Minimum mean square error approximation of unknown probability distribution functions.
Double stochastic approximation algorithm for minimizing mean square error in finite expansion of unknown probability distribution functions
Deuser, L. M.↗
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Discrete-time demodulation of continuous-time signals.
Nonlinear stochastic estimation theory is applied to the problem of obtaining discrete-time demodulator structures for the common types of analog communication signals. A stochastic communication model is presented that can be treated with current results in estimation theory. Approximate algorithms are developed for the estimation problem that yield mathematically realizable receiver structures for the cases of AM, PC, and FM. The digital receivers yield performance characteristics that compare favorably with those of their analog counterparts.
Kelly, C. N.↗
Multidimensional stochastic approximation using locally contractive functions
A Robbins-Monro type multidimensional stochastic approximation algorithm which converges in mean square and with probability one to the fixed point of a locally contractive regression function is developed. The algorithm is applied to obtain maximum likelihood estimates of the parameters for a mixture of multivariate normal distributions.
Lawton, W. M.↗
Advanced 3-D viscous SSME turbine rotor stator CFD algorithms
Current Space Shuttle Main Engine (SSME) high pressure fuel turbopump problems have generated a desire to analyze the flow field of rotating machinery. The status of Computational Fluid Dynamics (CFD) has reached the point that soon the capability to solve unsteady three-dimensional viscous flow fields will be at hand. The work presented involves upgrading the computational efficiency of an operational three-dimensional algorithm. The modifications include algorithm development, algorithm approximation and acceleration, and special coding optimizations. The overall result of these modifications has reduced processing time by nearly 80%.
Janus, J. Mark↗
Structural tailoring of advanced turboprops
A computer program has been developed for the performance of numerical optimizations of highly swept propfan blades by minimizing an objective function that is defined either as direct operating cost or the aeroelastic difference between a blade and its scaled model. Three component analysis categories are employed: an optimization algorithm, approximate analysis procedures for objective function and constraint evaluation, and refined analysis procedures for optimum design validation. The analyses conducted by the program encompass aerodynamic efficiency evaluation, finite element stress and vibration analysis, acoustics, flutter, and forced response life prediction.
Brown, K. W.↗
Remote noncontacting measurements of heat transfer coefficients for detection of boundary layer transition in wind tunnel tests
An infrared measurement system is used that consists of a laser heating source, an infrared camera for data acquisition, and a video recorder for data storage. A laser beam is scanned over an airfoil, heating its surface to a few degrees above ambient. An infrared camera then measures the temperature of the airfoil over a two-dimensional field, and these temperatures are stored as a function of time on a video recorder. The resulting temperature pictures are digitized and an iterative approximation algorithm is used to extract the heat transfer coefficient. The resulting values are normalized to the natural convection condition. The technique has been applied in low-speed wind tunnel tests and compared to well-established hot-film measurements which were made simultaneously to confirm the flow conditions. Heat transfer coefficients were determined using a linear scanning pattern, to indicate the position of natural and of artificially induced transition on an airfoil, at various wind speeds. The technique is shown to be sensitive to transition at low Mach numbers. The advantages of the technique are discussed.
Heath, D. Michele↗
Autoclass: An automatic classification system
The task of inferring a set of classes and class descriptions most likely to explain a given data set can be placed on a firm theoretical foundation using Bayesian statistics. Within this framework, and using various mathematical and algorithmic approximations, the AutoClass System searches for the most probable classifications, automatically choosing the number of classes and complexity of class descriptions. A simpler version of AutoClass has been applied to many large real data sets, has discovered new independently-verified phenomena, and has been released as a robust software package. Recent extensions allow attributes to be selectively correlated within particular classes, and allow classes to inherit, or share, model parameters through a class hierarchy. The mathematical foundations of AutoClass are summarized.
Stutz, John↗
Bayesian classification theory
The task of inferring a set of classes and class descriptions most likely to explain a given data set can be placed on a firm theoretical foundation using Bayesian statistics. Within this framework and using various mathematical and algorithmic approximations, the AutoClass system searches for the most probable classifications, automatically choosing the number of classes and complexity of class descriptions. A simpler version of AutoClass has been applied to many large real data sets, has discovered new independently-verified phenomena, and has been released as a robust software package. Recent extensions allow attributes to be selectively correlated within particular classes, and allow classes to inherit or share model parameters though a class hierarchy. We summarize the mathematical foundations of AutoClass.
Hanson, Robin↗
AutoBayes Program Synthesis System Users Manual
Program synthesis is the systematic, automatic construction of efficient executable code from high-level declarative specifications. AutoBayes is a fully automatic program synthesis system for the statistical data analysis domain; in particular, it solves parameter estimation problems. It has seen many successful applications at NASA and is currently being used, for example, to analyze simulation results for Orion. The input to AutoBayes is a concise description of a data analysis problem composed of a parameterized statistical model and a goal that is a probability term involving parameters and input data. The output is optimized and fully documented C/C++ code computing the values for those parameters that maximize the probability term. AutoBayes can solve many subproblems symbolically rather than having to rely on numeric approximation algorithms, thus yielding effective, efficient, and compact code. Statistical analysis is faster and more reliable, because effort can be focused on model development and validation rather than manual development of solution algorithms and code.
Schumann, Johann↗
Data transmission system and method
A method of transmitting data packets, where randomness is added to the schedule. Universal broadcast schedules using encoding and randomization techniques are also discussed, together with optimal randomized schedules and an approximation algorithm for finding near-optimal schedules.
Bruck, Jehoshua↗
Exact and Approximate Probabilistic Symbolic Execution
Probabilistic software analysis seeks to quantify the likelihood of reaching a target event under uncertain environments. Recent approaches compute probabilities of execution paths using symbolic execution, but do not support nondeterminism. Nondeterminism arises naturally when no suitable probabilistic model can capture a program behavior, e.g., for multithreading or distributed systems. In this work, we propose a technique, based on symbolic execution, to synthesize schedulers that resolve nondeterminism to maximize the probability of reaching a target event. To scale to large systems, we also introduce approximate algorithms to search for good schedulers, speeding up established random sampling and reinforcement learning results through the quantification of path probabilities based on symbolic execution. We implemented the techniques in Symbolic PathFinder and evaluated them on nondeterministic Java programs. We show that our algorithms significantly improve upon a state-of- the-art statistical model checking algorithm, originally developed for Markov Decision Processes.
Symbolic Execution↗
An improved digital algorithm for fast amplitude approximations of quadrature pairs
A computationally fast algorithm for approximating the amplitude (A) of a quadrature pair (I,Q) has been discovered. The piecewise linear formula, the unbiased estimate of A=X+1/8y when X or = 3Y and 7/8X + 1/2Y when X or = 3Y applies where X is congruent to the maximum absolute value of (I,Q) and Y is congruent to the minimum absolute value of (I,Q). This algorithm has been proven to be far more accurate then currently used approximations. An immediate application is the wideband digital spectrum analyzer under development for monitoring radio frequency interference at Deep Space Network stations.
Levitt, B. K.↗
Application of the Approximate Bayesian Computation Algorithm to Gamma-Ray Spectroscopy
Radioisotope identification (RIID) algorithms for gamma-ray spectroscopy aim to infer what isotopes are present and in what amounts in test items. RIID algorithms either use all energy channels in the analysis region or only energy channels in and near identified peaks. Because many RIID algorithms rely on locating peaks and estimating each peak’s net area, peak location and peak area estimation algorithms continue to be developed for gamma-ray spectroscopy. This paper shows that approximate Bayesian computation (ABC) can be effective for peak location and area estimation. Algorithms to locate peaks can be applied to raw or smoothed data, and among several smoothing options, the iterative bias reduction algorithm (IBR) is recommended; the use of IBR with ABC is shown to potentially reduce uncertainty in peak location estimation. Extracted peak locations and areas can then be used as summary statistics in a new ABC-based RIID. ABC allows for easy experimentation with candidate summary statistics such as goodness-of-fit scores and peak areas that are extracted from relatively high dimensional gamma spectra with photopeaks (1024 or more energy channels) consisting of count rates versus energy for a large number of gamma energies.
Burr, Tom↗
Evaluating the Limits of QAOA Parameter Transfer at High-Rounds on Sparse Ising Models With Geometrically Local Cubic Terms
The emergent practical applicability of the Quantum Approximate Optimization Algorithm (QAOA) for approximate combinatorial optimization is a subject of considerable interest. One of the primary limitations of QAOA is the task of finding a set of good parameters, which is usually done using a variational optimization loop. Parameter transfer, or parameter concentration, is a phenomenon where QAOA angles trained on problem instances that are self-similar tend to perform well for other problem instances from that similar class. This suggests a potentially highly efficient and scalable non-variational learning method for QAOA angle finding. In this work, we systematically study QAOA parameter transferability from small problem sizes (16 and 27 decision variables) onto large problem instances (up to 156 qubits) for heavy-hex graph Ising models with geometrically local higher order terms using the Julia based QAOA simulation tool \texttt{JuliQAOA} to perform classical angle finding for up to $49$ QAOA layers ($p$). Parameter transfer of the fixed angles is validated using a combination of full statevector, Projected Entangled Pair States (PEPS), Matrix Product State (MPS), and LOWESA numerical simulations. We find that the QAOA parameter transfer from single instances applied to other (unseen) problem instances does not in general provide monotonically improving performance as a function of $p$ - there are many cases where the performance temporarily decreases as a function of $p$ - but despite this the transferred angles have a general trend of improved expectation value as the QAOA depth increases, in many cases converging close to the true ground-state energy of the $100+$ qubit instances. We also sample the hardware-compatible Ising models using the ensemble of transfer-learned QAOA parameters on several superconducting qubit IBM Quantum processors with 127, 133, and 156 qubits. We find continuous solution quality improvement of the hardware-compatible QAOA circuits run on the IBM NISQ processors up to $p=5$ on \texttt{ibm\_fez}, up to $p=9$ on \texttt{ibm\_torino}, and up to $p=10$ on \texttt{ibm\_pittsburgh}.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Optimal Power Dispatch of DGs in Radial and Mesh AC Grids: A Hybrid Solution Methodology between the Salps Swarm Algorithm and Successive Approximation Power Flow Method
In this paper, we address the problem of the optimal power dispatch of Distributed Generators (DGs) in Alternating Current (AC) networks, better known as the Optimal Power Flow (OPF) problem. We used, as the objective function, the minimization of power losses (P loss ) associated with energy transport, which are subject to the set of constraints that compose AC networks in an environment of distributed generation. To validate the effectiveness of the proposed methodology in solving the OPF problem in any network topology, we employed one 10-node mesh test system and three radial text systems: 10, 33, and 69 nodes. In each test system, DGs were allowed to inject 20%, 40%, and 60% of the power supplied by the slack generator in the base case. To solve the OPF problem, we used a master–slave methodology that integrates the optimization method Salps Swarm Algorithm (SSA) and the load flow technique based on the Successive Approximation (SA) method. Moreover, for comparison purposes, we employed some of the algorithms reported in the specialized literature to solve the OPF problem (the continuous genetic algorithm, the particle swarm optimization algorithm, the black hole algorithm, the antlion optimization algorithm, and the Multi-Verse Optimizer algorithm), which were selected because of their excellent results in solving such problems. The results obtained by the proposed solution methodology demonstrate its superiority and convergence capacity in terms of minimization of P loss in both radial and mesh systems. It provided the best reduction in minimum P loss in short processing times and showed excellent repeatability in each test system and scenario under analysis.
32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
Approximate Latent Factor Algorithm for Scenario Selection and Weighting in Transmission Expansion Planning
One major difficulty in transmission expansion planning is selecting the representative scenarios to use to evaluate candidate transmission networks. The variability in demand and renewable generation makes the inclusion of several scenarios critical when calculating reliability and cost, but including too many scenarios in an optimization is computationally intractable. To reduce the number of representative operating conditions needed to obtain an accurate approximation of the system, we propose a method rooted in multivariate statistics that exploits the latent correlative structure between different scenarios and network configurations. The proposed algorithm includes an objective and rigorous way to select a subset of scenarios that provide as much information about the system as possible, and a method to accurately approximate the system cost from that scenario subset. The result is a set of scenarios and weights that are easily incorporated into traditional transmission expansion planning formulations. We apply this to a 312-bus WECC model with 8,736 distinct operating conditions. The transmission plans found with the proposed method are more reliable and have a lower total cost than those from other scenario reduction techniques, as well as a smaller error between the expected system performance from the optimization objective and the actual system performance.
42 ENGINEERING↗
Quantum computational phase transition in combinatorial problems
Quantum Approximate Optimization algorithm (QAOA) aims to search for approximate solutions to discrete optimization problems with near-term quantum computers. As there are no algorithmic guarantee possible for QAOA to outperform classical computers, without a proof that bounded-error quantum polynomial time (BQP) ≠ nondeterministic polynomial time (NP), it is necessary to investigate the empirical advantages of QAOA. We identify a computational phase transition of QAOA when solving hard problems such as SAT—random instances are most difficult to train at a critical problem density. We connect the transition to the controllability and the complexity of QAOA circuits. Moreover, we find that the critical problem density in general deviates from the SAT-UNSAT phase transition, where the hardest instances for classical algorithms lies. Then, we show that the high problem density region, which limits QAOA’s performance in hard optimization problems (reachability deficits), is actually a good place to utilize QAOA: its approximation ratio has a much slower decay with the problem density, compared to classical approximate algorithms. Indeed, it is exactly in this region that quantum advantages of QAOA over classical approximate algorithms can be identified.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
On improving the iterative convergence properties of an implicit approximate-factorization finite difference algorithm
The iterative convergence properties of an approximate-factorization implicit finite-difference algorithm are analyzed both theoretically and numerically. Modifications to the base algorithm were made to remove the inconsistency in the original implementation of artificial dissipation. In this way, the steady-state solution became independent of the time-step, and much larger time-steps can be used stably. To accelerate the iterative convergence, large time-steps and a cyclic sequence of time-steps were used. For a model transonic flow problem governed by the Euler equations, convergence was achieved with 10 times fewer time-steps using the modified differencing scheme. A particular form of instability due to variable coefficients is also analyzed.
Desideri, J. A.↗