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At least 469 records · Page 26

Optimization Methods for Large-Scale Machine Learning

Here this paper provides a review and commentary on the past, present, and future of numerical optimization algorithms in the context of machine learning applications. Through case studies on text classification and the training of deep neural networks, we discuss how optimization problems arise in machine learning and what makes them challenging. A major theme of our study is that large-scale machine learning represents a distinctive setting in which the stochastic gradient (SG) method has traditionally played a central role while conventional gradient-based nonlinear optimization techniques typically falter. Based on this viewpoint, we present a comprehensive theory of a straightforward, yet versatile SG algorithm, discuss its practical behavior, and highlight opportunities for designing algorithms with improved performance. This leads to a discussion about the next generation of optimization methods for large-scale machine learning, including an investigation of two main streams of research on techniques that diminish noise in the stochastic directions and methods that make use of second-order derivative approximations.

97 MATHEMATICS AND COMPUTING↗

Topology-aware task-assIGnment mappER (TIGER) v0.1

The general topology-aware task assignment problem is an NP-complete graph isomorphism problem. Existing task scheduling approaches are either heuristic or based on physical optimization algorithms, providing different speed and solution quality trade-offs. Physical Ising machines such as quantum and digital annealers have recently become available offering an alternative hardware solution to solve certain types of optimization problems. We propose an algorithm that allows expressing the problem in the compatible format. We present a domain specific partition strategy that enables to execute larger scale problems. TIGER - topology-aware task assignment mapper tool - implements the proposed algorithm and automatically integrates task- communication graph and an architecture graph into the quantum software environment.

Donofrio, David↗

An Efficient Numerical Algorithm for Solving Data Driven Feedback Control Problems

The goal of this paper is to solve a class of stochastic optimal control problems numerically, in which the state process is governed by an Itô type stochastic differential equation with control process entering both in the drift and the diffusion, and is observed partially. The optimal control of feedback form is determined based on the available observational data. In this work, we call this type of control problems the data driven feedback control. The computational framework that we introduce to solve such type of problems aims to find the best estimate for the optimal control as a conditional expectation given the observational information. To make our method feasible in providing timely feedback to the controlled system from data, we develop an efficient stochastic optimization algorithm to implement our computational framework.

97 MATHEMATICS AND COMPUTING↗

Dynamically Learning Incentives for Load Control

As electrical generation becomes more distributed and volatile, and loads become more uncertain, controllability of distributed energy resources (DERs), regardless of their ownership status, will be necessary for grid reliability. Grid operators lack direct control over end-users' grid interactions, such as energy usage, but incentives can influence behavior -- for example, an end-user that receives a grid-driven incentive may adjust their consumption or expose relevant control variables in response. A key challenge in studying such incentives is the lack of data about human behavior, which usually motivates strong assumptions, such as distributional assumptions on compliance or rational utility-maximization. In this paper, we propose a general incentive mechanism in the form of a constrained optimization problem -- our approach is distinguished from prior work by modeling human behavior (e.g., reactions to an incentive) as an arbitrary unknown function. We propose feedback-based optimization algorithms to solve this problem that each leverage different amounts of information and/or measurements. We show that each converges to an asymptotically stable incentive with (near)-optimality guarantees given mild assumptions on the problem. Finally, we evaluate our proposed techniques in voltage regulation simulations on standard test beds. We test a variety of settings, including those that break assumptions required for theoretical convergence (e.g., convexity, smoothness) to capture realistic settings. In this evaluation, our proposed algorithms are able to find near-optimal incentives even when the reaction to an incentive is modeled by a theoretically difficult (yet realistic) function.

demand response↗

A matrix-free cone complementarity approach for solving large-scale nonsmooth, rigid body dynamics.

This paper proposes an iterative method that can simulate mechanical systems featuring a large number of contacts and joints between rigid bodies. The numerical method behaves as a contractive mapping that converges to the solution of a cone complementarity problem by means of iterated fixed-point steps with separable projections onto convex manifolds. Since computational speed and robustness are important issues when dealing with a large number of frictional contacts, we have performed special algorithmic optimizations in order to translate the numerical scheme into a matrix-free algorithm with O(n) space complexity and easy implementation. A modified version, that can run on parallel computers is discussed. A multithreaded version of the method has been used to simulate systems with more than a million contacts with friction.

99 GENERAL AND MISCELLANEOUS↗

Performance Portability of Molecular Docking Miniapp On Leadership Computing Platforms

Rapidly changing computer architectures, such as those found at high-performance computing (HPC) facilities, present the need for mini-applications (miniapps) that capture essential algorithms used in large applications to test program performance and portability, aiding transitions to new systems. The COVID-19 pandemic has fueled a flurry of activity in computational drug discovery, including the use of supercomputers and GPU acceleration for massive virtual screens for therapeutics. Recent work targeting COVID-19 at the Oak Ridge Leadership Computing Facility (OLCF) used the GPU-accelerated program AutoDock-GPU to screen billions of compounds on the Summit supercomputer. In this paper we present the development of a new miniapp, miniAutoDock-GPU, that can be used to evaluate the performance and portability of GPU-accelerated protein-ligand docking programs on different computer architectures. These tests are especially relevant as facilities transition from petascale systems and prepare for upcoming exascale systems that will use a variety of GPU vendors. The key calculations, namely, the Lamarckian genetic algorithm combined with a local search using a Solis-Wets based random optimization algorithm, are implemented. We developed versions of the miniapp using several different programming models for GPU acceleration, including a version using the CUDA runtime API for NVIDIA GPUs, and the Kokkos middle-ware API which is facilitated by C++ template libraries. A third version, currently in progress, uses the HIP programming model. These efforts will help facilitate the transition to exascale systems for this important emerging HPC application, as well as its use on a wide range of heterogeneous platforms.

Thavappiragasam, Mathialakan↗

Spherical Region Queries on Multicore Architectures

In this short paper, we report the performance of multiple thread-parallel algorithms for spherical region queries on multicore architectures motivated by a challenging data analytics application in materials science. Performances of two tree-based algorithms and a naive algorithm are compared to identify the length scales at which these approaches perform optimally. The optimal algorithm is then used to scale the driving materials science application, which is shown to deliver over 17X speedup using 32 OpenMP threads on data sets containing many millions of atoms.

Lu, Hao↗

VULCON: A System for Vulnerability Prioritization, Mitigation, and Management

Vulnerability remediation is a critical task in operational software and network security management. In this paper, an effective vulnerability management strategy, called VULCON (VULnerability CONtrol), is developed and evaluated. The strategy is based on two fundamental performance metrics: i). Time-to-Vulnerability Remediation (TVR) and; ii). Total Vulnerability Exposure (TVE). VULCON takes as input real vulnerability scan reports, metadata about the discovered vulnerabilities, asset criticality, and personnel resources. VULCON uses a mixed integer multi-objective optimization algorithm to prioritize vulnerabilities for patching, such that the above performance metrics are optimized subject to the given resource constraints. VULCON has been tested on multiple months of real scan data from a Cyber-Security Operations Center (CSOC). Results indicate an overall Total Vulnerability Exposure reduction of 8.97\% when VULCON optimizes a realistic security analyst workforce's effort. Additionally, it is demonstrated that VULCON can determine monthly resources required to maintain a target TVE score. As such, VULCON provides valuable operational guidance for improving vulnerability response processes in CSOCs.

Farris, Katheryn A.↗

Surrogate Optimization of Computationally Expensive Black-Box Problems with Hidden Constraints (SHEBO) v1.0

SHEBO (surrogate optimization of problems with hidden constraints and expensive black-box objectives) is an efficient optimization algorithm that employs surrogate models to solve computationally expensive black-box simulation optimization problems that have hidden constraints. Hidden constraints are encountered when the objective function evaluation does not return a value for a parameter vector. These constraints are often encountered in optimization problems in which the objective function is computed by a black-box simulation code. SHEBO uses a combination of local and global search strategies together with an evaluability prediction function and a dynamically adjusted evaluability threshold to iteratively select new sample points.

Mueller, Juliane↗

LDRD Report: Topological Design Optimization of Convolutes in Next Generation Pulsed Power Devices.

This LDRD project was developed around the ambitious goal of applying PDE-constrained opti- mization approaches to design Z-machine components whose performance is governed by elec- tromagnetic and plasma models. This report documents the results of this LDRD project. Our differentiating approach was to use topology optimization methods developed for structural design and extend them for application to electromagnetic systems pertinent to the Z-machine. To achieve this objective a suite of optimization algorithms were implemented in the ROL library part of the Trilinos framework. These methods were applied to standalone demonstration problems and the Drekar multi-physics research application. Out of this exploration a new augmented Lagrangian approach to structural design problems was developed. We demonstrate that this approach has favorable mesh-independent performance. Both the final design and the algorithmic performance were independent of the size of the mesh. In addition, topology optimization formulations for the design of conducting networks were developed and demonstrated. Of note, this formulation was used to develop a design for the inner magnetically insulated transmission line on the Z-machine. The resulting electromagnetic device is compared with theoretically postulated designs.

42 ENGINEERING↗

A Survey of Distributed Optimization and Control Algorithms for Electric Power Systems

Historically, centrally computed algorithms have been the primary means of power system optimization and control. With increasing penetrations of distributed energy resources requiring optimization and control of power systems with many controllable devices, distributed algorithms have been the subject of significant research interest. Here, this paper surveys the literature of distributed algorithms with applications to optimization and control of power systems. In particular, this paper reviews distributed algorithms for offline solution of optimal power flow (OPF) problems as well as online algorithms for real-time solution of OPF, optimal frequency control, optimal voltage control, and optimal wide-area control problems.

24 POWER TRANSMISSION AND DISTRIBUTION↗

AI-Batt (Autonomous Identification of Battery Life Models) [SWR 21-36]

Autonomous Identification of Battery Life Models (AI-Batt) AI-Batt is a MATLAB code base for developing lifetime models for batteries from accelerated aging data. The code base provides many functions for processing, visualizing, and modeling battery aging data, making the data processing, exploration, and modeling workflow substantially faster. These tools are tailored for working with battery aging data sets, which usually consist of many separate time-series for each cell, with many test conditions and possible replicates at each condition, which makes it difficult to simply process or visualize the data set. Complex modeling tasks, such as cross-validation, sensitivity analysis, and uncertainty quantification have been implemented to enable thorough statistical investigation of model predictions. Additionally, several machine-learning algorithms are implemented to autonomously identify suitable models via symbolic regression. Data processing functions automatically cast data from the struct data type, which is commonly used to store experimental data, but is not an acceptable input for most algorithms, to the table data type, which can be easily used as input to any optimization algorithm. Also, the data can be separated into time-invariant and time-variant data tables, which is helpful for exploring the data set as well as developing separate models for time-variant and time-invariant aging mechanisms. For example, in aging tests with constant temperature, temperature is a time-invariant experimental condition. Visualization tools enable plotting of data, model fits, and model simulations possible with single-line function calls, empowering data exploration of complex data sets with both time-varying and time-invariant trends. Plots can be automatically generated for the whole data set, or separated by data group (groups of test replicates) or individual data series. Data points or data series can be automatically colored by the value of a variable with a variety of color maps, and model predictions can also be colored by the value of a fit statistic. Comparisons between data sets and the predictions/simulations of different models on the same data set can be easily plotted as well. Distributions of parameter values from bootstrap resampling can be plotted to visualize the reliability of parameter estimation, or determine any correlations between parameters. Modeling tools handle the complex task of creating and parsing symbolic equations for modeling battery lifetime. Equations are parsed to grab relevant data variables, parameter values, or specified sub-models for input into optimization, evaluation, or simulation functions. Models can be optimized locally (one set of parameters for each data series), bi-level (some parameters shared across the data set), or globally (single set of parameters for all data). Functions implementing symbolic regression algorithms help users to discover effective model equations, even in poorly sampled, high-dimensional data.

Smith, Kandler↗

Magnetostatic focal spot correction for x-ray tubes operating in strong magnetic fields using iterative optimization

Purpose: Combining x-ray fluoroscopy and MR imaging systems for guidance of interventional procedures has become more commonplace. By designing an x-ray tube that is immune to the magnetic fields outside of the MR bore, the two systems can be placed in close proximity to each other. A major obstacle to robust x-ray tube design is correcting for the effects of the magnetic fields on the x-ray tube focal spot. A potential solution is to design active shielding that locally cancels the magnetic fields near the focal spot. Methods: An iterative optimization algorithm is implemented to design resistive active shielding coils that will be placed outside the x-ray tube insert. The optimization procedure attempts to minimize the power consumption of the shielding coils while satisfying magnetic field homogeneity constraints. The algorithm is composed of a linear programming step and a nonlinear programming step that are interleaved with each other. The coil results are verified using a finite element space charge simulation of the electron beam inside the x-ray tube. To alleviate heating concerns an optimized coil solution is derived that includes a neodymium permanent magnet. Any demagnetization of the permanent magnet is calculated prior to solving for the optimized coils. The temperature dynamics of the coil solutions are calculated using a lumped parameter model, which is used to estimate operation times of the coils before temperature failure. Results: For a magnetic field strength of 88 mT, the algorithm solves for coils that consume 588 A/cm{sup 2}. This specific coil geometry can operate for 15 min continuously before reaching temperature failure. By including a neodymium magnet in the design the current density drops to 337 A/cm{sup 2}, which increases the operation time to 59 min. Space charge simulations verify that the coil designs are effective, but for oblique x-ray tube geometries there is still distortion of the focal spot shape along with deflections of approximately 3 mm in the radial and circumferential directions on the anode. Conclusions: Active shielding is an attractive solution for correcting the effects of magnetic fields on the x-ray focal spot. If extremely long fluoroscopic exposure times are required, longer operation times can be achieved by including a permanent magnet with the active shielding design.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Define baseline levels of segments per beam for intensity-modulated radiation therapy delivery for brain, head and neck, thoracic, abdominal, and prostate applications

The purpose of this study was to evaluate the number of segments per beam for intensity-modulated radiation therapy (IMRT) treatments and its effects on the plan quality, treatment delivery time, machine quality assurance, and machine maintenance. We have retrospectively analyzed 24 patients treated with IMRT. Five were selected within each of the following regions: head and neck, thoracic, abdomen, and prostate. Four patients were optimized within the brain region. The clinically treated plans were re-optimized using Philips Pinnacle3 v. 8 with the direct machine parameter optimization algorithm. The number of segments per beam from the treated plan was systematically reduced by 80%, 60%, 40%, and 30%, and the following statistics have been analyzed for plan quality: target min, mean, and max doses; critical structure doses; and integral dose. We have attempted to define the smallest number of segments per beam for IMRT treatment plans. Results indicate that IMRT plans can be delivered with acceptable quality with approximately 3-6 segments per beam for the anatomical regions analyzed. A reduction in the number of segments decreases treatment delivery time, reduces machine wear and tear, and minimizes the amount of time the patient is on the treatment table, which in turn reduces the chances of intrafractional uncertainties.

61 RADIATION PROTECTION AND DOSIMETRY↗

Numerical optimization of a low emittance lattice cell

In the lattice designs for the next generation storage ring light sources, longitudinal gradient bending magnets and anti-bending magnets have been adopted. A logical question raised by the trend of varying the longitudinal distribution of dipole strength is: what are the optimal distributions of the dipole and quadrupole fields in a lattice cell for the purpose of minimizing the natural emittance? We studied this problem by numerically optimizing the dipole and quadrupole distributions of the normalized cell optics using the particle swarm optimization algorithm. Furthermore the results reveal the features of the longitudinal field variation of the optimized cell and show that when the quadrupole gradient is increased enough, the cell tends to split into two identical cells with similar features.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Observation Targeting for the Tehachapi Pass and Mid-Columbia Basin: WindSENSE Phase III Project Summary Report

The overall goal of this multi-phased research project known as WindSENSE is to develop an observation system deployment strategy that would improve wind power generation forecasts. The objective of the deployment strategy is to produce the maximum benefit for 1- to 6-hour ahead forecasts of wind speed at hub-height (~80 m). In Phase III of the project, the focus was on the Mid-Columbia Basin region which encompasses the Bonneville Power Administration (BPA) wind generation area shown in Figure 1 that includes Klondike, Stateline, and Hopkins Ridge wind plants. The typical hub height of a wind turbine is approximately 80-m above ground level (AGL). So it would seem that building meteorological towers in the region upwind of a wind generation facility would provide data necessary to improve the short-term forecasts for the 80-m AGL wind speed. However, this additional meteorological information typically does not significantly improve the accuracy of the 0- to 6-hour ahead wind power forecasts because processes controlling wind variability change from day-to-day and, at times, from hour-to-hour. It is also important to note that some processes causing significant changes in wind power production function principally in the vertical direction. These processes will not be detected by meteorological towers at off-site locations. For these reasons, it is quite challenging to determine the best type of sensors and deployment locations. To address the measurement deployment problem, Ensemble Sensitivity Analysis (ESA) was applied in the Phase I portion of the WindSENSE project. The ESA approach was initially designed to produce spatial fields that depict the sensitivity of a forecast metric to a set of prior state variables selected by the user. The best combination of variables and locations to improve the forecast was determined using the Multiple Observation Optimization Algorithm (MOOA) developed in Phase I. In Zack et al. (2010a), the ESA-MOOA approach was applied and evaluated for the wind plants in the Tehachapi Pass region for a period during the warm season. That research demonstrated that forecast sensitivity derived from the dataset was characterized by well-defined, localized patterns for a number of state variables such as the 80-m wind and the 25-m to 1-km temperature difference prior to the forecast time. The sensitivity patterns produced as part of the Tehachapi Pass study were coherent and consistent with the basic physical processes that drive wind patterns in the Tehachapi area. In Phase II of the WindSENSE project, the ESA-MOOA approach was extended and applied to the wind plants located in the Mid-Columbia Basin wind generation area of Washington-Oregon during the summer and to the Tehachapi Pass region during the winter. The objective of this study was to identify measurement locations and variables that have the greatest positive impact on the accuracy of wind forecasts in the 0- to 6-hour look-ahead periods for the two regions and to establish a higher level of confidence in ESA-MOOA for mesoscale applications. The detailed methodology and results are provided in separate technical reports listed in the publications section below. Ideally, the data assimilation scheme used in the Phase III experiments would have been based upon an ensemble Kalman filter (EnKF) that was similar to the ESA method used to diagnose the Mid-Columbia Basin sensitivity patterns in the previous studies. However, running an EnKF system at high resolution is impractical because of the very high computational cost. Thus, it was decided to use a three-dimensional variational (3DVAR) analysis scheme that is less computationally intensive. The objective of this task is to develop an observation system deployment strategy for the mid Columbia Basin (i.e. the BPA wind generation region) that is designed to produce the maximum benefit for 1- to 6-hour ahead forecasts of hub-height (~80 m) wind speed with a focus on periods of large changes in wind speed. There are two tasks in the current project effort designed to validate the ESA observational system deployment approach in order to move closer to the overall goal: (1) Perform an Observing System Experiment (OSE) using a data denial approach. (2) Conduct a set of Observing System Simulation Experiments (OSSE) for the Mid-Columbia basin region.

17 WIND ENERGY↗

DEVELOPMENT AND APPLICATION OF RISK ANALYSIS TOOLKIT FOR PLANT RESOURCE OPTIMIZATION

This paper presents the development of methods and tools that are being designed to optimize plant operations (e.g., maintenance/replacement schedules and optimal maintenance postures for plant components) in a manner that is more cost effective than current approaches and makes better use of available component health and cost data. These methods include both data- and model-based optimization methods. Model-based optimization methods directly include reliability and cost models to determine an optimal plant operational strategy. We consider gradient-based and evolutionary (based on genetic algorithms) optimization methods. The second class of methods target more specific use cases (e.g., project schedule optimization) and are not based on reliability models directly, but they require specific component reliability and cost data. This class of methods is based on variants of the knapsack problem with an aim to determine an optimal project schedule that maximizes the overall NPV. This paper also presents multi-objective methods designed to identify an optimal maintenance posture based on a Pareto frontier analysis. Rather than dictating the “right” tradeoff (i.e., identify the absolute best posture), we show how it is possible to perform a trade space exploration approach (i.e., identify value and costs of several postures and let the analysis account for desired value and cost metrics). This is performed by identifying maintenance postures that maximize value (e.g., system availability) and minimize operational costs, i.e., the Pareto frontier in a value-cost trade space. For all these methods we present detailed applicative examples that show their validity from a decision-making perspective.

97 - MATHEMATICS AND COMPUTING↗