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DOE OSTI2020

On the Derivation of Quasi-Newton Formulas for Optimization in Function Spaces

Newton’s method is usually preferred when solving optimization problems due to its superior convergence properties compared to gradient-based or derivative-free optimization algorithms. However, deriving and computing second-order derivatives needed by Newton’s method often is not trivial and, in some cases, not possible. In such cases quasi-Newton algorithms are a great alternative. In this paper, we provide a new derivation of well-known quasi-Newton formulas in an infinite-dimensional Hilbert space setting. Furthermore, it is known that quasi-Newton update formulas are solutions to certain variational problems over the space of symmetric matrices. In this paper, we formulate similar variational problems over the space of bounded symmetric operators in Hilbert spaces. By changing the constraints of the variational problem we obtain updates (for the Hessian and Hessian inverse) not only for the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method but also for Davidon–Fletcher–Powell (DFP), Symmetric Rank One (SR1), and Powell-Symmetric-Broyden (PSB). In addition, for an inverse problem governed by a partial differential equation (PDE), we derive DFP and BFGS “structured” secant formulas that explicitly use the derivative of the regularization and only approximates the second derivative of the misfit term. We show numerical results that demonstrate the desired mesh-independence property and superior performance of the resulting quasi-Newton methods.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Global stellarator coil optimization with quadratic constraints and objectives

Most present stellarator designs are produced by costly two-stage optimization: the first for an optimized equilibrium, and the second for a coil design reproducing its magnetic configuration. Few proxies for coil complexity and forces exist at the equilibrium stage. Rapid initial state finding for both stages is a topic of active research. Most present convex coil optimization codes use the least square winding surface method by Merkel (NESCOIL), with recent improvements in conditioning, regularization, sparsity, and physics objectives. While elegant, the method is limited to modeling the norms of linear functions in coil current. We present QUADCOIL, a global coil optimization method that targets combinations of linear and quadratic functions of the current. It can directly constrain and/or minimize a wide range of physics objectives unavailable in NESCOIL and REGCOIL, including the Lorentz force, magnetic energy, curvature, field-current alignment, and the maximum density of a dipole array. QUADCOIL requires no initial guess and runs nearly $10$ 2 x faster than filament optimization. Integrating it in the equilibrium optimization stage can potentially exclude equilibria with difficult-to-design coils, without significantly increasing the computation time per iteration. QUADCOIL finds the exact, global minimum in a large parameter space when possible, and otherwise finds a well-performing approximate global minimum. It supports most regularization techniques developed for NESCOIL and REGCOIL. We demonstrate QUADCOIL’s effectiveness in coil topology control, minimizing non-convex penalties, and predicting filament coil complexity with three numerical examples.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2016

Materials and Methods for Streamlined Laboratory Analysis of Environmental Samples, FY 2016 Report

The International Atomic Energy Agency (IAEA) relies upon laboratory analysis of environmental samples (typically referred to as “swipes”) collected during on-site inspections of safeguarded facilities to support the detection and deterrence of undeclared activities. Unfortunately, chemical processing and assay of the samples is slow and expensive. A rapid, effective, and simple extraction process and analysis method is needed to provide certified results with improved timeliness at reduced costs (principally in the form of reduced labor), while maintaining or improving sensitivity and efficacy. To address these safeguard needs the Pacific Northwest National Laboratory (PNNL) explored and demonstrated improved methods for environmental sample (ES) analysis. Improvements for both bulk and particle analysis were explored. To facilitate continuity and adoption, the new sampling materials and processing methods will be compatible with existing IAEA protocols for ES analysis. PNNL collaborated with Oak Ridge National Laboratory (ORNL), which performed independent validation of the new bulk analysis methods and compared performance to traditional IAEA’s Network of Analytical Laboratories (NWAL) protocol. ORNL efforts are reported separately. This report describes PNNL’s FY 2016 progress, which was focused on analytical application supporting environmental monitoring of uranium enrichment plants and nuclear fuel processing. In the future the technology could be applied to other safeguard applications and analytes related to fuel manufacturing, reprocessing, etc. PNNL’s FY 2016 efforts were broken into two tasks and a summary of progress, accomplishments and highlights are provided below. Principal progress and accomplishments on Task 1, Optimize Materials and Methods for ICP-MS Environmental Sample Analysis, are listed below. • Completed initial procedure for rapid uranium extraction from ES swipes based upon carbonate-peroxide chemistry (delivered to ORNL for evaluation). • Explored improvements to carbonate-peroxide rapid uranium extraction chemistry. • Evaluated new sampling materials and methods (in collaboration with ORNL). • Demonstrated successful ES extractions from standard and novel swipes for a wide range uranium compounds of interest including UO 2 F 2 and UO 2 (NO 3 ) 2 , U 3 O 8 and uranium ore concentrate. • Completed initial discussions with commercial suppliers of PTFE swipe materials. • Submitted one manuscript for publication. Two additional drafts are being prepared. Principal progress and accomplishments on Task 2, Optimize Materials and Methods for Direct SIMS Environmental Sample Analysis, are listed below. • Designed a SIMS swipe sample holder that retrofits into existing equipment and provides simple, effective, and rapid mounting of ES samples for direct assay while enabling automation and laboratory integration. • Identified preferred conductive sampling materials with better performance characteristics. • Ran samples on the new PNNL NWAL equivalent Cameca 1280 SIMS system. • Obtained excellent agreement between isotopic ratios for certified materials and direct SIMS assay of very low levels of LEU and HEU UO 2 F 2 particles on carbon fiber sampling material. Sample activities range from 1 to 500 CPM (uranium mass on sample is dependent upon specific isotope ratio but is frequently in the subnanogram range). • Found that the presence of the UF molecular ions, as measured by SIMS, provides chemical information about the particle that is separate from the uranium isotopics and strongly suggests that those particles originated from an UF6 enrichment activity. • Submitted one manuscript for publication. Another manuscript is in preparation.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

DOE OSTI2020

Optimal control of coupled quantum systems based on the first-order Magnus expansion: Application to multiple dipole-dipole-coupled molecular rotors

This paper presents a method for performing approximate optimal control simulations for quantum systems with multiple coupled degrees of freedom. In this work, the time evolution is simulated using the first-order Magnus expansion in the interaction picture, where the couplings between different degrees of freedom are treated as the perturbation. A numerical implementation procedure is presented that leverages upon pairwise couplings and the separability of the zeroth-order time evolution operator to achieve a reduced computational cost, which is analyzed with respect to the number of degrees of freedom. The formulation is compatible with gradient-free methods to optimize the control field, and a stochastic hill climbing algorithm is adopted for this purpose. As illustrations, optimal control simulations are performed for systems of two and three dipole-dipole-coupled molecular rotors under the influence of a control field. For the two-rotor system, the field is optimized to achieve either orientation or entanglement objectives. For the three-rotor system, the field is optimized either to orient all three rotors in the same direction or to orient one rotor in a particular direction while the other two rotors point in the opposite direction.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2019

Development and Comparison of Purgeable Mercury Values in SRR Samples Measured by SRNL and Eurofins FGS

Savannah River Remediation (SRR) requested the development of mercury speciation capabilities at the Savannah River National Laboratory (SRNL) to support the Liquid Waste Operations at SRS. As part of that method development, SRR requested that SRNL Analytical Development (AD) compare their results with those obtained from their outside contract laboratory, Eurofins Frontier Global Sciences (FGS). This document reports on this method development work as well as the comparative analyses conducted between the two laboratories. Development, optimization, and validation were undertaken at SRNL to produce a method for the species-specific analysis of dissolved gaseous mercury (DGM) in samples from SRR. It was determined that DGM present in SRR samples represented a combination of various soluble and volatile mercury species- and is thus referred to in this document as purgeable mercury. A method has been developed and analytically validated for the analysis of purgeable mercury in caustic nuclear waste. Using multivariate optimization method, purge flow rate was determined to be highly correlated with increased response (p=0.023). Total recovery of spiked purgeable mercury from deionized water was 99.4 ±10.6% and 91.6 ±14.9% from spiked high-activity tank waste samples. Calibration, by external calibration and standard addition calibration, maintained a mean accuracy of 101 ±5% and 99.9 ±1.7%, respectively. This method represents a decrease in sample handling and processing over currently standard methods and represents a more amenable method for purgeable mercury analysis in liquid nuclear waste.1 An interlaboratory comparison was performed between SRNL and Eurofins FGS in the co-analysis of three quarterly Tank 50 samples. Two samples demonstrated no statistically significant difference (p=0.271, p=0.0811), with one sample biased 30% low to a statistically significant degree (p=0.0432). Large mean uncertainty was present in the results reported by both laboratories (±15% and 40% from SRNL and Eurofins), with no significant difference observed in uncertainty (p=0.934). Across all co-analyzed samples, no significantly difference was observed in precision (p=0.205) or reported values (p=0.352) between SRNL and Eurofins. These results indicate that SRNL-AD may provide data to the customer of statistically similar quality.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2021

Flexible optimized data handling in systems with multiple memories

Methods and systems for optimizing an application for a computing system having multiple distinct memory locations that are interconnected by one or more communication channels include determining one or more data handling properties for a data region in an application. One or more data handling policies for the data region are determined based on the one or more data handling properties. Data setup costs are determined for a scope in the application that uses the data region in different memory locations based on the one or more data handling properties. The application is optimized in accordance with the one or more data handling policies and the data setup costs for the different memory locations.

Chen, Tong↗

DOE OSTI2023

Flexible optimized data handling in systems with multiple memories

Chen, Tong↗

DOE OSTI2019

Distributed Energy Resources Coordination over Time-varying Directed Communication Networks

In this paper, we consider an optimal coordination problem for distributed energy resources (DERs) including distributed generators and energy storage devices. We first propose an algorithm based on the push-sum and gradient method to optimally coordinate storage devices and distributed generators in a distributed manner. In the proposed algorithm, each DER only maintains a set of variables and updates them through information exchange with a few neighboring DERs over a time-varying directed communication network. We show that the proposed distributed algorithm with appropriately chosen step-sizes solve the optimal DER coordination problem if the time-varying directed communication network is uniformly jointly strongly connected, which is a mild condition on the connectivity of communication topologies. The proposed distributed algorithm is illustrated and validated by numerical simulations.

Yang, Tao↗

DOE OSTI2015

Parallel implementation and performance optimization of the configuration-interaction method

The configuration-interaction (CI) method, long a popular approach to describe quantum many-body systems, is cast as a very large sparse matrix eigenpair problem with matrices whose dimension can exceed one billion. Such formulations place high demands on memory capacity and memory bandwidth - - two quantities at a premium today. In this paper, we describe an efficient, scalable implementation, BIGSTICK, which, by factorizing both the basis and the interaction into two levels, can reconstruct the nonzero matrix elements on the fly, reduce the memory requirements by one or two orders of magnitude, and enable researchers to trade reduced resources for increased computational time. We optimize BIGSTICK on two leading HPC platforms - - the Cray XC30 and the IBM Blue Gene/Q. Specifically, we not only develop an empirically-driven load balancing strategy that can evenly distribute the matrix-vector multiplication across 256K threads, we also developed techniques that improve the performance of the Lanczos reorthogonalization. Combined, these optimizations improved performance by 1.3-8× depending on platform and configuration.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

Multipinhole SPECT helical scan parameters and imaging volume

Purpose: The authors developed SPECT imaging capability on an animal PET scanner using a multiple-pinhole collimator and step-and-shoot helical data acquisition protocols. The objective of this work was to determine the preferred helical scan parameters, i.e., the angular and axial step sizes, and the imaging volume, that provide optimal imaging performance. Methods: The authors studied nine helical scan protocols formed by permuting three rotational and three axial step sizes. These step sizes were chosen around the reference values analytically calculated from the estimated spatial resolution of the SPECT system and the Nyquist sampling theorem. The nine helical protocols were evaluated by two figures-of-merit: the sampling completeness percentage (SCP) and the root-mean-square (RMS) resolution. SCP was an analytically calculated numerical index based on projection sampling. RMS resolution was derived from the reconstructed images of a sphere-grid phantom. Results: The RMS resolution results show that (1) the start and end pinhole planes of the helical scheme determine the axial extent of the effective field of view (EFOV), and (2) the diameter of the transverse EFOV is adequately calculated from the geometry of the pinhole opening, since the peripheral region beyond EFOV would introduce projection multiplexing and consequent effects. The RMS resolution results of the nine helical scan schemes show optimal resolution is achieved when the axial step size is the half, and the angular step size is about twice the corresponding values derived from the Nyquist theorem. The SCP results agree in general with that of RMS resolution but are less critical in assessing the effects of helical parameters and EFOV. Conclusions: The authors quantitatively validated the effective FOV of multiple pinhole helical scan protocols and proposed a simple method to calculate optimal helical scan parameters.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2024

Surrogate Model Guided Optimization of Expensive Black-Box Multi-Objective Problems: A Posteriori Methods

Many engineering applications require the simultaneous optimization of multiple conflicting objective functions. Often, these objective functions are evaluated using highly accurate computer simulations that are computationally too expensive to be evaluated hundreds or thousands of times during optimization. Thus, the goal is to find good approximations of the Pareto front using as few of these expensive simulations as possible. Here, we describe an optimization approach based on surrogate models and diverse sampling strategies to accelerate the search for the Pareto solutions. We use a separate surrogate model for approximating each objective function and then we use the surrogate models to inform where additional expensive simulations should be run. The surrogate models are updated in an active learning framework whenever new information from the expensive simulations becomes available. The sampling strategies aim at balancing local improvements of the approximate Pareto front and global exploration to identify the extrema and fill in large gaps of the approximate Pareto front. We demonstrate on a large set of benchmark problems the effectiveness of the method for finding good approximations of the Pareto front.

MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Combined Dimensional and Topology Optimization of Synchronous Machine Rotors Using a Material Density Interpolation Method

This article presents a magneto-structural combined dimensional and topology optimization technique for interior permanent magnet synchronous machine (IPMSM) and wound field synchronous machine (WFSM) rotors. Dimensional changes to the permanent magnet (PM) and rotor winding location or size are accomplished by interpolating or projecting a smoothed Heaviside rectangular function representing the presence of PM material onto the IPMSM rotor design domain mesh, whereas the presence of copper material for WFSM rotor is interpolated in the same manner. A density based Solid Isotropic Material with Penalization (SIMP) topology optimization approach is then used to vary the presence of electrical steel in mesh elements to form flux barriers around the PM. The proposed method enforces a defined shape for the PM without requiring the mesh in the design domain to be deformed. Four examples are presented to demonstrate the technique: Two flat bar IPMSM, one V-shaped IPMSM, and a WFSM. Here, a comparative study is performed on one of the flat bar IPMSMs using Metamodel of Optimal Prognosis (MOP) based method.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2020

Online Parameter Estimation Methods for Adaptive Cruise Control Systems

Modeling Adaptive Cruise Control (ACC) vehicles enables the understanding of the impact of these vehicles on traffic flow. In this work, two online methods are used to provide real time system identification of ACC enabled vehicles. The first technique is a recursive least squares (RLS) approach, while the second method solves a nonlinear joint state and parameter estimation problem via particle filtering (PF). We provide a parameter identifiability analysis for both methods to analytically show that the model parameters are not identifiable using equilibrium driving. The accuracy and computational runtime of the online methods are compared to a commonly used offline simulation-based optimization (i.e., batch optimization) approach. The methods are tested on synthetic data as well as on empirical data collected directly from a 2019 model year ACC vehicle using data from sensors that are part of the stock ACC system. The online methods are scalable and provide comparable accuracy to the batch method. RLS runs in real time and is two orders of magnitude faster than the batch method for modest sized (e.g., 15 min) datasets. The particle filter also runs in real- time, and is also suitable in streaming applications in which the datasets can grow arbitrarily large.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2026

Discovering the Most Severe K-Point Failure Based on Reinforcement Learning: Preprint

Smart devices are essential to ensure the stability of the power grid and resilience to intermittent energy production. However, smart devices can also be the target of cyber adversaries that may exploit false data injection attacks (FDIAs) to induce unstable grid conditions. A practical consideration of FDIA mitigation approaches is addressed here: given a finite available budget, for which smart device should cyber-threat mitigation be deployed first? In this work, this question is answered by identifying the so-called most-sensitive devices, i.e., the devices that, if compromised, can let an adversary induce the most serious grid instabilities. The method proposed utilizes an adversarial reinforcement learning (RL) framework to identify the k-mostsensitive smart devices (here, smart inverters). The adversarial agent can tamper with the compromised inverters' active and reactive operating power setup points, with the goal of maximizing voltage deviations. Numerical results show that the proposed RL method finds the optimal attack scenarios for 1-point failure and the near-optimal solution for the 2-point case. Additionally, the proposed RL method achieves an 8.8 speed-up ratio in running time compared to the brute force method for the 2-point case.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Autotuning PolyBench benchmarks with LLVM Clang/Polly loop optimization pragmas using Bayesian optimization

Here, we develop a ytopt autotuning framework that leverages Bayesian optimization to explore the parameter space search and compare four different supervised learning methods within Bayesian optimization and evaluate their effectiveness. We select six of the most complex PolyBench benchmarks and apply the newly developed LLVM Clang/Polly loop optimization pragmas to the benchmarks to optimize them. We then use the autotuning framework to optimize the pragma parameters to improve their performance. The experimental results show that our autotuning approach outperforms the other compiling methods to provide the smallest execution time for the benchmarks syr2k, 3mm, heat-3d, lu, and covariance with two large datasets in 200 code evaluations for effectively searching the parameter spaces with up to 170,368 different configurations. We find that the Floyd-Warshall benchmark did not benefit from autotuning. To cope with this issue, we provide some compiler option solutions to improve the performance. Then we present loop autotuning without a user's knowledge using a simple mctree autotuning framework to further improve the performance of the Floyd-Warshall benchmark. We also extend the ytopt autotuning framework to tune a deep learning application.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2014

A Cutting Surface Algorithm for Semi-Infinite Convex Programming with an Application to Moment Robust Optimization

In this paper, we present and analyze a central cutting surface algorithm for general semi-infinite convex optimization problems and use it to develop a novel algorithm for distributionally robust optimization problems in which the uncertainty set consists of probability distributions with given bounds on their moments. Moments of arbitrary order, as well as nonpolynomial moments, can be included in the formulation. We show that this gives rise to a hierarchy of optimization problems with decreasing levels of risk-aversion, with classic robust optimization at one end of the spectrum and stochastic programming at the other. Although our primary motivation is to solve distributionally robust optimization problems with moment uncertainty, the cutting surface method for general semi-infinite convex programs is also of independent interest. The proposed method is applicable to problems with nondifferentiable semi-infinite constraints indexed by an infinite dimensional index set. Examples comparing the cutting surface algorithm to the central cutting plane algorithm of Kortanek and No demonstrate the potential of our algorithm even in the solution of traditional semi-infinite convex programming problems, whose constraints are differentiable, and are indexed by an index set of low dimension. After the rate of convergence analysis of the cutting surface algorithm, we extend the authors' moment matching scenario generation algorithm to a probabilistic algorithm that finds optimal probability distributions subject to moment constraints. The combination of this distribution optimization method and the central cutting surface algorithm yields a solution to a family of distributionally robust optimization problems that are considerably more general than the ones proposed to date.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Optimization of Pineapple Leaf Fibre Extraction Methods and Their Biodegradabilities for Soil Cover Application

Cellulosic natural fibres from pineapple leaves are considered as a green alternative to the conventional polyethylene (PE) soil cover in agro-industry. The use of pineapple leaf fibres (PALFs) soil cover can overcome the disposal problem of the conventional plastic covers which take hundreds of years to degrade. This research was undertaken to study the effectiveness methods of extracting the PALFs. The mechanical method utilized ‘roller and bladder system’, where the chemical method involved the extraction with 6% NaOH, 20% aqueous acetone, and pineapple juice solution. The semi-mechanical method was a combination of “roller and bladder” system and a chemical retting process using 6% NaOH alkaline solutions. The characteristics of the extracted fibers were determined using X-ray diffraction (XRD) and Fourier transform infrared spectroscopy (FTIR). Kappa number test of the fibres extracted with semi-mechanical method showed the lowest percentage of lignin (3.39%). Based on XRD results, the highest percentage of crystallinity was recorded when PALF was extracted using the semi-mechanical method. A remarkable change on the morphological surface the biodegraded PALF soil cover was observed after 90 days of soil burial test. Biodegradability of soil cover made from PALF was higher than the commercial degradable soil cover i.e. PE/starch (80 wt% PE/ 20 wt% starch). Meanwhile, the growing rate and the soil fertility of chili tree that used PALFs soil cover showed better results than the chili tree that used conventional PE/starch soil cover.

36 MATERIALS SCIENCE↗

DOE OSTI2020

NEAMS Milestone Report: M2MS–20OR030102 FW–CADIS PWR Ex-Core Analysis with Shift Through VERA

This report presents the work completed for the NEAMS milestone M2MS–20OR030102 titled "FW–CADIS PWR Ex-Core Analysis with Shift through VERA." The work completed for this milestone includes the implementation, integration, and optimization of memory and performance improvement methods in Shift for fully coupled ex-core calculations through Virtual Environment for Reactor Applications (VERA). Fully coupled in this context means the transfer of moderator boron concentration, pin-wise fission source, depleted compositions, temperatures, and moderator densities from MPACT (with COBRA-TF (CTF)) to Shift. The ability to run ex-core calculations with VERA has been enabled and used for several years by Consortium for Advanced Simulation of Light Water Reactors (CASL) partners. However, this implementation was limited and potentially computationally burdensome. This work has enabled the ability to run higher-fidelity ex-core calculations on moderate computing clusters by focusing on multithreading, domain decomposition, and Forward-Weighted CADIS (FW-CADIS) variance reduction. Tests performed on small cores, a small modular reactor (SMR), and CASL progression problems show very promising memory reduction and computational performance. Recommendations for settings when running fully coupled high-fidelity ex-core calculations with VERA are documented. Without these optimization methods, many processors on a compute node would be left unused for the entire ex-core calculation. Therefore, these methods enable the user to better use the resources available and reduce computation time.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗