol loops parameter modification to achieve the final (high) loop SNR in the shortest time possible. The fast acquisition algorithm is implemented in the Block V Receiver (BVR). This article describes the complete algorithm design, the extensive computer simulation work done for verification of the design and the analysis, implementation issues in the BVR, and the acquisition times of the algorithm. In the expected case of the Galileo spacecraft at Jupiter orbit insertion PD/No equals 14.6 dB-Hz, R(sym) equals 16 symbols per sec, and the predicted acquisition time of the algorithm (to attain a 0.2-dB degradation from each loop to the output symbol SNR) is 38 sec.
Aung, M.↗
Ordinal judgments of numerical symbols by macaques (Macaca mulatta)
Two rhesus monkeys (Macaca mulatta) learned that the arabic numerals 0 through 9 represented corresponding quantities of food pellets. By manipulating a joystick, the monkeys were able to make a selection of paired numerals presented on a computer screen. Although the monkeys received a corresponding number of pellets even if the lesser of the two numerals was selected, they learned generally to choose the numeral of greatest value even when pellet delivery was made arrhythmic. In subsequent tests, they chose the numerals of greater value when presented in novel combinations or in random arrays of up to five numerals. Thus, the monkeys made ordinal judgments of numerical symbols in accordance with their absolute or relative values.
Washburn, David A.↗
Hardware Implementation of Serially Concatenated PPM Decoder
A prototype decoder for a serially concatenated pulse position modulation (SCPPM) code has been implemented in a field-programmable gate array (FPGA). At the time of this reporting, this is the first known hardware SCPPM decoder. The SCPPM coding scheme, conceived for free-space optical communications with both deep-space and terrestrial applications in mind, is an improvement of several dB over the conventional Reed-Solomon PPM scheme. The design of the FPGA SCPPM decoder is based on a turbo decoding algorithm that requires relatively low computational complexity while delivering error-rate performance within approximately 1 dB of channel capacity. The SCPPM encoder consists of an outer convolutional encoder, an interleaver, an accumulator, and an inner modulation encoder (more precisely, a mapping of bits to PPM symbols). Each code is describable by a trellis (a finite directed graph). The SCPPM decoder consists of an inner soft-in-soft-out (SISO) module, a de-interleaver, an outer SISO module, and an interleaver connected in a loop (see figure). Each SISO module applies the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm to compute a-posteriori bit log-likelihood ratios (LLRs) from apriori LLRs by traversing the code trellis in forward and backward directions. The SISO modules iteratively refine the LLRs by passing the estimates between one another much like the working of a turbine engine. Extrinsic information (the difference between the a-posteriori and a-priori LLRs) is exchanged rather than the a-posteriori LLRs to minimize undesired feedback. All computations are performed in the logarithmic domain, wherein multiplications are translated into additions, thereby reducing complexity and sensitivity to fixed-point implementation roundoff errors. To lower the required memory for storing channel likelihood data and the amounts of data transfer between the decoder and the receiver, one can discard the majority of channel likelihoods, using only the remainder in operation of the decoder. This is accomplished in the receiver by transmitting only a subset consisting of the likelihoods that correspond to time slots containing the largest numbers of observed photons during each PPM symbol period. The assumed number of observed photons in the remaining time slots is set to the mean of a noise slot. In low background noise, the selection of a small subset in this manner results in only negligible loss. Other features of the decoder design to reduce complexity and increase speed include (1) quantization of metrics in an efficient procedure chosen to incur no more than a small performance loss and (2) the use of the max-star function that allows sum of exponentials to be computed by simple operations that involve only an addition, a subtraction, and a table lookup. Another prominent feature of the design is a provision for access to interleaver and de-interleaver memory in a single clock cycle, eliminating the multiple clock-cycle latency characteristic of prior interleaver and de-interleaver designs.
Moision, Bruce↗
Differential equations from unitarity cuts: nonplanar hexa-box integrals
We compute ϵ-factorized differential equations for all dimensionally-regularized integrals of the nonplanar hexa-box topology, which contribute for instance to 2-loop 5-point QCD amplitudes. A full set of pure integrals is presented. For 5-point planar topologies, Gram determinants which vanish in 4 dimensions are used to build compact expressions for pure integrals. Using unitarity cuts and computational algebraic geometry, we obtain a compact IBP system which can be solved in 8 hours on a single CPU core, overcoming a major bottleneck for deriving the differential equations. Alternatively, assuming prior knowledge of the alphabet of the nonplanar hexa-box, we reconstruct analytic differential equations from 30 numerical phase-space points, making the computation almost trivial with current techniques. We solve the differential equations to obtain the values of the master integrals at the symbol level. Full results for the differential equations and solutions are included as supplementary material.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Interleaver design for trellis-coded differential 8-PSK modulation with non-coherent detection
The effect of finite interleaver size on bit error rate (BER) performance of coded 8-DPSK is determined by means of computer simulations. The losses evaluated in this way include the SNR degradation due to the timing and frequency errors of the symbol synchronizer and the automatic frequency control (AFC) of the receiver. BER measurements are presented using a conventional 2/3 rate convolutional 8-state trellis-code for typical Rayleigh and Rician fading channels. It is shown that for a Rician channel with a Rician parameter of 7 dB, a Doppler spread of 100 Hz and a data rate of 2400 bps, an interleaver with size 16 x 16 symbols performs nearly as well as a very large interleaver. It is also shown that for very fast Rayleigh channels, the BER-curves flatten out at large SNR.
Edbauer, Franz↗
Army-NASA aircrew/aircraft integration program (A3I) software detailed design document, phase 3
The capabilities and design approach of the MIDAS (Man-machine Integration Design and Analysis System) computer-aided engineering (CAE) workstation under development by the Army-NASA Aircrew/Aircraft Integration Program is detailed. This workstation uses graphic, symbolic, and numeric prototyping tools and human performance models as part of an integrated design/analysis environment for crewstation human engineering. Developed incrementally, the requirements and design for Phase 3 (Dec. 1987 to Jun. 1989) are described. Software tools/models developed or significantly modified during this phase included: an interactive 3-D graphic cockpit design editor; multiple-perspective graphic views to observe simulation scenarios; symbolic methods to model the mission decomposition, equipment functions, pilot tasking and loading, as well as control the simulation; a 3-D dynamic anthropometric model; an intermachine communications package; and a training assessment component. These components were successfully used during Phase 3 to demonstrate the complex interactions and human engineering findings involved with a proposed cockpit communications design change in a simulated AH-64A Apache helicopter/mission that maps to empirical data from a similar study and AH-1 Cobra flight test.
Banda, Carolyn↗
Optical Verification Laboratory Demonstration System for High Security Identification Cards
Document fraud including unauthorized duplication of identification cards and credit cards is a serious problem facing the government, banks, businesses, and consumers. In addition, counterfeit products such as computer chips, and compact discs, are arriving on our shores in great numbers. With the rapid advances in computers, CCD technology, image processing hardware and software, printers, scanners, and copiers, it is becoming increasingly easy to reproduce pictures, logos, symbols, paper currency, or patterns. These problems have stimulated an interest in research, development and publications in security technology. Some ID cards, credit cards and passports currently use holograms as a security measure to thwart copying. The holograms are inspected by the human eye. In theory, the hologram cannot be reproduced by an unauthorized person using commercially-available optical components; in practice, however, technology has advanced to the point where the holographic image can be acquired from a credit card-photographed or captured with by a CCD camera-and a new hologram synthesized using commercially-available optical components or hologram-producing equipment. Therefore, a pattern that can be read by a conventional light source and a CCD camera can be reproduced. An optical security and anti-copying device that provides significant security improvements over existing security technology was demonstrated. The system can be applied for security verification of credit cards, passports, and other IDs so that they cannot easily be reproduced. We have used a new scheme of complex phase/amplitude patterns that cannot be seen and cannot be copied by an intensity-sensitive detector such as a CCD camera. A random phase mask is bonded to a primary identification pattern which could also be phase encoded. The pattern could be a fingerprint, a picture of a face, or a signature. The proposed optical processing device is designed to identify both the random phase mask and the primary pattern [1-3]. We have demonstrated experimentally an optical processor for security verification of objects, products, and persons. This demonstration is very important to encourage industries to consider the proposed system for research and development.
Javidi, Bahram↗
Program Helps Generate And Manage Graphics
Living Color Frame Maker (LCFM) computer program generates computer-graphics frames. Graphical frames saved as text files, in readable and disclosed format, easily retrieved and manipulated by user programs for wide range of real-time visual information applications. LCFM implemented in frame-based expert system for visual aids in management of systems. Monitoring, diagnosis, and/or control, diagrams of circuits or systems brought to "life" by use of designated video colors and intensities to symbolize status of hardware components (via real-time feedback from sensors). Status of systems can be displayed. Written in C++ using Borland C++ 2.0 compiler for IBM PC-series computers and compatible computers running MS-DOS.
Truong, L. V.↗
Quicklist: The basis for a computer aided logic design system
Quicklist, a preprocessor for an existing wire list program that cuts the description of the wire list by about 67 percent over previous methods, is described. Quicklist uses two different methods to shorten the input data. The first of these is the use of parentheses to allow a compact way of describing signal names which increment (or decrement) by one, i.e., typical signal names in a bus. The other method used is the equal sign. Using this symbol in a signal list says that the rest of the signals on that chip are the same as those on the previous chip described. Quicklist is intended to be the basis of a computer aided logic design system.
Lushbaugh, W. A.↗