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DOE OSTI2023

Optimization of transformer ratio and beam loading in a plasma wakefield accelerator with a structure-exploiting algorithm

Plasma-based acceleration has emerged as a promising candidate as an accelerator technology for a future linear collider or a next-generation light source. We consider the plasma wakefield accelerator (PWFA) concept where a plasma wave wake is excited by a particle beam and a trailing beam surfs on the wake. For a linear collider, the energy transfer efficiency from the drive beam to the wake and from the wake to the trailing beam must be large, while the emittance and energy spread of the trailing bunch must be preserved. One way to simultaneously achieve this when accelerating electrons is to use longitudinally shaped bunches and nonlinear wakes. In the linear regime, there is an analytical formalism to obtain the optimal shapes. In the nonlinear regime, however, the optimal shape of the driver to maximize the energy transfer efficiency cannot be precisely obtained because currently no theory describes the wake structure and excitation process for all degrees of nonlinearity. In addition, the ion channel radius is not well defined at the front of the wake where the plasma electrons are not fully blown out by the drive beam. We present results using a novel optimization method to effectively determine a current profile for the drive and trailing beam in PWFA that provides low energy spread, low emittance, and high acceleration efficiency. We parameterize the longitudinal beam current profile as a piecewise-linear function and define optimization objectives. For the trailing beam, the algorithm converges quickly to a nearly inverse trapezoidal trailing beam current profile similar to that predicted by the ultrarelativistic limit of the nonlinear wakefield theory. For the drive beam, the beam profile found by the optimization in the nonlinear regime that maximizes the transformer ratio also resembles that predicted by linear theory. Furthermore, the current profiles found from the optimization method provide higher transformer ratios compared with the linear ramp predicted by the relativistic limit of the nonlinear theory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Improving cosmological analyses of HI clustering by reducing stochastic noise

High-number-density tracers of large-scale structure, such as the HI-rich galaxies measured by 21 cm intensity mapping, have low sampling noise, making them particularly promising as cosmological probes. At large scales, this sampling noise can be subdominant to other scale-independent contributions to the power spectrum; such contributions arise from nonlinear bias, and exceed the sampling noise if at least one of the associated bias coefficients is sufficiently large. This has important consequences for cosmological constraints obtained from such tracers, since it indicates that using the power spectrum does not lead to optimal constraints even in the linear regime. In this paper, we provide a conservative estimate of the possible improvement in constraining power of a 21 cm survey if one were to use an optimal analysis strategy (such as field-level analysis), where only the true sampling noise enters the error budget. We find that improvements in uncertainties on some cosmological parameters can be as large as 50%, depending on redshift, foreground cleaning efficiency, scales used in the analysis, and instrumental noise. One byproduct of our work is measurements of bias parameters and stochasticity for neutral hydrogen in the IllustrisTNG simulation over a wide range of redshifts; we provide simple fitting formulas for these measurements. Furthermore, our results motivate further exploration of new optimal analysis techniques and provide important insights into the constraining power of current and future 21 cm surveys.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Structure optimization with stochastic density functional theory

Linear-scaling techniques for Kohn–Sham density functional theory are essential to describe the ground state properties of extended systems. Still, these techniques often rely on the localization of the density matrix or accurate embedding approaches, limiting their applicability. In contrast, stochastic density functional theory (sDFT) achieves linear- and sub-linear scaling by statistically sampling the ground state density without relying on embedding or imposing localization. In return, ground state observables, such as the forces on the nuclei, fluctuate in sDFT, making optimizing the nuclear structure a highly non-trivial problem. In this work, we combine the most recent noise-reduction schemes for sDFT with stochastic optimization algorithms to perform structure optimization within sDFT. We compare the performance of the stochastic gradient descent approach and its variations (stochastic gradient descent with momentum) with stochastic optimization techniques that rely on the Hessian, such as the stochastic Broyden–Fletcher–Goldfarb–Shanno algorithm. In conclusion, we further provide a detailed assessment of the computational efficiency and its dependence on the optimization parameters of each method for determining the ground state structure of bulk silicon with varying supercell dimensions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Efficient numerical methods to solve sparse linear equations with application to PageRank

Over the last two decades, the PageRank problem has received increased interest from the academic community as an efficient tool to estimate web-page importance in information retrieval. Despite numerous developments, the design of efficient optimization algorithms for the PageRank problem is still a challenge. Here, we propose three new algorithms with a linear time complexity for solving the problem over a bounded-degree graph. The idea behind them is to set up the PageRank as a convex minimization problem over a unit simplex, and then solve it using iterative methods with small iteration complexity. Our theoretical results are supported by an extensive empirical justification using real-world and simulated data.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

The Recommendations for Linear Measurement Techniques on the Measurements of Nonlinear System Parameters of a Joint.

In the study of the dynamics of nonlinear systems, experimental measurements often convolute the response of the nonlinearity of interest and the effects of the experimental setup. To reduce the influence of the experimental setup on the deduction of the parameters of the nonlinearity, the response of a mechanical joint is investigated under various experimental setups. These experiments first focus on quantifying how support structures and measurement techniques affect the natural frequency and damping of a linear system. The results indicate that support structures created from bungees have negligible influence on the system in terms of frequency and damping ratio variations. The study then focuses on the effects of the excitation technique on the response for a linear system. The findings suggest that thinner stingers should not be used, because under the high force requirements the stinger bending modes are excited adding unwanted torsional coupling. The optimal configuration for testing the linear system is then applied to a nonlinear system in order to assess the robustness of the test configuration. Finally, recommendations are made for conducting experiments on nonlinear systems using conventional/linear testing techniques.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Substation-Level Grid Topology Optimization Using Bus Splitting: Preprint

Operations of substation circuit breakers are of high significance for performing system maintenance and topology optimization. Bus splitting is one type of topology changes where the two bus-bars at a substation become electrically disconnected after certain actions of circuit breakers. As these events involve detailed substation modeling, they are not typically considered in power system routine operation and control. In this paper, an improved substation-level topology optimization is developed by expanding traditional line switching with breaker-level bus splitting, which can further reduce grid congestion and generation costs. A tight McCormick relaxation is proposed to reformulate the bi-linear terms in the resultant topology optimization model. Thus, a tractable mixed-integer linear program formulation is presented which can be efficiently solved for real-time control. Numerical studies on the IEEE 14-bus and 118-bus systems demonstrate the performance and economic benefits of the proposed topology optimization approach.

bus split↗

DOE OSTI2019

An Efficient Parallel-in-Time Method for Optimization with Parabolic PDEs

To solve optimization problems with parabolic PDE constraints, often methods working on the reduced objective functional are used. They are computationally expensive due to the necessity of solving both the state equation and a backward-in-time adjoint equation to evaluate the reduced gradient in each iteration of the optimization method. In this study, we investigate the use of the parallel-in-time method PFASST in the setting of PDE-constrained optimization. In order to develop an efficient fully time-parallel algorithm, we discuss different options for applying PFASST to adjoint gradient computation, including the possibility of doing PFASST iterations on both the state and the adjoint equations simultaneously. Here, we also explore the additional gains in efficiency from reusing information from previous optimization iterations when solving each equation. Numerical results for both a linear and a nonlinear reaction-diffusion optimal control problem demonstrate the parallel speedup and efficiency of different approaches.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Real-Time Optimization Workflow Status Update

Economically optimal and safe operation of integrated energy systems (IES) requires optimization at many different time scales. A real-time optimization (RTO) workflow will attempt to maximize revenue and minimize operational costs on a time scale of minutes to hours. Such a workflow requires the use of a digital twin (DT), which is a virtual representation of a physical system. The DT is updated using real-time data from the physical system, and serves as a model in an optimization framework. The optimization results are then sent back to the physical system to complete the loop. This report details the progress made in developing building blocks for a DT/RTO framework. The Risk Analysis Virtual Environment (RAVEN) platform within the Framework for Optimization of Resources and Economics (FORCE) tool suite can perform many of the tasks required for building a DT and performing RTO. The first item of this report details RAVEN enhancements that enable RAVEN workflows to be run in various environments. Data communication between the physical system and its DT is essential for successful RTO. This includes preprocessing real-time data, loading data into a data warehouse, and querying the stored data. The second section of this report describes the progress made in implementing an adapter in Python in order for Deep Lynx to handle the data communication. Typical dispatch optimization frameworks are built on linear programming (LP). The prototype RTO workflow developed in this report uses an LP problem as a part of a receding-horizon- or economic model predictive control (EMPC) based optimization. The third section of this report details the framework of an RTO workflow in which the system consists of a simple electrical storage device. A DT can be built from a reduced-order model (ROM). Integrating a ROM into a typical LP optimization framework has been challenging because most optimization packages require the user to write algebraic expressions for the system model. The final section of this report shows how an externally built RAVEN ROM can be integrated in an RTO framework by using the Python package Pyomo. This demonstrates the RTO workflow capability from a software-only perspective and is an important step in demonstrating the capability to implement an RTO workflow for a physical system.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Modeling and Integration of Flexible Demand in Heat and Electricity Integrated Energy System

This paper is focused on utilizing customers' flexible energy demand, including both heat demand and electricity demand, to provide balancing resources and relieve the difficulties of integrating variable wind power with the combined heat and power. The integration of heat and electricity energy systems providing customers with multiple options for fulfilling their energy demand is described. Customer aggregators are introduced to supply downstream demand in the most economical way. Controlling customers' energy consumption behaviors enables aggregators to adjust their energy demand in response to supply conditions. Incorporating aggregators' flexible energy demand into the centralized energy dispatch model, a two-level optimization problem (TLOP) is first formed where the system operatormaximizes social welfare subject to aggregators' strategies, which minimize the energy purchase cost. Furthermore, the subproblems are linearized based on several reasonable assumptions. Optimal conditions of the subproblems are then transformed as energy demands to be described as explicit piecewise-linear functions of electricity prices corresponding to the demand bid curves. In this way, the TLOP is transformed to a standard optimization problem, which requires aggregators to only submit a demand bid to run the centralized energy dispatch program. All the parameters pertaining to the aggregators' energy consumption models are internalized in the bid curves. The proposed technique is illustrated in a modified testing system.

combined heat and power (CHP)↗

DOE OSTI2017

Enhancement of flow measurements using fluid-dynamic constraints

Novel experimental modalities acquire spatially resolved velocity measurements for steady state and transient flows which are of interest for engineering and biological applications. One of the drawbacks of such high resolution velocity data is their susceptibility to measurement errors. In this paper, we propose a novel filtering strategy that allows enhancement of the noisy measurements to obtain reconstruction of smooth divergence free velocity and corresponding pressure fields which together approximately comply to a prescribed flow model. The main step in our approach consists of the appropriate use of the velocity measurements in the design of a linearized flow model which can be shown to be well-posed and consistent with the true velocity and pressure fields up to measurement and modeling errors. The reconstruction procedure is then formulated as an optimal control problem for this linearized flow model. The resulting filter has analyzable smoothing and approximation properties. We briefly discuss the discretization of the approach by finite element methods and comment on the efficient solution by iterative methods. The capability of the proposed filter to significantly reduce data noise is demonstrated by numerical tests including the application to experimental data. In addition, we compare with other methods like smoothing and solenoidal filtering.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Exploring the benefits of utilizing small modular device for sustainable and flexible shale gas water management

Growing shale gas extraction in recent years has triggered wide discussions on the associated freshwater requirement and wastewater management. Many optimization approaches have been developed for shale gas water management; however, most of the studies assumed permanent utilization of wastewater treatment facilities with fixed capacities. Considering the rapidly declining characteristics of shale gas wastewater production, these treatment facilities could remain largely underutilized after the first few months/years of production, making them less economically attractive. To maximize the capacity utilization of treatment facilities and further improve the economic performance of shale gas development, this study develops a systematic optimization framework, where the capacity strategy of conventional treatment facilities and utilization of the recent concept of modular manufacturing are both considered for flexible shale gas water management. The proposed mixed-integer linear programming (MILP) model simultaneously optimizes the design and planning of integrated shale gas and water supply chain, with a focus on capacity planning for both large-scale conventional treatment facilities and small-scale modular devices. A series of Marcellus-based case studies are performed to illustrate the applicability of the proposed model and provide general insights into the trade-offs between the multiple types of treatment facilities. The optimization results reveal that the combinatorial utilization of conventional facilities and modular devices for wastewater treatment (66% by conventional facilities and 34% by modular devices) brings 9.3% more reused water for other well development and 6.2% savings in water-related costs, compared to flexible management of only conventional facilities. Furthermore, this work suggests that taking modular device as auxiliary equipment for shale gas water management is most beneficial to increase the capacity utilization of treatment facilities and achieve a more economic and sustainable shale gas production system.

04 OIL SHALES AND TAR SANDS↗

DOE OSTI2019

Decomposing the Train-Scheduling Problem into Integer-Optimal Polytopes

This paper presents conditions for which the linear relaxation for the train-scheduling problem is integer optimal. These conditions are then used to identify how to partition a general problem’s feasible region into integer-optimal polytopes. Such an approach yields an extended formulation that contains far fewer binary variables. Our computational experiments show that this approach results in significant computational savings. Moreover, this approach scales well when the train-scheduling problem is modeled using smaller time increments, allowing for higher fidelity models to be solved without significantly increasing the required computational time.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

Planning Optimization for Inductively Charged On-demand Automated Electric Shuttles Project at Greenville, South Carolina

Wireless charging technology presents an ideal fit for autonomous electric vehicles for realizing a fully automated system (vehicle and charger). This paper presents a planning optimization analysis for a pilot project of in-route wireless charging infrastructure serving fixed-route on-demand shared automated electric shuttles (SAESs) at Greenville, South Carolina, USA. A single-objective non-linear mixed integer system planning optimization problem is formulated. A comprehensive cost model representing the overall inductively charged SAESs system is developed, considering road construction, power electronics and materials, traction battery, and installation costs. The optimization problem is solved to determine the best combination of the system key design parameters (number and allocations of wireless chargers, charging power level, track length and on-board battery capacity) that show the most cost-effective solution and allow the SAESs to achieve charge-sustaining operation. The planning platform incorporates representative simulated traffic data (driving speed and routes) for four SAESs in the Greenville using the Simulation of Urban Mobility tool. These data are fed to a vehicle powertrain model and a wireless charger power model to predict the battery power, energy and state-of-charge profiles, which are provided to the search algorithm to assess the design objectives under specific constraints. Finally, the results indicate that implementing high-power (100 kW) wireless charger at a few designated stops for fixed-route SAESs with the proper track length allows the vehicles to realize charge-sustaining operation, infinite range, and zero recharge downtime, with a significant reduction in the on-board battery (36%) and road coverage (69%), at minimum cost.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2016

Impulsive Control for Continuous-Time Markov Decision Processes: A Linear Programming Approach

In this paper, we investigate an optimization problem for continuous-time Markov decision processes with both impulsive and continuous controls. We consider the so-called constrained problem where the objective of the controller is to minimize a total expected discounted optimality criterion associated with a cost rate function while keeping other performance criteria of the same form, but associated with different cost rate functions, below some given bounds. Our model allows multiple impulses at the same time moment. The main objective of this work is to study the associated linear program defined on a space of measures including the occupation measures of the controlled process and to provide sufficient conditions to ensure the existence of an optimal control.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

Acceleration of GPU-based Krylov solvers via data transfer reduction

Krylov subspace iterative solvers are often the method of choice when solving large sparse linear systems. At the same time, hardware accelerators such as graphics processing units continue to offer significant floating point performance gains for matrix and vector computations through easy-to-use libraries of computational kernels. However, as these libraries are usually composed of a well optimized but limited set of linear algebra operations, applications that use them often fail to reduce certain data communications, and hence fail to leverage the full potential of the accelerator. In this study, we target the acceleration of Krylov subspace iterative methods for graphics processing units, and in particular the Biconjugate Gradient Stabilized solver that significant improvement can be achieved by reformulating the method to reduce data-communications through application-specific kernels instead of using the generic BLAS kernels, e.g. as provided by NVIDIA’s cuBLAS library, and by designing a graphics processing unit specific sparse matrix-vector product kernel that is able to more efficiently use the graphics processing unit’s computing power. Furthermore, we derive a model estimating the performance improvement, and use experimental data to validate the expected runtime savings. Finally, considering that the derived implementation achieves significantly higher performance, we assert that similar optimizations addressing algorithm structure, as well as sparse matrix-vector, are crucial for the subsequent development of high-performance graphics processing units accelerated Krylov subspace iterative methods.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Modeling the AC Power Flow Equations with Optimally Compact Neural Networks: Application to Unit Commitment

Nonlinear power flow constraints render a variety of power system optimization problems computationally intractable. Emerging research shows, however, that the nonlinear AC power flow equations can be successfully modeled using neural networks. These neural networks can be exactly transformed into mixed integer linear programs and embedded inside challenging optimization problems, thus replacing nonlinearities that are intractable for many applications with tractable piecewise linear approximations. Such approaches, though, suffer from an explosion of the number of binary variables needed to represent the neural network. Accordingly, this paper develops a technique for training an "optimally compact'' neural network, i.e., one that can represent the power flow equations with a sufficiently high degree of accuracy while still maintaining a tractable number of binary variables. We demonstrate the use of this neural network as an approximator of the nonlinear power flow equations by embedding it in the AC unit commitment problem, transforming the problem from a mixed integer nonlinear program into a more manageable mixed integer linear program. We use the 14-, 57-, and 89-bus networks as test cases and compare the AC-feasibility of commitment decisions resulting from the neural network, DC, and linearized power flow approximations. Our results show that the neural network model outperforms both the DC and linearized power flow approximations when embedded in the unit commitment problem. The neural network formulation most often selects a feasible unit commitment schedule, and furthermore, it only s

AC power flow↗

DOE OSTI2019

O(N) Quantum Molecular Dynamics (QMD) Algorithms, Code Requirements, Release Notes, and Library Deployment

The Exascale Computing Project (ECP) Co-design Center for Particle Applications (CoPA) is addressing the challenges for particle applications to run on upcoming exascale computing architectures. This includes short- and long-range molecular dynamics (MD), particle-in-cell (PIC), and quantum molecular dynamics (QMD). This document addresses $\mathcal{O}(N)$ QMD. The goal of this CoPA team is to develop $\mathcal{O}(N)$ linear scaling methods for QMD optimized for new and next generation architectures. This will provide the capability to simulate larger systems and run for longer timeframes than is possible today. Focus is initially on the density matrix construction. This requires efficient matrix formats and linear algebra operations for distributed architectures. A significant reduction in the wallclock time for an MD timestep is necessary to achieve practical large scale QMD. Equally challenging is to develop scalable distributed implementations. This requires the exploration of efficient data formats (dense, sparse, etc.), data decomposition and distribution across compute nodes using block- and graph-based methods. Traditional programming models such as MPI/OpenMP, hybrid MPI/OpenMP/Accelerator, as well as asynchronous task-based models will be explored to achieve maximum parallelism. Parallelism at the level of a matrix operation, solver, and/or application needs to be explored to gain the most benefit on new and emerging architectures. This report serves as a “living document” of the additions and enhancements throughout the ECP CoPA project for $\mathcal{O}(N)$ QMD. The following sections address the applications we are working with, the quantum chemistry libraries (BML and PROGRESS), and our co-design exploration through the use of a proxy application.

36 MATERIALS SCIENCE↗

DOE OSTI2014

SU-E-T-462: Fixed-Jaw Optimization for Critical Structure Sparing in IMRT Treatment Planning: Beam Modeling Cautions for Non-Routine Use

Purpose: Multiple publications exist concerning fixed-jaw utilization to avoid linac carriage shifts and reduce intensity modulated radiotherapy (IMRT) treatment times. The purpose of this work is to demonstrate delivery QA discrepancies and illustrate the need for improved treatment planning system (TPS) commissioning for non-routine use. Methods: A 6cm diameter spherical target was delineated on a virtual phantom containing the Iba Matrixx linear array within the Varian Eclipse TPS. Optimization was performed for target coverage for the following 3 scenarios: a single open, zero degree field where the X and Y jaws completely cover the target; the same field using an asymmetric, fixed-jaw technique where the upper Y jaw does not cover the superior 2cm of the target; and both of the aforementioned directed at the target at 315 and 45 degree gantry angles, respectively. This final orientation was also irradiated on a linac for delivery analysis. A sarcoma patient case was also analyzed where the fixed jaw technique was utilized for kidney sparing. Results: The open beam results were as predicted but the fixed-jaw results demonstrate a pronounced fluence increase along the asymmetric, upper jaw. Analysis of the delivery of the combined beam plan Resultin 83% of pixels evaluated passing gamma criteria of 3%, 3mm DTA. Analysis for the sarcoma patient, in the plane of the shielded kidney, indicated 93% passing although the maximum dose discrepancies in this region were approximately 23%. Conclusion: Optimization within the target is routinely performed using MLC leaf-end characteristics. The fixed-jaw technique forces optimization of target coverage to utilize the penumbra profiles of the associated beamdefining jaw. If the profiles were collected using a common 0.125cc ionization chamber, the resolution may be insufficient resulting in a planvs.-delivery mismatch. It is recommended that high-resolution beam characteristics be considered when non-routine planning methods are utilized.

60 APPLIED LIFE SCIENCES↗