Results for “Algorithmic Optimization” — Page 54

DOE OSTI2017

Initial CEED API (CEED-MS10)

Key components of CEED software development involve fast finite element operator storage and evaluation, architecture optimizations, performant algorithms for all orders, global kernels for finite element operators, efficient use of the memory sub-system, optimal data locality and motion, enhanced scalability and parallelism, and fast tensor contractions. As ultimate goals of the project, CEED is exploring and identifying the best algorithms for the full range of discretizations and applying algorithmic and software development to support ECP applications’ needs. In this milestone, we initiated the development and implementation of a common CEED API consisting of two main components: low-level and high-level APIs. We accomplished the goal of having the low-level component ready for the release of CEED v1.0 in the next quarter, see CEED-MS13. In this report we also provide a highlight from CEED’s integration with the MARBL app and the corresponding Laghos miniapp. A main theme in this work has been the systematic transition of advanced algorithms, developed and tested in Laghos, to the large-scale multi-physics settings of the MARBL code. The low-level CEED API provides a set of FE kernels and components for writing new low-level kernels. Examples include: vector and sparse linear algebra, element matrix assembly over a batch of elements, partial assembly and action for efficient high-order operators like mass, diffusion, advection, etc. The main goal of the low-level API is to establish the basis for the high-level API. Also, identifying such low-level kernels and providing a reference implementation for them serves as the basis for collaboration with vendors and STs. Another goal for the low-level API is to make it easy for applications with their own discretization infrastructure, who do not want to switch directly to using the high-level CEED API, to still evaluate and use the core operations provided by the low-level API. One of the challenges with high-order methods is that a global sparse matrix is no longer a good representation of a high-order linear operator, both with respect to the FLOPs needed for its evaluation, as well as the memory transfer needed for a matvec. Thus, another important question we tried to address while developing the low-level API is: is it possible to abstract out in a natural and efficient way the different implementations and data structures that arise when dealing with various computational device types: CPUs, GPUs, etc. Fully answering this question is beyond the scope of this particular milestone, since that requires longer time as we develop and expand the devices we support. The future high-level API will be the frontend provided by CEED consisting of high-level abstractions such as meshes, finite element spaces and solutions, bilinear forms, solvers, etc. At this high-level, an important aspect of the API will be to provide a uniform abstraction layer for writing code in a portable manner. To achieve that, we plan to utilize the MPI programming model combined with a device abstraction layer (DAL) for finite element computations that we will develop. The DAL will serve as the bridge between the low- and the high-level APIs, allowing a variety of programming models to be used for the low-level kernel implementations. The software artifacts delivered as part of this milestone include an initial CEED API software implementation (libCEED) provided through the CEED website, http://ceed.exascaleproject.org and the CEED GitHub organization, http://github.com/ceed. In addition to details and results from the above R&D efforts, in this document we are also reporting on other project-wide activities performed in Q1 of FY18, including: the Nek5000 v17.0 MFEM v3.3.2 and PETSc v3.8 releases, collaborations with ECP/ST and SciDAC projects, the inaugural Nek5000 hackathon and various outreach activities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Optimization on Manifolds via Graph Gaussian Processes

This paper integrates manifold learning techniques within a Gaussian process upper confidence bound algorithm to optimize an objective function on a manifold. Our approach is motivated by applications where a full representation of the manifold is not available and querying the objective is expensive. We rely on a point cloud of manifold samples to define a graph Gaussian process surrogate model for the objective. Query points are sequentially chosen using the posterior distribution of the surrogate model given all previous queries. We establish regret bounds in terms of the number of queries and the size of the point cloud. Several numerical examples complement the theory and illustrate the performance of our method.

Bayesian optimization↗

DOE OSTI2016

Sci-Fri PM: Radiation Therapy, Planning, Imaging, and Special Techniques - 01: On the use of proton radiography to reduce beam range uncertainties and improve patient positioning accuracy in proton therapy

To present two related developments of proton radiography (pRad) to minimize range uncertainty in proton therapy. The first combines a pRad with an X-ray CT to produce a patient-specific relative stopping power (RSP) map. The second aims to improve the pRad spatial resolution for accurate registration prior to the first. The enhanced-pRad can also be used in a novel proton-CT reconstruction algorithm. Monte Carlo pRad were computed from three phantoms; the Gammex, the Catphan and an anthropomorphic head. An optimized cubic-spline estimator derives the most likely path. The length crossed by the protons voxel-by-voxel was calculated by combining their estimated paths with the CT. The difference between the theoretical (length×RSP) and measured energy loss was minimized through a least squares optimization (LSO) algorithm yielding the RSP map. To increase pRad spatial resolution for registration with the CT, the phantom was discretized into voxels columns. The average column RSP was optimized to maximize the proton energy loss likelihood (MLE). Simulations showed precise RSP (<0.75%) for Gammex materials except low-density lung (<1.2%). For the head, accurate RSP were obtained (µ=−0.10%1.5σ=1.12%) and the range precision was improved (ΔR80 of −0.20±0.35%). Spatial resolution was increased in pRad (2.75 to 6.71 lp/cm) and pCT from MLE-enhanced pRad (2.83 to 5.86 lp/cm). The LSO decreases the range uncertainty (R80σ<1.0%) while the MLE-enhanced pRad spatial resolution (+244%) and is a great candidate for pCT reconstruction.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2021

Dakota A Multilevel Parallel Object-Oriented Framework for Design Optimization Parameter Estimation Uncertainty Quantification and Sensitivity Analysis (V.6.14) (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: Theory Manual (V.6.15)

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 OSTI2018

CO 2 water-alternating-gas injection for enhanced oil recovery: Optimal well controls and half-cycle lengths

We report that CO 2 water-alternating-gas (WAG) injection is an enhanced oil recovery method designed to improve sweep efficiency during CO 2 injection with the injected water to control the mobility of CO 2 and to stabilize the gas front. Optimization of CO 2 -WAG injection is widely regarded as a viable technique for controlling the CO 2 and oil miscible process. Poor recovery from CO 2 -WAG injection can be caused by inappropriately designed WAG parameters. In previous study (Chen and Reynolds, 2016), we proposed an algorithm to optimize the well controls which maximize the life-cycle net-present-value (NPV). However, the effect of injection half-cycle lengths for each injector on oil recovery or NPV has not been well investigated. In this paper, an optimization framework based on augmented Lagrangian method and the newly developed stochastic-simplex-approximate-gradient (StoSAG) algorithm is proposed to explore the possibility of simultaneous optimization of the WAG half-cycle lengths together with the well controls. Finally, the proposed framework is demonstrated with three reservoir examples.

42 ENGINEERING↗

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↗

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↗

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↗

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↗

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↗

DOE OSTI2019

Capacity assessment and co-optimization of CO 2 storage and enhanced oil recovery in residual oil zones

Residual oil zones (ROZs) are increasingly being commercially exploited using CO 2 -enhanced oil recovery (CO 2 -EOR) method. In this study, CO 2 storage potential, long-term CO 2 fate and oil recovery potential in ROZs are characterized based on a reservoir model for Goldsmith-Landreth San Andres Unit in the Permian Basin. The effects of CO 2 injection rates, well patterns (five-spot and line-drive), well spacings, injection modes (continuous CO 2 injection and water-alternatinggas injection) on the CO 2 retention in the reservoir and the oil production are investigated. After the preliminary assessment of CO 2 storage and EOR potentials in ROZs, we next develop a novel approach based on a newly developed optimization algorithm-Stochastic Simplex Approximate Gradient (StoSAG) and predictive empirical models constructed using machine learning technique to co-optimize CO 2 storage and oil recovery in ROZs. The performance of co-optimization of CO 2 storage and oil recovery is compared with the performance of optimization of only CO 2 storage.

58 GEOSCIENCES↗

DOE OSTI2021

Proof-of-concept of a reinforcement learning framework for wind farm energy capture maximization in time-varying wind

Here, we present a proof-of-concept distributed reinforcement learning framework for wind farm energy capture maximization. The algorithm we propose uses Q-Learning in a wake-delayed wind farm environment and considers time-varying, though not yet fully turbulent, wind inflow conditions. These algorithm modifications are used to create the Gradient Approximation with Reinforcement Learning and Incremental Comparison (GARLIC) framework for optimizing wind farm energy capture in time-varying conditions, which is then compared to the FLOw Redirection and Induction in Steady State (FLORIS) static lookup table wind farm controller baseline.

17 WIND ENERGY↗