SEARCH · Engineering Papers
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.
Symbolic regression is the task of finding tractable mathematical expressions that best fit an input dataset. Deep symbolic regression (DSR) searches the space of tractable mathematical expressions by using a recurrent neural network that generates mathematical expressions. The network is trained using reinforcement learning.
Abstract We develop a materials informatics workflow to build an interpretable surrogate model for micromagnetic simulations. Our goal is to predict the energy barrier of a moving isolated skyrmion in rare-earth-free $$\hbox {Mn}_4$$ Mn 4 N. Our approach integrates adaptive learning with post hoc model explanation and symbolic regression methods. We discuss an unexplored acquisition function (information condensing active learning) within the adaptive learning loop and compare it with the known standard deviation function for efficient navigation of the search space. Model-agnostic post hoc explanation techniques then uncover trends learned by the trained model, which we then leverage to constrain the expressions used for symbolic regression. Graphical abstract
The Clifford group is a finite subgroup of the unitary group generated by the Hadamard, the CNOT, and the Phase gates. This group plays a prominent role in quantum error correction, randomized benchmarking protocols, and the study of entanglement. Here we consider the problem of finding a short quantum circuit implementing a given Clifford group element. Our methods aim to minimize the entangling gate count assuming all-to-all qubit connectivity. First, we consider circuit optimization based on template matching and design Clifford-specific templates that leverage the ability to factor out Pauli and SWAP gates. Second, we introduce a symbolic peephole optimization method. It works by projecting the full circuit onto a small subset of qubits and optimally recompiling the projected subcircuit via dynamic programming. CNOT gates coupling the chosen subset of qubits with the remaining qubits are expressed using symbolic Pauli gates. Software implementation of these methods finds circuits that are only 0.2% away from optimal for 6 qubits and reduces the two-qubit gate count in circuits with up to 64 qubits by 64.7% on average, compared with the Aaronson-Gottesman canonical form.
Abstract The physical characteristics and atmospheric chemical composition of newly discovered exoplanets are often inferred from their transit spectra, which are obtained from complex numerical models of radiative transfer. Alternatively, simple analytical expressions provide insightful physical intuition into the relevant atmospheric processes. The deep-learning revolution has opened the door for deriving such analytical results directly with a computer algorithm fitting to the data. As a proof of concept, we successfully demonstrate the use of symbolic regression on synthetic data for the transit radii of generic hot-Jupiter exoplanets to derive a corresponding analytical formula. As a preprocessing step, we use dimensional analysis to identify the relevant dimensionless combinations of variables and reduce the number of independent inputs, which improves the performance of the symbolic regression. The dimensional analysis also allowed us to mathematically derive and properly parameterize the most general family of degeneracies among the input atmospheric parameters that affect the characterization of an exoplanet atmosphere through transit spectroscopy.
Two computer programs - one written in FORMAC to generate the desired symbolic expressions, the other in FORTRAN 4 to numerically evaluate the expressions are announced. The FORTRAN program accepts the symbolic punched output from the FORMAC program in either unexpanded or expanded form. It numerically evaluates the expressions.
The computer program SNAP (symbolic network analysis program) generates symbolic network functions for networks containing R, L, and C type elements and all four types of controlled sources. The program is efficient with respect to program storage and execution time. A discussion of the basic algorithms is presented, together with user's and programmer's guides.
An unconventional approach is considered to a computer-aided analysis of the dynamics of large systems. The proposed approach is based on the use of symbolic computing methods that are applied directly to the system equations. Other areas of application of this symbolic method are also pointed out.
Multilevel amplitude-shift-keying (MASK) and quadrature amplitude-shift-keying (QASK) as signaling techniques for multilevel digital communications systems, and the problem of providing symbol synchronization in the receivers of such systems are discussed. A technique is presented for extracting symbol sync from an MASK or QASK signal. The scheme is a generalization of the data transition tracking loop used in PSK systems. The performance of the loop was analyzed in terms of its mean-squared jitter and its effects on the data detection process in MASK and QASK systems.
The Shuttle S-Band relay communications links via TDRS are coded and may operate at symbol signal-to-noise ratios (Es/No) as low as -5dB. A brass-board all-digital bit synchronizer with very low (0.05dB) degradation relative to an idealized analog model has been designed to process the 216 KBPS Manchester data symbols. This all-digital bit synchronizer, which provides soft decision detected outputs to a convolutional decoder, may be operated at any rate below 216 KBPS by merely changing the master clock frequency.
Results pertinent to predicting the performance of convolutionally encoded binary phase-shift keyed communication links were presented. The details of the development are provided in four sections. These sections are concerned with developing the bit error probability performance degradations due to PN despreading by a time-shared delay locked loop, the Costas demodulation process, symbol synchronization effects and cycle slipping phenomena in the Costas loop. In addition, Costas cycle slipping probabilities are studied as functions of Doppler count time and signal-to-noise conditions. The effect of cycle slipping in the symbol synchronizer is also studied as a function of channel Doppler and other frequency uncertainties.
A FORTRAN computer program for anisotropic shallow-shell finite elements with variable curvature is described. A listing of the program is presented together with printed output for a sample case. Computation times and central memory requirements are given for several different elements. The program is based on a stiffness (displacement) finite-element model in which the fundamental unknowns consist of both the displacement and the rotation components of the reference surface of the shell. Two triangular and four quadrilateral elements are implemented in the program. The triangular elements have 6 or 10 nodes, and the quadrilateral elements have 4 or 8 nodes. Two of the quadrilateral elements have internal degrees of freedom associated with displacement modes which vanish along the edges of the elements (bubble modes). The triangular elements and the remaining two quadrilateral elements do not have bubble modes. The output from the program consists of arrays corresponding to the stiffness, the geometric stiffness, the consistent mass, and the consistent load matrices for individual elements. The integrals required for the generation of these arrays are evaluated by using symbolic (or analytic) integration in conjunction with certain group-theoretic techniques. The analytic expressions for the integrals are exact and were developed using the symbolic and algebraic manipulation language.
The MACSYMA's symbolic ordinary differential equation solver ODE2 is described. The code for this routine is delineated, which is of interest because it is written in top-level MACSYMA language, and may serve as a good example of programming in that language. Other symbolic ordinary differential equation solvers are mentioned.
A MACSYMA program is described which performs symbolic vector algebra and vector calculus. The program can combine and simplify symbolic expressions including dot products and cross products, together with the gradient, divergence, curl, and Laplacian operators. The distribution of these operators over sums or products is under user control, as are various other expansions, including expansion into components in any specific orthogonal coordinate system. There is also a capability for deriving the scalar or vector potential of a vector field. Examples include derivation of the partial differential equations describing fluid flow and magnetohydrodynamics, for 12 different classic orthogonal curvilinear coordinate systems.
Minimum-shift-keying (MSK), which is a special case of continuous phase frequency-shift-keying (CPFSK) with frequency deviation ratio equal to 0.5, is known to be spectrally equivalent to a form of offset quadrature phase-shift-keying (OQPSK) in which the symbol pulse shape is a half-cycle sinusoid rather than the usual rectangular form. Appropriate shaping of the input data symbols allows one to generate an entire class of constant envelope, MSK-type signals, whose spectral properties are in some applications more desirable than those of MSK or OQPSK. The present study derives and presents a set of conditions on the input pulse shaping which in turn describes the class of envelope shapes allowable. The autocorrelation function and power spectral density of this class of signals are then derived, and specific examples are given to illustrate the desirable spectral properties. Such properties are important considerations in system design where interchannel and intersymbol interference degradations must be kept to a minimum.
The implementation and tracking performance of symbol synchronizers for Manchester coded data is presented with motivation provided by maximum a posteriori (MAP) estimation theory. Certain physically relizable closed-loop structures, readily implemented in practice, are suggested by the theory for uncoded data symbols with arbitrary data transition probabilities. The tracking performance of these loops is optimized and comparisons are made among the various configurations over a wide range of system parameters. Although not the major intent of the paper, the acquisition problem is briefly addressed.
A computer program is described that can automatically generate symbolic equations of motion for systems of hinge-connected rigid bodies with tree topologies. The dynamical formulation underlying the program is outlined, and examples are given to show how a symbolic language is used to code the formulation. The program is applied to generate the equations of motion for a four-body model of the Galileo spacecraft. The resulting equations are shown to be a factor of three faster in execution time than conventional numerical subroutines.
About 95 percent of faults detected. Programable instrument periodically checks for failures in system that generates alphanumerical and other symbol voltages for cathode-ray-tube displays. Symbol-generator tester compares gated test-point voltages with predetermined voltage limits while circuit under test performs commanded operation. A go/no-go indication given, depending on whether test voltage is or is not within its specification. Tester in plug-in modular form, temporarily wired to generator test points, or permanently wired to these points.
Methods of detection and synchronization in a highly efficient direct detection optical communication system are reported. Results of measurements on this moderate-rate demonstration system capable of transmitting 2.5 bits/detected photon in low-background situations indicate that symbol slot synchronization is not a problem, and that a simple symbol detection scheme is adequate for this situation. This system is a candidate for interplanetary optical communications.