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All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Dakota A Multilevel Parallel Object-Oriented Framework for Design Optimization Parameter Estimation Uncertainty Quantification and Sensitivity Analysis: Version 6.12 Theory Manual

The Dakota toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a theoretical manual for selected algorithms implemented within the Dakota software. It is not intended as a comprehensive theoretical treatment, since a number of existing texts cover general optimization theory, statistical analysis, and other introductory topics. Rather, this manual is intended to summarize a set of Dakota-related research publications in the areas of surrogate-based optimization, uncertainty quantification, and optimization under uncertainty that provide the foundation for many of Dakota's iterative analysis capabilities.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Dakota, A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis: Version 6.13 Theory Manual

The Dakota toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a theoretical manual for selected algorithms implemented within the Dakota software. It is not intended as a comprehensive theoretical treatment, since a number of existing texts cover general optimization theory, statistical analysis, and other introductory topics. Rather, this manual is intended to summarize a set of Dakota-related research publications in the areas of surrogate-based optimization, uncertainty quantification, and optimization under uncertainty that provide the foundation for many of Dakota's iterative analysis capabilities.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Dakota, A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis: Version 6.16 Theory Manual

The Dakota toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a theoretical manual for selected algorithms implemented within the Dakota software. It is not intended as a comprehensive theoretical treatment, since a number of existing texts cover general optimization theory, statistical analysis, and other introductory topics. Rather, this manual is intended to summarize a set of Dakota-related research publications in the areas of surrogate-based optimization, uncertainty quantification, and optimization under uncertainty that provide the foundation for many of Dakota’s iterative analysis capabilities.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Leveraging Multiple Connected Traffic Light Signals in an Energy-Efficient Speed Planner

Connecting automated vehicles to traffic lights can lead to significant energy savings by enabling them to pass through intersections in an energy-efficient way without unnecessary stops. A cellular-based communication system connecting multiple traffic lights can help realize the full potential of energy-efficient driving at intersections. Thus, we propose a hierarchical speed planner that can leverage information from multiple connected traffic lights. The proposed speed planner consists of two modules: a green window selector and a reference trajectory generator. The green window selector, based on Dijkstra’s algorithm, finds a series of "green windows" for connected traffic lights that builds an energy-optimal path for vehicles to follow. The reference trajectory generator finds optimal entering times, based on the selected green window at each intersection, and then computes reference trajectories. Deriving and using analytical optimal entering speeds as a function of entering times allows us to guarantee the computational simplicity suitable for real-time implementation. We also demonstrate how to balance energy and traffic flow perspectives in the reference trajectory generator. Lastly, a high-fidelity simulation framework is used to evaluate the proposed speed planner and quantify the extent to which it can save energy in various real-world urban route scenarios.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2023

Certifiably Correct Range-Aided SLAM

We present the first algorithm capable of efficiently computing certifiably optimal solutions to range-aided simultaneous localization and mapping (RA-SLAM) problems. Robotic navigation systems are increasingly incorporating point-to-point ranging sensors, leading state estimation which takes the form of RA-SLAM. However, the RA-SLAM problem is more difficult to solve than traditional pose-graph SLAM; ranging sensor models introduce additional non-convexity, unlike pose-pose or pose-landmark measurements, a single range measurement does not uniquely determine the relative transform between the involved sensors, and RA-SLAM inference is highly sensitive to initial estimates. Our approach relaxes the RA-SLAM problem to a semidefinite program (SDP), which we show how to solve efficiently using the Riemannian staircase methodology. The solution of this SDP provides a high-quality initialization for our original RA-SLAM problem, which is subsequently refined via local optimization, as well as a lower-bound on the RA-SLAM problem's optimal value. Our algorithm, named certifiably correct RA-SLAM (CORA), applies to problems comprised of arbitrary pose-pose, pose-landmark, and ranging measurements. Evaluation on simulated and real-world marine examples shows that our algorithm frequently produces certifiably optimal RA-SLAM solutions; moreover, even suboptimal estimates are typically within 1-2\% of the optimal value.

Papalia, Alan↗
NASA NTRS2004

Autonomous In-Situ Resources Prospector

This presentation will describe the concept of an autonomous, intelligent, rover-based rapid surveying system to identify and map several key lunar resources to optimize their ISRU (In Situ Resource Utilization) extraction potential. Prior to an extraction phase for any target resource, ground-based surveys are needed to provide confirmation of remote observation, to quantify and map their 3-D distribution, and to locate optimal extraction sites (e.g. ore bodies) with precision to maximize their economic benefit. The system will search for and quantify optimal minerals for oxygen production feedstock, water ice, and high glass-content regolith that can be used for building materials. These are targeted because of their utility and because they are, or are likely to be, variable in quantity over spatial scales accessible to a rover (i.e., few km). Oxygen has benefits for life support systems and as an oxidizer for propellants. Water is a key resource for sustainable exploration, with utility for life support, propellants, and other industrial processes. High glass-content regolith has utility as a feedstock for building materials as it readily sinters upon heating into a cohesive matrix more readily than other regolith materials or crystalline basalts. Lunar glasses are also a potential feedstock for oxygen production, as many are rich in iron and titanium oxides that are optimal for oxygen extraction. To accomplish this task, a system of sensors and decision-making algorithms for an autonomous prospecting rover is described. One set of sensors will be located in the wheel tread of the robotic search vehicle providing contact sensor data on regolith composition. Another set of instruments will be housed on the platform of the rover, including VIS-NIR imagers and spectrometers, both for far-field context and near-field characterization of the regolith in the immediate vicinity of the rover. Also included in the sensor suite are a neutron spectrometer, ground-penetrating radar, and an instrumented cone penetrometer for subsurface assessment. Output from these sensors will be evaluated autonomously in real-time by decision-making software to evaluate if any of the targeted resources has been detected, and if so, to quantify their abundance. Algorithms for optimizing the mapping strategy based on target resource abundance and distribution are also included in the autonomous software. This approach emphasizes on-the-fly survey measurements to enable efficient and rapid prospecting of large areas, which will improve the economics of ISRU system approaches. The mature technology will enable autonomous rovers to create in-situ resource maps of lunar or other planetary surfaces, which will facilitate human and robotic exploration.

Dissly, R. W.↗
DOE OSTI2020

K-Spin Hamiltonian for Quantum-Resolvable Markov Decision Processes

The Markov decision process is the mathematical formalization underlying the modern field of reinforcement learning when transition and reward functions are unknown. We derive a pseudo-Boolean cost function that is equivalent to a K-spin Hamiltonian representation of the discrete, finite, discounted Markov decision process with infinite horizon. This K-spin Hamiltonian furnishes a starting point from which to solve for an optimal policy using heuristic quantum algorithms such as adiabatic quantum annealing and the quantum approximate optimization algorithm on near-term quantum hardware. In arguing that the variational minimization of our Hamiltonian is approximately equivalent to the Bellman optimality condition for a prevalent class of environments we establish an interesting analogy with classical field theory. Along with proof-of-concept calculations to corroborate our formulation by simulated and quantum annealing against classical Q-Learning, we analyze the scaling of physical resources required to solve our Hamiltonian on quantum hardware.

Hamiltonian↗
DOE OSTI2022

Quantum algorithm for electronic band structures with local tight-binding orbitals

While the main thrust of quantum computing research in materials science is to accurately measure the classically intractable electron correlation effects due to Coulomb repulsion, designing optimal quantum algorithms for simpler problems with well-understood solutions is a useful tactic to advance our quantum “toolbox”. With this in mind, we consider the quantum calculation of a periodic system’s single-electron band structure over a path through reciprocal space. Previous efforts have used the Variational Quantum Eigensolver algorithm to solve the energy of each band, which involves numerically optimizing the parameters of a variational quantum circuit to minimize a cost function, constructed as the expectation value of a Hamiltonian operator. Traditionally, a unique Hamiltonian operator is constructed for each k-point, so that many cost functions, each with their own parameter space, must be optimized to generate a single band. Similarly, calculating higher bands than the first has traditionally involved modifying the cost function with additional overlap terms to ensure higher-energy eigenstates are orthogonal to those of lower bands. In this paper, we adopt a direct space approach, using a novel hybrid first/second-quantized qubit mapping which allows us to construct a single Hamiltonian, and a single cost-function, suitable for solving the entire electronic band structure. In contrast to previous approaches, the k-point and the band index are selected by additional parameters in our quantum circuit, rather than through modifications to the cost function. The result is a technically and conceptually simpler approach to band structure calculations on a quantum computer. Moreover, we expect that the tools developed herein will motivate new strategies for tackling highly-correlated materials beyond the grasp of classical computing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2001

Pre-Hardware Optimization of Spacecraft Image Processing Software Algorithms and Hardware Implementation

Spacecraft telemetry rates have steadily increased over the last decade presenting a problem for real-time processing by ground facilities. This paper proposes a solution to a related problem for the Geostationary Operational Environmental Spacecraft (GOES-8) image processing application. Although large super-computer facilities are the obvious heritage solution, they are very costly, making it imperative to seek a feasible alternative engineering solution at a fraction of the cost. The solution is based on a Personal Computer (PC) platform and synergy of optimized software algorithms and re-configurable computing hardware technologies, such as Field Programmable Gate Arrays (FPGA) and Digital Signal Processing (DSP). It has been shown in [1] and [2] that this configuration can provide superior inexpensive performance for a chosen application on the ground station or on-board a spacecraft. However, since this technology is still maturing, intensive pre-hardware steps are necessary to achieve the benefits of hardware implementation. This paper describes these steps for the GOES-8 application, a software project developed using Interactive Data Language (IDL) (Trademark of Research Systems, Inc.) on a Workstation/UNIX platform. The solution involves converting the application to a PC/Windows/RC platform, selected mainly by the availability of low cost, adaptable high-speed RC hardware. In order for the hybrid system to run, the IDL software was modified to account for platform differences. It was interesting to examine the gains and losses in performance on the new platform, as well as unexpected observations before implementing hardware. After substantial pre-hardware optimization steps, the necessity of hardware implementation for bottleneck code in the PC environment became evident and solvable beginning with the methodology described in [1], [2], and implementing a novel methodology for this specific application [6]. The PC-RC interface bandwidth problem for the class of applications with moderate input-output data rates but large intermediate multi-thread data streams has been addressed and mitigated. This opens a new class of satellite image processing applications for bottleneck problems solution using RC technologies. The issue of a science algorithm level of abstraction necessary for RC hardware implementation is also described. Selected Matlab functions already implemented in hardware were investigated for their direct applicability to the GOES-8 application with the intent to create a library of Matlab and IDL RC functions for ongoing work. A complete class of spacecraft image processing applications using embedded re-configurable computing technology to meet real-time requirements, including performance results and comparison with the existing system, is described in this paper.

Kizhner, Semion↗
NASA NTRS1994

Massively Parallel Algorithms for Real-Time Wavefront Control of a Dense Adaptive Optics System

In this paper massively parallel algorithms and architectures for real-time wavefront control of a dense adaptive optic system (SELENE) are presented. We have already shown that the computation of a near optimal control algorithm for SELENE can be reduced to the solution of a discrete Poisson equation on a regular domain. Although this represents an optimal computation, due the large size of the system and the high sampling rate requirement, the implementation of this control algorithm poses a computationally challenging problem since it demands a sustained computational throughput of the order of 10 GFlops. We develop a novel algorithm, designated as Fast Invariant Imbedding algorithm, which offers a massive degree of parallelism with simple communication and synchronization requirements. Due to these features, our algorithm is significantly more efficient than other Fast Poisson Solvers for implementation on massively parallel architectures.

massively↗
DOE OSTI2023

Automatic Code Generation for High-Performance Graph Algorithms

Graph problems are common across fields of scientific computing and social sciences. However, despite their importance, implementing graph algorithms effectively on modern computing systems is a challenging task that requires significant programming effort and generally results in customized implementations. Current computing and memory hierarchies are not architected for irregular computations resulting in challenges for graph algorithms to achieve high performance on those architectures. In this paper, we present GraphX, a novel compiler framework and DSL designed to simplify the development of efficient graph algorithms and achieve high performance on modern computing systems. GraphX consists of a DSL for efficient implementation of graph algorithms, various optimizations, such as support for sparse linear algebra and workspace transformations, optimized graph primitives, including semiring and masking, and a high-performance code generation engine. Using GraphX, users can implement graph algorithms using a semantically-rich language with graph-oriented operators. GraphX uses these semantics to automatically generate efficient code for target architectures, increasing performance and portability across architectures. The composable nature of GraphX makes it possible to extend the set of optimizations and architectures without modifying the source code. We demonstrate GraphX outperforms state-of-the-art graph libraries, such as LAGraph, up to $3.7 speedup in semiring operations, $2.19 speedup in an important sparse computational kernel, and $9.05 speedup in graph processing algorithms.

compiler, graph algorithms, semiring, masking, wor↗
NASA NTRS1992

A study of equation solvers for linear and non-linear finite element analysis on parallel processing computers

Concurrent computing environments provide the means to achieve very high performance for finite element analysis of systems, provided the algorithms take advantage of multiple processors. The authors have examined several algorithms for both linear and nonlinear finite element analysis. The performance of these algorithms on an Alliant FX/80 parallel supercomputer has been studied. For single load case linear analysis, the optimal solution algorithm is strongly problem dependent. For multiple load cases or nonlinear analysis through a modified Newton-Raphson method, decomposition algorithms are shown to have a decided advantage over element-by-element preconditioned conjugate gradient algorithms.

Watson, Brian C.↗
DOE OSTI2016

Performance of Canberra TruckScan Waste Assay Measurement System - 16361

After the Fukushima accident, large (approximately cubic meter) super-sacks of potentially contaminated soil and vegetation were stored at various temporary locations throughout the prefecture. Canberra has developed the TruckScan system to perform rapid and accurate assay measurements for these waste sacks loaded on trucks to determine the individual and total sack activities for Cs-137 and Cs-134. The measurement system consists of eight 3x3 inch shielded and collimated NaI(Tl) gamma-ray detectors. Data collected with the eight detectors is analyzed using a maximum entropy fitting algorithm which optimizes and predicts the mean and maximum possible activity concentration present in each of the sacks. The algorithm uses SuperISOCS to generate detection efficiencies for each detector-sack combination in the measurement, which are then used to solve for the distribution of activity concentrations in each sack that yields the best agreement with the count rates observed in each detector. Throughout the summer and fall of 2015, a prototype system was developed and tested at Canberra's Meriden CT facility. In October 2015, the prototype system was installed and demonstrated in Japan. Results of the demonstration measurements are presented along with estimates of the total measurement uncertainty (TMU) budget. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
NASA NTRS2005

Distributed Optimization

We demonstrate a new framework for analyzing and controlling distributed systems, by solving constrained optimization problems with an algorithm based on that framework. The framework is ar. information-theoretic extension of conventional full-rationality game theory to allow bounded rational agents. The associated optimization algorithm is a game in which agents control the variables of the optimization problem. They do this by jointly minimizing a Lagrangian of (the probability distribution of) their joint state. The updating of the Lagrange parameters in that Lagrangian is a form of automated annealing, one that focuses the multi-agent system on the optimal pure strategy. We present computer experiments for the k-sat constraint satisfaction problem and for unconstrained minimization of NK functions.

Macready, William↗
NASA NTRS1983

Solution algorithms for non-linear singularly perturbed optimal control problems

The applicability and usefulness of several classical and other methods for solving the two-point boundary-value problem which arises in non-linear singularly perturbed optimal control are assessed. Specific algorithms of the Picard, Newton and averaging types are formally developed for this class of problem. The computational requirements associated with each algorithm are analysed and compared with the computational requirement of the method of matched asymptotic expansions. Approximate solutions to a linear and a non-linear problem are obtained by each method and compared.

Ardema, M. D.↗
DOE OSTI2018

Fuel Efficient Speed Optimization for Real-World Highway Cruising

This paper introduces an eco-driving highway cruising algorithm based on optimal control theory that is applied to a conventionally-powered connected and automated vehicle. Thanks to connectivity to the cloud and/or to infrastructure, speed limit and slope along the future route can be known with accuracy. This can in turn be used to compute the control variable trajectory that will minimize energy consumption without significantly impacting travel time. Automated driving is necessary to the implementation of this concept, because the chosen control variables (e.g., torque and gear) impact vehicle speed. An optimal control problem is built up where quadratic models are used for the powertrain. The optimization is solved by applying Pontryagin’s minimum principle, which reduces the problem to the minimization of a cost function with parameters called co-states. The proposed algorithm assumes piecewise constant slopes and speed limits, and it solves the transition vehicle speeds for each junction of such segments. In addition, a method to extract route information from digital maps is presented, which complies with the proposed optimization algorithm. The algorithms are evaluated in simulation, using Autonomie, a simulation tool for vehicle energy consumption modeling. The optimal control trajectory (e.g., torque, gear) is first computed offline. It is then applied in an open-loop fashion in online simulation, using a forward-looking model of the vehicle in Autonomie. Simulation results show over 8% fuel saving for two selected real-world routes.

Simulation and modeling, Optimization, Vehicle net↗