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This code provides fast Gaussian process prediction algorithms based on the MuyGPs scalable hyperparameter optimization algorithm. This code is the companion to a research paper preprint soon to be made publicly available.
We developed an optimization workflow based on DNN-based fast-simulation and reconstruction algorithms. We used these methods to advance the design of calorimeter systems for the Electron-Ion Collider (EIC). This DNN-driven optimization provides a blueprint for integrating gradient-based methods into detector-design workflows. All software pipelines and methods have been released publicly and incorporated into the EIC collaboration’s physics studies, broadening their impact. Three journal articles detailing the methods developed here serve as a reference for the design and optimal use of next generation high-granularity calorimeter systems in nuclear and particle physics.
Neutron and gamma irradiation is known to compact silica, resulting in macroscopic changes in refractive index (RI) and geometric structure. The change in RI and linear compaction in a radiation environment is caused by three well-known mechanisms: (i) radiation-induced attenuation (RIA), (ii) radiation-induced compaction (RIC), and (iii) radiation-induced emission (RIE). These macroscopic changes induce errors in monitoring physical parameters such as temperature, pressure, and strain in optical fiber-based sensors, which limit their application in radiation environments. We present a cascaded Fabry–Perot interferometer (FPI) technique to measure macroscopic properties, such as radiation-induced change in RI and length compaction in real time to actively account for sensor drift. The proposed cascaded FPI consists of two cavities: the first cavity is an air cavity, and the second is a silica cavity. The length compaction from the air cavity is used to deduce the RI change within the silica cavity. We utilize fast Fourier transform (FFT) algorithm and two bandpass filters for the signal extraction of each cavity. Inclusion of such a simple cascaded FPI structure will enable accurate determination of physical parameters under the test.
The n-dimensional scattering problem is solved by means of a k-space formulation of the field equations, thereby replacing the conventional integral equation formulation by a set of two algebraic equations in two unknowns in two spaces (the constitutive equation being an algebraic equation in x-space). These equations are solved by an iterative method with the aid of the fast Fourier transform (FFT) algorithm connecting the two spaces, requiring very simple initial approximations. Since algebraic and FFT equations are used, the number of arithmetic multiple-add operations and storage allocations required for a numerical solution are reduced from the order of N sq (for solving the matrix equations resulting from the conventional integral equations) to the order of N(log base 2 of N) and N, respectively (where N is the number of data points required for the specification of the problem). The advantage gained in speed and storage is thus of the order of N/log base 2 of N and N, respectively. This method is thus considerably more efficient than the conventional matrix method, and permits exact numerical solutions for much larger problems. Arguments are presented toward the view that the field equations are more fundamental in k-space. The details and some numerical results of the application of this method to the three-dimensional electromagnetic scattering problems are presented as an example.
Given the locations of several landmarks on a satellite acquired image and their true geographic coordinates, the position and orientation of the satellite can be determined. Two methods for automatically locating the image coordinates of specified landmarks are described. The first, a particularly fast sequential similarity detection algorithm for template matching was originally described by Nagel and Rosenfeld. The second method involves iteratively resampling the picture function in the vicinity of the anticipated landmark. A variety of other speedup methods is also described. An application to SMS imagery is envisioned.
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.
Fourier-like transforms over GF(F sub n), where F sub n = 2(2n) + 1 is a Fermat prime, are applied in decoding Reed-Solomon codes. It is shown that such transforms can be computed using high-radix fast Fourier transform (FFT) algorithms requiring considerably fewer multiplications than the more usual radix 2 FFT algorithm. A special 256-symbol, 16-symbol-error-correcting, Reed-Solomon (RS) code for space communication-link applications can be encoded and decoded using this high-radix FFT algorithm over GF(F sub 3).
The modeling via transfer matrices of mixed lumped-distributed parameter systems with feedback control is discussed and novel methods of obtaining information on the controlled system's dynamic response via numerical methods is presented. These methods utilize numerical searches in the complex plane for the roots of the transcendental characteristic equation to determine the closed loop system eigenvalues. The fast Fourier transform (FFT) algorithm is utilized but in the inverse fashion (from frequency domain to time domain). The information obtained is identical to that contained in a model in modal coordinates, and can be used to construct such a model. An interactive computer program to do the required calculation is described, as well as its application to a manipulator arm design problem.
Range pseudo-residuals may be improved to the level required for data validation by a measurement updating process which utilizes Bierman's adaptation of the Kalman filter measurement updating algorithms together with process noise compensation to account for model errors. This algorithm involves combining the currently available range predictions and measurements to produce an updated range residual measurement whose accuracy is constrained by the range data quality and by the estimated error in the prediction. The algorithm is compact and fast, and is thus suitable for on-line applications in network control or at the station.
It is shown that Reed-Solomon (RS) codes can be decoded by using a fast Fourier transform (FFT) algorithm over finite fields GF(F sub n), where F sub n is a Fermat prime, and continued fractions. This new transform decoding method is simpler than the standard method for RS codes. The computing time of this new decoding algorithm in software can be faster than the standard decoding method for RS codes.
A fast polynomial transform (FPT) algorithm for computing two-dimensional cyclic convolutions on a general-purpose computer is demonstrated and compared with the FFT approach. An FPT program for two-dimensional convolutions written in FORTRAN is shown to be 20% faster than the conventional FFT algorithm. This higher speed advantage makes the FPT algorithm a candidate for many two-dimensional digital image filtering applications.
An iteration technique is described which numerically evaluates the acoustic pressure and velocity on and near unbaffled, finite, thin plates vibrating in air. The technique is based on Rayleigh's integral formula and its inverse. These formulas are written in their angular spectrum form so that the fast Fourier transform (FFT) algorithm may be used to evaluate them. As an example of the technique the pressure on the surface of a vibrating, unbaffled disk is computed and shown to be in excellent agreement with the exact solution using oblate spheroidal functions. Furthermore, the computed velocity field outside the disk shows the well-known singularity at the rim of the disk. The radiated fields from unbaffled flat sources of any geometry with prescribed surface velocity may be evaluated using this technique. The use of the FFT to perform the integrations in Rayleigh's formulas provides a great savings in computation time compared with standard integration algorithms, especially when an array processor can be used to implement the FFT.
An expression for the transmitted sound field near (within a fraction of a wavelength) an array of slits is derived under the assumption that the normal component of the particle velocity is the same, in the slits, as if no grating were present and zero everywhere else in the plane of the grating. The expression is in the form of an inverse Fourier transform and can be evaluated quickly using a standard fast-Fourier-transform (FFT) algorithm. Using this technique, the sound pressure on the axis of symmetry normal to the grating was evaluated for a plane-wave incident at various angles with respect to the normal to the grating, and the results were found to provide an excellent qualitative (and to a significant degree quantitative) description of some experimental measurements. Extensions of the method to oscillating pistons of arbitrary (but planar) configuration in a rigid baffle are indicated.
An acousto-ultrasonic nondestructive testing method used to monitor damage during static and fatigue loading of thin graphite epoxy laminates is described. The experimental procedure, the signal analysis by the Fast Fourier Transform (FFT) algorithm, and the results of this analysis are discussed. Quasi-static tension tests showed a sharp decrease in the quantitative parameters when transverse cracks developed in the 90 degrees plies of a (0, 90/2/)s laminate. When internal micro-delaminations unite to form macro-delaminations, a sharp decrease in the parameters is also observed. The parameters are found to correlate well with other indications of damage development such as stiffness and degradation. The root mean square value of the moment is found to be more sensitive to damage than stiffness. Various signals and spectrums of graphite epoxy systems are presented.
A continuum algorithm based on a Segmented Upper Hull method (SUH) is described. An upper hull is performed on segments of a spectrum defined by local minima and maxima. The segments making a complete spectrum are then combined. The definition of the upper hull allows the continuum to be both concave and/or convex, adapting to the shape of the spectrum. The method performs multiple passes on a spectrum by segmenting each local maximum to minimum and performing an upper hull. The algorithm naturally adapts to the widths of absorption features, so that all features are found, including the nature of doublets, triplets, etc. The algorithm is also reasonably fast on common minicomputers so that it might be applied to the large data sets from imaging spectrometers.
A combinatorial optimization methodology is developed, which enables the efficient use of hypercube multiprocessors onboard mobile intelligent robots dedicated to time-critical missions. The methodology is implemented in terms of large-scale concurrent algorithms based either on fast simulated annealing, or on nonlinear asynchronous neural networks. In particular, analytic expressions are given for the effect of single-neuron perturbations on the systems' configuration energy. Compact neuromorphic data structures are used to model effects such as precedence constraints, processor idling times, and task-schedule overlaps. Results for a typical robot-dynamics benchmark are presented.
The forced steady response of a single degree of freedom system involving a large nonlinearity, represented by unsymmetric piecewise-linear stiffness, is determined by a harmonic balance Newton-Raphson method with the application of the fast Fourier transformation (FFT) algorithm. All possible subharmonic, harmonic, and superharmonic responses are sought. The responses of two systems involving subharmonic and superharmonic dominant motions are calculated by the newly developed method and compared with previously published findings. The results obtained by using this method reveal the details of the response of the systems more efficiently than previous methods.
A probabilistic structural analysis method (PSAM) is described which makes an approximate calculation of the structural response of a system, including the associated probabilistic distributions, with minimal computation time and cost, based on a simplified representation of the geometry, loads, and material. The method employs the fast probability integration (FPI) algorithm of Wu and Wirsching. Typical solution strategies are illustrated by formulations for a representative critical component chosen from the Space Shuttle Main Engine (SSME) as part of a major NASA-sponsored program on PSAM. Typical results are presented to demonstrate the role of the methodology in engineering design and analysis.