Efficient Subspace Method Research Articles

New Subspace Method for Unconstrained Derivative-Free Optimization

This article defines an efficient subspace method, called SSDFO , for unconstrained derivative-free optimization problems where the gradients of the objective function are Lipschitz continuous but only exact function values are available. SSDFO employs line searches along directions constructed on the basis of quadratic models. These approximate the objective function in a subspace spanned by some previous search directions. A worst-case complexity bound on the number of iterations and function evaluations is derived for a basic algorithm using this technique. Numerical results for a practical variant with additional heuristic features show that, on the unconstrained CUTEst test problems, SSDFO has superior performance compared to the best solvers from the literature.

Uncertainty Quantification, Sensitivity Analysis, and Data Assimilation for Nuclear Systems Simulation

Reliable evaluation of nuclear data will play a major role in reduction of nuclear systems simulation uncertainties via the use of advanced sensitivity analysis (SA), uncertainty quantification (UQ), and data assimilation (DA) methodologies. This follows since nuclear data have proven to constitute a major source of neutronics uncertainties. This paper will overview the use of the Efficient Subspace Method (ESM), developed at NCSU, to overcome one of the main deficiencies of existing methodologies for SA/UQ/DA, that is the ability to handle codes with large input and output (I/O) data streams, where neither the forward nor the adjoint approach alone are appropriate. We demonstrate the functionality of ESM for an LWR core, a boiling water reactor, and a fast reactor benchmark experiment, the ZPR6/7A assembly. This work demonstrates the capability of adjusting cross section data thereby providing guidance to cross section evaluation efforts by identification of key cross sections and associated energy ranges that contribute the most to the propagated core attributes uncertainties.

Efficient Subspace Methods-Based Algorithms for Performing Sensitivity, Uncertainty, and Adaptive Simulation of Large-Scale Computational Models

This paper introduces the concepts and derives the mathematical theory of efficient subspace methods (ESMs) applied to the simulation of large-scale complex models, of which nuclear reactor simulation will serve as a test basis. ESMs are intended to advance the capabilities of predictive simulation to meet the functional requirements of future energy system simulation and overcome the inadequacies of current design methods. Some of the inadequacies addressed by ESM include lack of rigorous approach to perform comprehensive validation of the multitudes of models and input data used in the design calculations and lack of robust mathematical approaches to enhance fidelity of existing and advanced computational codes. To accomplish these tasks, the computational tools must be capable of performing the following three applications with both accuracy and efficiency: (a) sensitivity analysis of key system attributes with respect to various input data; (b) uncertainty quantification for key system attributes; and (c) adaptive simulation, also known as data assimilation, for adapting existing models based on the assimilated body of experimental information to achieve the best possible prediction accuracy. These three applications, involving large-scale computational models, are now considered computationally infeasible if both the input data and key system attributes or experimental information fields are large. This paper will develop the mathematical theory of ESM-based algorithms for these three applications. The treatment in this paper is based on linearized approximation of the associated computational models. Extension to higher-order approximations represents the focus of our ongoing research.

Source detection and tracking in 3‐D space using efficient subspace methods

This presentation will demonstrate the versatility and robustness of a MUSIC‐based subspace algorithm for acoustic source detection and tracking. The new algorithm (MUSIC3D) is designed for use with spherical arrays and performs three dimensional source detection and tracking. MUSIC3D operates on a spherical decomposition of the received array signals which results in its high efficiency. Spherical decomposition of the array signals allows for data reduction, frequency selection, and direct subspace calculations. The appeal of the MUSIC3D algorithm is that it offers a large variety of implementations which can be tailored for specific environments, signal sources or noise sources. Source tracking is accomplished through a combination of a Kalman‐based filter and the MUSIC3D algorithm.

Adaptive Core Simulation Employing Discrete Inverse Theory - Part I: Theory

Use of adaptive simulation is intended to improve the fidelity and robustness of important core attribute predictions such as core power distribution, thermal margins, and core reactivity. Adaptive simulation utilizes a selected set of past and current reactor measurements of reactor observables, i.e., in-core instrumentation readings, to adapt the simulation in a meaningful way. A meaningful adaption will result in high-fidelity and robust adapted core simulator models. To perform adaption, we propose an inverse theory approach in which the multitudes of input data to core simulators, i.e., reactor physics and thermal-hydraulic data, are to be adjusted to improve agreement with measured observables while keeping core simulator models unadapted. At first glance, devising such adaption for typical core simulators with millions of input and observables data would spawn not only several prohibitive challenges but also numerous disparaging concerns. The challenges include the computational burdens of the sensitivity-type calculations required to construct Jacobian operators for the core simulator models. Also, the computational burdens of the uncertainty-type calculations required to estimate the uncertainty information of core simulator input data present a demanding challenge. The concerns however are mainly related to the reliability of the adjusted input data. The methodologies of adaptive simulation are well established in the literature of data adjustment. We adopt the same general framework for data adjustment; however, we refrain from solving the fundamental adjustment equations in a conventional manner. We demonstrate the use of our so-called Efficient Subspace Methods (ESMs) to overcome the computational and storage burdens associated with the core adaption problem. We illustrate the successful use of ESM-based adaptive techniques for a typical boiling water reactor core simulator adaption problem.