An Inexact Trust-Region Algorithm for Nonsmooth Risk-Averse Optimization
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Kouri, Drew Philip↗
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An Inexact Trust-Region Algorithm for Nonsmooth Risk-Averse Optimization
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Kouri, Drew Philip [Sandia National Laboratories (↗
An Inexact Trust-Region Algorithm for Nonsmooth Risk-Averse Optimization
Explore the source record for details and available documents.
Kouri, Drew Philip [Sandia National Laboratories (↗
Parallel Solution Algorithms and Modeling Tools for Dynamic Optimization.
Abstract not provided.
Nicholson, Bethany L.↗
Optimal Control of Evolution Mixed Variational Inclusions
Optimal control problems of primal and dual evolution mixed variational inclusions, in reflexive Banach spaces, are studied. The solvability analysis of the mixed state systems is established via duality principles. The optimality analysis is performed in terms of perturbation conjugate duality methods, and proximation penalty-duality algorithms to mixed optimality conditions are further presented. Applications to nonlinear diffusion constrained problems as well as quasistatic elastoviscoplastic bilateral contact problems exemplify the theory.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DPP-PMRF: Rethinking Optimization for a Probabilistic Graphical Model Using Data-Parallel Primitives
We present a new parallel algorithm for probabilistic graphical model optimization. The algorithm relies on data-parallel primitives (DPPs), which provide portable performance over hardware architecture. We evaluate results on CPUs and GPUs for an image segmentation problem. Compared to a serial baseline, we observe runtime speedups of up to 13X (CPU) and 44X (GPU). We also compare our performance to a reference, OpenMP-based algorithm, and find speedups of up to 7X (CPU).
97 MATHEMATICS AND COMPUTING↗
Approximate Scheduling of DERs with Discrete Complex Injections
Rapid penetration of renewable energy based Distributed Energy Resources (DER) has the potential to exacerbate the challenges inherent in grid frequency and voltage regulation. However, their real time controllability can be leveraged to not only mitigate such challenges, but improve the economics and quality of grid operations. A plethora of DER scheduling algorithms have been developed for fast and efficient scheduling of these resources. These algorithms schedule the complex - real and reactive power injected into (or drawn from) the grid by the DERs under various cost objective functions and grid constraints. However, a vast majority of such algorithms assume the feasible range of power injections to be continuous. In reality, the control options available for several DERs form a discrete space. This implies that the feasible range of power injections also forms a discrete space. This makes DER scheduling an NP-hard problem. Integer/Mixed Integer program based algorithms, which guarantee optimality in the objective value, have been developed. But these are prohibitively expensive in terms of computational time requirements. On the other hand, fast heuristic based solutions have also been developed. But as they do not provide any guarantee on the optimality of the objective, or on satisfying the constraints, they are unreliable for grid operations. Recent works have developed approximation algorithms which offer the best of both the approaches above: (near) optimality and low computational complexity, both of which are governed by a user defined accuracy parameter ϵ. In this work, we significantly improve upon such existing works by developing an approximation algorithm which schedules DERs with complex injections (as opposed to only real injection) and whose runtime is polynomial (as opposed to exponential) in 1/ϵ. We provide theoretical analysis and support them with experimental results to validate the guarantees provided by our approximation algorithm.
14 SOLAR ENERGY↗
Optimization of the magnetic horn for the nuSTORM non-conventional neutrino beam using the genetic algorithm
This paper describes the strategy for optimizing the magnetic horn for the neutrinos from STORed Muons (nuSTORM) facility. The nuSTORM magnetic horn is the primary collection device for the secondary particles generated by bombarding a solid target with 120 GeV protons. As a consequence of the non-conventional beamline designed for nuSTORM, the requirements on the horn are different from those for a conventional neutrino beamline. At nuSTORM, muons decay while circulating in the storage ring, and the detectors are placed downstream of the production straight so as to be exposed to the neutrinos from muon decay. nuSTORM aims at precisely measuring the neutrino cross sections, and providing a definitive statement about the existence of sterile neutrinos. The nuSTORM horn aims at focusing the pions into a certain phase space so that more muons from pion decay can be accepted by the decay ring. The paper demonstrates a numerical method that was developed to optimize the horn design to gain higher neutrino flux from the circulating muons. A Genetic Algorithm (GA) was applied to the simultaneous optimization of the two objectives in this study. In conclusion, the application of the technique discussed in this paper is not limited to either the nuSTORM facility or muon based facilities, but can be used for other neutrino facilities that use magnetic horns as collection devices.
43 PARTICLE ACCELERATORS↗
Optimizing group structures using hierarchical division
Creating group structures with few groups that give low errors is a difficult problem in reactor analysis. In recent years, automated optimization techniques have been applied to this task. We continue this trend by applying the hierarchical division algorithm to generate optimized group structures that minimize a cost function. At each stage, the algorithm adds a single group boundary to an existing group structure, dividing one group into two to increase the resolution of the group structure. The location of the added boundary is the one that gives the lowest error over all possible new boundary locations. Our implementation requires a beginning group structure, a set of candidate new boundary locations, and a set of reference reaction rates. As a proof of concept, we used WIMS-69 as the initial group structure, XMAS-172 as the ending group structures, and a 344-group reference group structure. Testing on two simple, homogenized reactor problems, we found that hierarchical division was able to reduce the error by a factor of around 5 with an increase of only 15% in the number of groups. Because hierarchical division can get stuck in local minima, it often reaches a plateau in its error reduction capability as many groups are added. Nevertheless, we find hierarchical division has strong potential to make good group structures into great group structures at a modest increase in computational cost. (authors)
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Market-based Co-optimization of Energy and Ancillary Services with Distributed Energy Resource Flexibilities
Energy storage systems and flexible loads have attracted significant interests due to their capabilities to provide various grid services. In this paper, the flexibilities are optimally allocated among multiple distributed energy resource aggregators with energy storage systems and flexible buildings by the utility coordinator through market-based co-optimization. An iterative market clearing algorithm is developed to determine the optimal energy and ancillary service prices, with consideration of both local dynamics and network constraints. Simulation results demonstrate the effectiveness of the proposed algorithm and the benefits of co-optimizing the energy and ancillary service markets.
Ma, Ke↗
Optimization of the Coupled Cluster Implementation in NWChem on Petascale Parallel Architectures
Coupled cluster singles and doubles (CCSD) algorithm has been optimized in NWChem software package. This modification alleviated the communication bottleneck and provided from 2- to 5-fold speedup in the CCSD iteration time depending on the problem size and available memory. Sustained 0.60 petaflop/sec performance on CCSD(T) calculation has been obtained on NCSA Blue Waters. This number included all stages of the calculation from initialization till termination, iterative computation of single and double excitations, and perturbative accounting for triple excitations. In the section of perturbative triples alone, the computation maintained 1.18 petaflop/sec performance level. CCSD computations have been performed on Guanine-Cytosine deoxydinucleotide monophosphate (GC-dDMP) to probe the conformational energy difference in DNA single strand in A- and B-conformations. The computation revealed significant discrepancy between CCSD and classical force fields in prediction of relative energy of A- and B-conformations of GC-dDMP.
calculations↗
NEW TECHNIQUES FOR HIGH-CONTRAST IMAGING WITH ADI: THE ACORNS-ADI SEEDS DATA REDUCTION PIPELINE
We describe Algorithms for Calibration, Optimized Registration, and Nulling the Star in Angular Differential Imaging (ACORNS-ADI), a new, parallelized software package to reduce high-contrast imaging data, and its application to data from the SEEDS survey. We implement several new algorithms, including a method to register saturated images, a trimmed mean for combining an image sequence that reduces noise by up to {approx}20%, and a robust and computationally fast method to compute the sensitivity of a high-contrast observation everywhere on the field of view without introducing artificial sources. We also include a description of image processing steps to remove electronic artifacts specific to Hawaii2-RG detectors like the one used for SEEDS, and a detailed analysis of the Locally Optimized Combination of Images (LOCI) algorithm commonly used to reduce high-contrast imaging data. ACORNS-ADI is written in python. It is efficient and open-source, and includes several optional features which may improve performance on data from other instruments. ACORNS-ADI requires minimal modification to reduce data from instruments other than HiCIAO. It is freely available for download at www.github.com/t-brandt/acorns-adi under a Berkeley Software Distribution (BSD) license.
79 ASTRONOMY AND ASTROPHYSICS↗
Improving Schrödinger Equation Implementations with Gray Code for Adiabatic Quantum Computers
We reformulate the continuous-space Schrödinger equation in terms of spin Hamiltonians. For the kinetic energy operator, the critical concept facilitating the reduction in model complexity is the idea of position encoding. A binary encoding of position produces a spin-1/2 Heisenberg-like model and yields exponential improvement in space complexity when compared to classical computing. Encoding with a binary reflected Gray code (BRGC), and a Hamming-distance-2 Gray code (H2GC) reduces the model complexity down to the 𝑋𝑍 and transverse Ising model, respectively. For 𝐴 qubits BRGC yields 2 𝐴 positions and is reduced to its 2-local form with O(𝐴) ancillary qubits. H2GC yields 2 𝐴/2+1 positions with O(𝐴 2 ) three-local penalty terms. We also identify the bijective mapping between diagonal unitaries and the Walsh series, producing the mapping of any real potential to a series of 𝑘 -local Ising models through the fast Walsh transform. Finally, in a finite volume, we provide some numerical evidence to support the claim that the total time needed for adiabatic evolution is protected by the infrared cutoff of the system. As a result, initial state preparation from a free-field wave function to an interacting system is expected to exhibit polynomial time complexity with volume and constant scaling with respect to lattice discretization for all encodings. For H2GC, if the evolution starts with the transverse Hamiltonian due to hardware restrictions, then penalties are dynamically introduced such that the low-lying spectrum reproduces the energy levels of the Laplacian. The adiabatic evolution of the penalty Hamiltonian is therefore sensitive to the ultraviolet scale. It is expected to exhibit polynomial time complexity with lattice discretization, or exponential time complexity with respect to the number of qubits given a fixed volume.
97 MATHEMATICS AND COMPUTING↗
Overall chilled water system energy consumption modeling and optimization
The emergence of increasingly affordable variable-speed drive technology has changed the approach used to control chilled water systems equipped with these drives. The purpose of this research was to develop an integrated chilled water modeling technique that can determine the optimal system setpoints and estimate the energy saving potential of chiller system. The chiller system equipped with Variable Frequency Drives (VFDs) on cooling tower fans and condenser water pumps. To accomplish the objective, physical component models of the centrifugal chiller, cooling tower and condenser water pump were established with the goal of incorporating the system’s condenser water flow rate and cooling tower fan speeds as optimization variables. Furthermore, a cooling load prediction algorithm was developed using a multiple non-linear regression model to approximate the building’s cooling load subject to a range of environmental conditions. The inputs and outputs of the individual component models were linked to estimate how adjusting the cooling tower fan and condenser water pump speed would influence the system’s comprehensive performance. Here, the overall system model was then optimized using a generalized reduced gradient optimization algorithm to determine the potential energy savings through speed control with VFDs and to ascertain a control logic strategy for the building automation system to operate the heating and cooling system. A case-study was performed on a single chiller system at a museum and the model was calibrated according to logged data collected over four months. Results showed that for the system analyzed, the energy saving of optimizing the cooling tower fan system was found to be 12–15%, while the energy saving potential of optimizing the condenser water pump with the cooling tower fan was negligible. Additionally, comparing different cooling tower fan control strategies showed that a wet-bulb approach-based cooling tower control strategy was shown to have the highest correlation to the optimized fan speed with an R 2 of 0.924.
32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
A unified funnel restoration SQP algorithm
We consider nonlinearly constrained optimization problems and discuss a generic double-loop framework consisting of basic algorithmic ingredients that unifies a broad range of nonlinear optimization solvers. This framework has been implemented in the open-source solver Uno, a Swiss Army knife-like C++ optimization framework that unifies many nonlinearly constrained nonconvex optimization solvers. We illustrate the framework with a sequential quadratic programming (SQP) algorithm that maintains an acceptable upper bound on the constraint violation, called a funnel, that is monotonically decreased to control the feasibility of the iterates. Infeasible quadratic subproblems are handled by a feasibility restoration strategy. Globalization is controlled by a line search or a trust-region method. We prove global convergence of the trust-region funnel SQP method, building on known results from filter methods. We implement the algorithm in Uno, and we provide extensive test results for the trust-region line-search funnel SQP on small CUTEst instances.
Kiessling, David [Katholieke Univ. Leuven, Heverle↗
From Optimization to Sampling Through Gradient Flows
Optimization and sampling algorithms play a central role in science and engineering as they enable finding optimal predictions, policies, and recommendations, as well as expected and equilibrium states of complex systems. The notion of “optimality” is formalized by the choice of an objective function, while the notion of an “expected” state is specified by a probabilistic model for the distribution of states. Optimizing rugged objective functions and sampling multimodal distributions is computationally challenging, especially in high-dimensional problems. Here, for this reason, many optimization and sampling methods have been developed by researchers working in disparate fields such as Bayesian statistics, molecular dynamics, genetics, quantum chemistry, machine learning, weather forecasting, econometrics, and medical imaging.
Trillos, N. García↗
EBIS Beam Intensity Online Optimization with GPTune and Offline Analysis with XGBoost
The application of machine learning techniques to accelerator research has led to significant breakthroughs in optimization strategies. This paper presents a pioneering study using a novel machine learning algorithm, GPTune, to optimize beam intensity by adjusting parameters in the EBIS injection and extraction beam lines. Our research demonstrates substantial improvements, achieving a remarkable 22% and 70% increase in beam intensity at two separate measurement locations.
43 PARTICLE ACCELERATORS↗
Machine Learning Classical Interatomic Potentials for Molecular Dynamics from First-Principles Training Data
The ever-increasing power of modern super-computers, along with the availability of highly scalable atomistic simulation codes, has begun to revolutionize predictive modeling of materials. In particular, molecular dynamics (MD) has led to breakthrough advances in diverse fields, including tribology, catalysis, sensing, and nanoparticle self-assembly. Furthermore, recent integration of MD simulations with X-ray characterization has demonstrated promise in real-time 3-D characterization of materials on the atomic scale. The popularity of MD is driven by its applicability at disparate length/time scales, ranging from ab initio MD (hundreds of atoms and tens of picoseconds) to all-atom classical MD (millions of atoms over microseconds), and coarse-grained (CG) models (micrometers and tens of microseconds). Nevertheless, a substantial gap persists between AIMD, which is highly accurate but restricted to extremely small sizes, and those based on classical force fields (atomistic and CG) with limited accuracy but access to larger length/time scales. The accuracy and predictive power of classical MD simulations is dictated by the empirical force fields, and their capability to capture the relevant physics. Here, we discuss some of our recent work on the use of machine learning (ML) to combine the accuracy and flexibility of electronic structure calculations with the speed of classical potentials. Our ML framework attempts to bridge the significant gulf that exists between the handful of research groups that develop new interatomic potential models (often requiring several years of effort), and the increasingly large user community from academia and industry that applies these models. Our data-driven approach represents significant departure from the status quo and involves several steps including generation and manipulation of extensive training data sets through electronic structure calculations, defining novel potential functional forms, employing state-of-the-art ML algorithms to formulate highly optimized training procedures, and subsequently developing user-friendly workflow tools integrating these algorithms on high-performance computers (HPCs). Our ML approach shows marked success in developing force fields for a wide range of materials from metals, oxides, nitrides, and heterointerfaces to two-dimensional (2D) materials.
Chan, Henry↗