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Results for “Stochastic optimization”

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.

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At least 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

Control system estimation and design for aerospace vehicles with time delay

The problems of estimation and control of discrete, linear, time-varying systems are considered. Previous solutions to these problems involved either approximate techniques, open-loop control solutions, or results which required excessive computation. The estimation problem is solved by two different methods, both of which yield the identical algorithm for determining the optimal filter. The partitioned results achieve a substantial reduction in computation time and storage requirements over the expanded solution, however. The results reduce to the Kalman filter when no delays are present in the system. The control problem is also solved by two different methods, both of which yield identical algorithms for determining the optimal control gains. The stochastic control is shown to be identical to the deterministic control, thus extending the separation principle to time delay systems. The results obtained reduce to the familiar optimal control solution when no time delays are present in the system.

Allgaier, G. R.↗
NASA NTRS1975

The effects of stability augmentation on the gust response of a STOL aircraft during a curved manual approach

The task of investigating the effect of SAS was formulated as two optimal control problems for stochastic systems: (1) to compute SAS gains with a rate model in the performance index algorithm; and (2) to calculate the pilot gains and system gust response using an optimal pilot model. Both problems were solved to yield reasonable low gains for the pilot and SAS, and the lateral directional mode poles and the longitudinal short period poles could be placed accurately by the model matching algorithm. Of the longitudinal (SAS) poles achieved, the vertical rms path error was least for the unaugmented poles. The lateral rms path error was an order of magnitude larger than the vertical error and showed a plus or minus 50 percent variation with SAS. It increased with dutch roll frequency and damping, and it decreased most significantly with increased roll stability. The variation in lateral error with bank angle for curved flight was also a significant function of the augmented poles.

Porter, M. B., Jr.↗
DOE OSTI2024

Two-Stage Estimation and Variance Modeling for Latency-Constrained Variational Quantum Algorithms

The quantum approximate optimization algorithm (QAOA) has enjoyed increasing attention in noisy, intermediate-scale quantum computing with its application to combinatorial optimization problems. QAOA has the potential to demonstrate a quantum advantage for NP-hard combinatorial optimization problems. As a hybrid quantum-classical algorithm, the classical component of QAOA resembles a simulation optimization problem in which the simulation outcomes are attainable only through a quantum computer. The simulation that derives from QAOA exhibits two unique features that can have a substantial impact on the optimization process: (i) the variance of the stochastic objective values typically decreases in proportion to the optimality gap, and (ii) querying samples from a quantum computer introduces an additional latency overhead. In this paper, we introduce a novel stochastic trust-region method derived from a derivative-free, adaptive sampling trust-region optimization method intended to efficiently solve the classical optimization problem in QAOA by explicitly taking into account the two mentioned characteristics. The key idea behind the proposed algorithm involves constructing two separate local models in each iteration: a model of the objective function and a model of the variance of the objective function. Exploiting the variance model allows us to restrict the number of communications with the quantum computer and also helps navigate the nonconvex objective landscapes typical in QAOA optimization problems. In conclusion, we numerically demonstrate the superiority of our proposed algorithm using the SimOpt library and Qiskit when we consider a metric of computational burden that explicitly accounts for communication costs.

Derivative-free Optimization↗
NASA NTRS1987

Stochastic control of infinite dimensional systems in Hilbert space: A factorization perspective

A factorization perspective on problems of optimal causal estimation and optimal causal control of linear stochastic systems defined on an infinite-dimensional Hilbert space is presented. A separation principle is derived for the case in which the system input/output map is generated by an abstract evolution operator. The factorization formalism allows for an essentially algebraic approach to these problems.

Milman, Mark M.↗
NASA NTRS1973

Solution of the stochastic control problem in unbounded domains.

Bellman's dynamic programming equation for the optimal index and control law for stochastic control problems is a parabolic or elliptic partial differential equation frequently defined in an unbounded domain. Existing methods of solution require bounded domain approximations, the application of singular perturbation techniques or Monte Carlo simulation procedures. In this paper, using the fact that Poisson impulse noise tends to a Gaussian process under certain limiting conditions, a method which achieves an arbitrarily good approximate solution to the stochastic control problem is given. The method uses the two iterative techniques of successive approximation and quasi-linearization and is inherently more efficient than existing methods of solution.

Robinson, P.↗
DOE OSTI2025

Robust A-Optimal Experimental Design for Sensor Placement in Bayesian Linear Inverse Problems

Optimal design of experiments for Bayesian inverse problems has recently gained wide popularity and attracted much attention, especially in the computational science and Bayesian inversion communities. An optimal design maximizes a predefined utility function that is formulated in terms of the elements of an inverse problem, an example being optimal sensor placement for parameter identification. The state-of-the-art algorithmic approaches following this simple formulation generally overlook misspecification of the elements of the inverse problem, such as the prior or the measurement uncertainties. This work presents an efficient algorithmic approach for designing optimal experimental design schemes for Bayesian linear inverse problems such that the optimal design is robust to misspecification of elements of the inverse problem. Specifically, we consider a worst-case scenario approach for the uncertain or misspecified parameters, formulate robust objectives, and propose an algorithmic approach for optimizing such objectives. Furthermore, both relaxation and stochastic solution approaches are discussed with detailed analysis and insight into the interpretation of the problem and the proposed algorithmic approach. Extensive numerical experiments to validate and analyze the proposed approach are carried out for sensor placement in a parameter identification problem.

Bayesian inverse problems↗
NASA NTRS2015

Random Predictor Models for Rigorous Uncertainty Quantification: Part 2

This and a companion paper propose techniques for constructing parametric mathematical models describing key features of the distribution of an output variable given input-output data. By contrast to standard models, which yield a single output value at each value of the input, Random Predictors Models (RPMs) yield a random variable at each value of the input. Optimization-based strategies for calculating RPMs having a polynomial dependency on the input and a linear dependency on the parameters are proposed. These formulations yield RPMs having various levels of fidelity in which the mean, the variance, and the range of the model's parameter, thus of the output, are prescribed. As such they encompass all RPMs conforming to these prescriptions. The RPMs are optimal in the sense that they yield the tightest predictions for which all (or, depending on the formulation, most) of the observations are less than a fixed number of standard deviations from the mean prediction. When the data satisfies mild stochastic assumptions, and the optimization problem(s) used to calculate the RPM is convex (or, when its solution coincides with the solution to an auxiliary convex problem), the model's reliability, which is the probability that a future observation would be within the predicted ranges, is bounded rigorously.

Crespo, Luis G.↗
NASA NTRS2015

Random Predictor Models for Rigorous Uncertainty Quantification: Part 1

This and a companion paper propose techniques for constructing parametric mathematical models describing key features of the distribution of an output variable given input-output data. By contrast to standard models, which yield a single output value at each value of the input, Random Predictors Models (RPMs) yield a random variable at each value of the input. Optimization-based strategies for calculating RPMs having a polynomial dependency on the input and a linear dependency on the parameters are proposed. These formulations yield RPMs having various levels of fidelity in which the mean and the variance of the model's parameters, thus of the predicted output, are prescribed. As such they encompass all RPMs conforming to these prescriptions. The RPMs are optimal in the sense that they yield the tightest predictions for which all (or, depending on the formulation, most) of the observations are less than a fixed number of standard deviations from the mean prediction. When the data satisfies mild stochastic assumptions, and the optimization problem(s) used to calculate the RPM is convex (or, when its solution coincides with the solution to an auxiliary convex problem), the model's reliability, which is the probability that a future observation would be within the predicted ranges, can be bounded tightly and rigorously.

Crespo, Luis G.↗
NASA NTRS2014

Interval Predictor Models with a Formal Characterization of Uncertainty and Reliability

This paper develops techniques for constructing empirical predictor models based on observations. By contrast to standard models, which yield a single predicted output at each value of the model's inputs, Interval Predictors Models (IPM) yield an interval into which the unobserved output is predicted to fall. The IPMs proposed prescribe the output as an interval valued function of the model's inputs, render a formal description of both the uncertainty in the model's parameters and of the spread in the predicted output. Uncertainty is prescribed as a hyper-rectangular set in the space of model's parameters. The propagation of this set through the empirical model yields a range of outputs of minimal spread containing all (or, depending on the formulation, most) of the observations. Optimization-based strategies for calculating IPMs and eliminating the effects of outliers are proposed. Outliers are identified by evaluating the extent by which they degrade the tightness of the prediction. This evaluation can be carried out while the IPM is calculated. When the data satisfies mild stochastic assumptions, and the optimization program used for calculating the IPM is convex (or, when its solution coincides with the solution to an auxiliary convex program), the model's reliability (that is, the probability that a future observation would be within the predicted range of outputs) can be bounded rigorously by a non-asymptotic formula.

Crespo, Luis G.↗
NASA NTRS1974

Optimal design of an unsupervised adaptive classifier with unknown priors

An adaptive detection scheme for M hypotheses was analyzed. It was assumed that the probability density function under each hypothesis was known, and that the prior probabilities of the M hypotheses were unknown and sequentially estimated. Each observation vector was classified using the current estimate of the prior probabilities. Using a set of nonlinear transformations, and applying stochastic approximation theory, an optimally converging adaptive detection and estimation scheme was designed. The optimality of the scheme lies in the fact that convergence to the true prior probabilities is ensured, and that the asymptotic error variance is minimum, for the class of nonlinear transformations considered. An expression for the asymptotic mean square error variance of the scheme was also obtained.

Kazakos, D.↗
DOE OSTI2025

Unraveling Adsorbate-Induced Structural Evolution of Iron Carbide Nanoparticles

Iron carbide (Fe x C y ) nanoparticles (NPs) are promising candidates for replacing platinum group metals in industrial applications, such as high-temperature Fischer–Tropsch synthesis. However, due to their amorphous nature, characterization of the active sites has been challenging experimentally and computationally. Here, using a combined density functional theory (DFT), neural network interatomic potential-assisted global optimization, and ensemble learning study, we evaluate dynamic surface changes associated with syngas (H and CO) interactions. For this purpose, we have developed a general procedure that we use to model an experimentally relevant 270-atom Fe 182 C 88 NP using the neural network-assisted stochastic surface walk global optimization algorithm (SSW-NN). Once generated, the Fe 182 C 88 NP active sites and particle morphology are thoroughly characterized before the effects of syngas adsorbate interactions are explored by using DFT and molecular dynamics simulations. Lastly, we explore correlations between geometric and electronic features of the active sites and the adsorption of H (H ads ), using a regularized random forest machine learning algorithm. In doing so, we identified the Fe–C coordination number and p orbital occupancy as the most important descriptors affecting H ads . Furthermore, using a combined ML and quantum chemistry approach, our work demonstrates a general and efficient procedure for generating and probing complex surface phenomena on binary nanoparticles.

Adsorption↗
NASA NTRS1968

Design techniques - Stochastic controllers

Analytic techniques aid in the design of nearly optimal linear time-varying sampled-data stochastic controllers. The techniques also aid in the simplification and automation of program designing for control computers.

Widnall, W. S.↗
NASA NTRS2010

Initialization and Restart in Stochastic Local Search: Computing a Most Probable Explanation in Bayesian Networks

For hard computational problems, stochastic local search has proven to be a competitive approach to finding optimal or approximately optimal problem solutions. Two key research questions for stochastic local search algorithms are: Which algorithms are effective for initialization? When should the search process be restarted? In the present work we investigate these research questions in the context of approximate computation of most probable explanations (MPEs) in Bayesian networks (BNs). We introduce a novel approach, based on the Viterbi algorithm, to explanation initialization in BNs. While the Viterbi algorithm works on sequences and trees, our approach works on BNs with arbitrary topologies. We also give a novel formalization of stochastic local search, with focus on initialization and restart, using probability theory and mixture models. Experimentally, we apply our methods to the problem of MPE computation, using a stochastic local search algorithm known as Stochastic Greedy Search. By carefully optimizing both initialization and restart, we reduce the MPE search time for application BNs by several orders of magnitude compared to using uniform at random initialization without restart. On several BNs from applications, the performance of Stochastic Greedy Search is competitive with clique tree clustering, a state-of-the-art exact algorithm used for MPE computation in BNs.

Mengshoel, Ole J.↗
NASA NTRS1972

On the adaptive control of linear systems using the open-loop-feedback-optimal approach.

This paper considers the suboptimal stochastic control of linear discrete-time dynamical systems with unknown or stochastically varying parameters. The suboptimal scheme is based upon the use of the open-loop-feedback-optimal (O.L.F.O.) method. The state and parameter estimates are generated by an extended Kalman filter algorithm. Numerical results for first order systems are presented.

Ku, R.↗
NASA NTRS1973

On the adaptive control of linear systems using the open-loop-feedback-optimal approach.

This paper considers the suboptimal stochastic control of linear discrete-time dynamical systems with uncertain or stochastically varying parameters. The suboptimal scheme is based upon the use of the open-loop-feedback-optimal (OLFO) method. The state and parameter estimates are generated by an extended Kalman filter algorithm. Numerical results for first-order systems are presented.

Ku, R.↗
DOE OSTI2024

Optimization using pathwise algorithmic derivatives of electromagnetic shower simulations

Among the well-known methods to approximate derivatives of expectancies computed by Monte-Carlo simulations, averages of pathwise derivatives are often the easiest one to apply. Computing them via algorithmic differentiation typically does not require major manual analysis and rewriting of the code, even for very complex programs like simulations of particle-detector interactions in high-energy physics. However, the pathwise derivative estimator can be biased if there are discontinuities in the program, which may diminish its value for applications. This work integrates algorithmic differentiation into the electromagnetic shower simulation code HepEmShow based on G4HepEm, allowing us to study how well pathwise derivatives approximate derivatives of energy depositions in a sampling calorimeter with respect to parameters of the beam and geometry. We found that when multiple scattering is disabled in the simulation, means of pathwise derivatives converge quickly to their expected values, and these are close to the actual derivatives of the energy deposition. Additionally, we demonstrate the applicability of this novel gradient estimator for stochastic gradient-based optimization in a model example.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗