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At least 253 records · Page 14

Grover-QAOA for 3-SAT: quadratic speedup, fair-sampling, and parameter clustering

Abstract The SAT problem is a prototypical NP-complete problem of fundamental importance in computational complexity theory with many applications in science and engineering; as such, it has long served as an essential benchmark for classical and quantum algorithms. This study shows numerical evidence for a quadratic speedup of the Grover Quantum Approximate Optimization Algorithm (G-QAOA) over random sampling for finding all solutions to 3-SAT (All-SAT) and Max-SAT problems. G-QAOA is less resource-intensive and more adaptable for these problems than Grover’s algorithm, and it surpasses conventional QAOA in its ability to sample all solutions. We show these benefits by classical simulations of many-round G-QAOA on thousands of random 3-SAT instances. We also observe G-QAOA advantages on the IonQ Aria quantum computer for small instances, finding that current hardware suffices to determine and sample all solutions. Interestingly, a single-angle-pair constraint that uses the same pair of angles at each G-QAOA round greatly reduces the classical computational overhead of optimizing the G-QAOA angles while preserving its quadratic speedup. We also find parameter clustering of the angles. The single-angle-pair protocol and parameter clustering significantly reduce obstacles to classical optimization of the G-QAOA angles.

Zhang, Zewen (ORCID:000000032258613X)↗

Quantum approximate optimization of the long-range Ising model with a trapped-ion quantum simulator

Quantum computers and simulators may offer significant advantages over their classical counterparts, providing insights into quantum many-body systems and possibly improving performance for solving exponentially hard problems, such as optimization and satisfiability. Here, we report the implementation of a low-depth Quantum Approximate Optimization Algorithm (QAOA) using an analog quantum simulator. We estimate the ground-state energy of the Transverse Field Ising Model with long-range interactions with tunable range, and we optimize the corresponding combinatorial classical problem by sampling the QAOA output with high-fidelity, single-shot, individual qubit measurements. We execute the algorithm with both an exhaustive search and closed-loop optimization of the variational parameters, approximating the ground-state energy with up to 40 trapped-ion qubits. We benchmark the experiment with bootstrapping heuristic methods scaling polynomially with the system size. We observe, in agreement with numerics, that the QAOA performance does not degrade significantly as we scale up the system size and that the runtime is approximately independent from the number of qubits. We finally give a comprehensive analysis of the errors occurring in our system, a crucial step in the path forward toward the application of the QAOA to more general problem instances.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Development of Control System Functional Capabilities within the IES Plug-and-Play Simulation Environment

The concept of an Integrated Energy System (IES) is meant to combine different energy technologies in synergistic ways to achieve a more secure and economical energy supply. The RAVEN-based HYBRID framework is used to find the optimal installed capacity and the optimal economical dispatch of each component of the IES. A new RAVEN (Risk Analysis Virtual ENvironment) plugin for grid and capacity optimization (HERON) has been developed for optimizing the production variables of the IES given the demand profile. Currently, only the limits that affect the production variables and their corresponding time rates of change are considered (explicit constraints). However, other variables are additionally subject to constraints, but the associated limits are not accounted for (implicit constraints). In particular, for the power dispatch problem, the optimization algorithm takes into account the limits on the electrical power output and the corresponding hourly power variations but does not consider other constraints on process variables whose response effects the service life of the IES. This report describes a scheme that allows accounting for implicit constraints without increasing the size of the optimization problem. The Reference Governor (RG) algorithm is traditionally used for enforcing state and control constraints by modifying the set-point trajectories supplied to the feedback regulators. In our application, the RG is coupled within an iterative loop with the HERON-power dispatcher to generate optimal trajectories that ensure the operational constraints are met. A data-driven procedure to derive a representation of the dynamics of the controlled system was developed. First, the variables that represented the state of the system are selected (PCA-based approach), and then state-space representation matrices are derived from the collected measurements (DMDc algorithm). A preliminary version of the developed workflow based on Linear Time Invariant matrices was assessed by adopting a two-unit test case. More sophisticated versions of this workflow foreseeing the on-line derivation of system matrices will be deployed in FY 2021. Finally, a “plug-and-play” library of controllers and state observers was developed in Dymola. Some aspects of the current configuration of the IES unit components, e.g., the encapsulation of the control schemes into dedicated blocks, are consistent with the “plug-and-play” philosophy. Other features, e.g., the system buses collecting the input and the output variables, are not. For this reason, once listed and described the limits of the current configuration, necessary modifications to the plant model interface are presented. As a test-case, the interfaces of the SES model in the RAVEN-based HYBRID framework were reworked accordingly, and two different control schemes were applied to the same plant model.

24 POWER TRANSMISSION AND DISTRIBUTION↗

FY20 ASC IC L2 Milestone 7180: Performance Portability of SIERRA Mechanics Applications to ATS-1 and ATS-2. Executive Summary

The overall goal of this work was to accelerate simulations supporting the nuclear deterrence (ND) mission through improved performance of key algorithms in the ASC IC Sierra multi-physics application suite. This work focused on porting and optimizing algorithms for the graphics processing units (GPU) on the second ASC advanced technology system (ATS-2), while maintaining or improving performance on commodity technology systems (CTS) and ATS-1. Furthermore, these algorithmic developments used the ASC developed Kokkos performance portability abstraction library to maintain high performance across platforms using identical code, and enable sustainable reduced-cost migration and performance optimization to emerging hardware.

97 MATHEMATICS AND COMPUTING↗

Towards an Agent-Based Blackboard System for Reactor Design Optimization

The field of reactor design is rich with opportunities for applications of computational optimization algorithms; these applications can range from preliminary core design to reactor shuffling patterns. Many of these schemes rely on sets of previously generated solutions (sometimes referred to as “generations”) to inform future decisions. While it is important to build upon prior knowledge, this process requires a full generation of solutions to be formed before future solutions can be examined. Rather than relying on a generational scheme to perform an optimization, we propose using an agent-based approach in conjunction with a blackboard framework for performing reactor design optimizations. Utilizing an agent-based approach allows agents to perform tasks independently, while retaining the ability to build off of previous solutions. We develop an agent-based blackboard system (ABBS) for determining the Pareto front (PF) in sodium fast reactor design optimization problems and compared this with the Non-Dominated Sorting Genetic Algorithm II (NSGA-II). Our goal is to evaluate the viability of the ABBS in producing a PF that is comparable with the NSGA-II algorithm. The design space consists of the fuel height, fuel smear, and plutonium fraction in the core, and we seek to minimize the reactivity swing and plutonium mass, while maximizing the burnup. The diversity, coverage, and spread of the PFs generated by the two methods are examined, and the ABBS is able to converge to the same PF as the NSGA-II algorithm. These results show that the ABBS is able to find optimal designs that are similar to those found by the NSGA-II algorithm. We conclude our study by applying the ABBS to the design of a sodium-cooled fast reactor to dispose of weapons-grade plutonium. The ABBS finds a core design that can burn upwards of 17.5 kg of weapons-grade plutonium per year and degrade an additional 195 kg of weapons-grade plutonium per year into non-weapons-grade material.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Combining the synergistic control capabilities of modeling and experiments: Illustration of finding a minimum-time quantum objective

A common way to manipulate a quantum system, for example spins or artificial atoms, is to use properly tailored control pulses. In order to accomplish quantum information tasks before coherence is lost, it is crucial to implement the control in the shortest possible time. Here we report the near time-optimal preparation of a Bell state with fidelity higher than 99% in an NMR experiment, which is feasible by combining the synergistic capabilities of modeling and experiments operating in tandem. In this work, the pulses preparing the Bell state are found by experiments that are recursively assisted with a gradient-based optimization algorithm working with a model. Thus, we exploit the interplay between model-based numerical optimal design and experimental-based learning control. Utilizing the balanced synergism between the dual approaches, as dictated by the case specific capabilities of each approach, should have broad applications for accelerating the search for optimal quantum controls.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Intelligent Partitioning based Fully Parallel AC Security-Constrained Optimal Power Flow

Today’s power grid is becoming more diverse and integrated with high-level distributed energy resources and smart control technologies that is creating a new set of grid management challenges in terms of large-scale, nonlinear, and non-convex problem modeling, complex and time-consuming computation, as well as difficult uncertainty handling. This project focused on solving a challenging multi-period security-constrained generation scheduling problem, which is of great importance for maximizing the social welfare of real-time dispatch, day-ahead market, as well as weekly planning of power systems. Our developed software explored parallel optimization algorithms for complex and realistic power system models, and develop fast, efficient, and robust grid optimization solutions on the high-performance computing platform that will enable increased grid economics, flexibility, resilience, as well as energy security in the United States.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Testing Surrogate-Based Optimization with the Fortified Branin-Hoo Extended to Four Dimensions

Some popular functions used to test global optimization algorithms have multiple local optima, all with the same value, making them all global optima. It is easy to make them more challenging by fortifying them via adding a localized bump at the location of one of the optima. In previous work the authors illustrated this for the Branin-Hoo function and the popular differential evolution algorithm, showing that the fortified Branin-Hoo required an order of magnitude more function evaluations. This paper examines the effect of fortifying the Branin-Hoo function on surrogate- based optimization, which usually proceeds by adaptive sampling. Two algorithms are considered. The EGO algorithm, which is based on a Gaussian process (GP) and an algorithm based on radial basis functions (RBF). EGO is found to be more frugal in terms of the number of required function evaluations required to identify the correct basin, but it is expensive to run on a desktop, limiting the number of times the runs could be repeated to establish sound statistics on the number of required function evaluations. The RBF algorithm was cheaper to run, providing more sound statistics on performance. A four-dimensional version of the Branin-Hoo function was introduced in order to assess the effect of dimensionality. Furthermore, it was found that the difference between the ordinary function and the fortified one was much more pronounced for the four-dimensional function compared to the two dimensional one.

97 MATHEMATICS AND COMPUTING↗

Optimization of a High Pressure Turbine Blade and Sector-Based Annular Rig Design for Supercritical CO2 Power Cycle Representative Testing

Abstract As part of the ongoing research into the design of hardware for zero emission cycles, a first-stage high-pressure turbine (HPT) blade is optimized for a 300 MWe supercritical CO2 (sCO2) power cycle using the surrogate-assisted genetic algorithm optimizer in Numeca FINE/Design three-dimensional with objectives of increasing efficiency and decreasing heat load to the blade. Supercritical CO2 property tables are constructed from NIST REFPROP data for the condensable gas simulation in FINE/Turbo. A detailed mesh sensitivity study is performed for a baseline design to identify the proper-grid refinement and efficiently allocate resources for the optimization. Seventy design variables are selected for the initial population generation. Self-organizing maps are then used to focus the design variables on the most important ones affecting the objective functions. The optimization results in approximately 3000 three-dimensional Reynolds Averaged Navier Stokes simulations of different blade shapes with increases in efficiency of up to 0.85% and decreases in heat load of 14%. Families of blade shapes are identified for experimental testing in an annular rig at the Purdue Experimental Turbine Aerothermal Laboratory. A design to adapt the annular cascade for testing optimized geometries is introduced, which features eccentric radius sectors allowing for scaled-up geometries of sCO2 optimized blade profiles to be tested at design cycle representative conditions at high Reynolds numbers in dry air. Analysis into the effects of Reynolds number, working fluid, and geometric relations are presented to prove the efficacy of the test method.

Engineering↗

Blade and Rim Seal Design of a First Stage High Pressure Turbine for a 300 MWe Supercritical CO2 Power Cycle

A first stage high-pressure turbine (HPT) blade is optimized for a 300 MWe supercritical CO2 (sCO2) power cycle using the surrogate-assisted genetic algorithm optimizer in Numeca FINE/Design 3D with objectives of increasing efficiency and decreasing heat load to the blade. The National Institute of Standards and Technology Reference Fluid Thermodynamic and Transport Properties Database (NIST REFPROP) [1] data for supercritical CO2 is formatted into tables of bicubic polynomial coefficients for use in condensable gas simulations in FINE/Turbo. Nearly 3000 unique shapes are evaluated via three-dimensional Reynolds Averaged Navier Stokes simulations, yielding increases in efficiency of up to 0.85 percentage points and decreases in heat load of 14%. A final blade, deemed the advanced blade, is chosen for future experimental analysis. Following this, a squealer tip optimization is performed on both the baseline and advanced blade designs. This optimization resulted in a performance gain of 1.25 points in efficiency and 15% reduction in tip heat load compared to the baseline flat tip design at the same clearance. In tandem, an optimization of the rotor-stator platform rim seal is performed using a parametrized geometry allowing for straight, meandering, and knife seal cavities. This multi-objective optimization focuses on decreasing the cooling mass flow and increasing the heat flux from the rotor and stator disk. The optimization resulted in cooling mass flow decreases of up to 26% while maintaining the average heat flux on the rim seal.

Tuite, Logan↗

Automated Identification of Molecular Crystals’ Packing Motifs

Packing motifs—patterns in how molecules orient relative to one another in a crystal structure—are an important concept in many subdisciplines of materials science because of correlations observed between specific packing motifs and properties of interest. That said, packing motif data sets have remained small and noisy due to intensive manual labeling processes and insufficient labeling schemes. The most prominent labeling algorithms calculate relative interplanar angles of nearest neighbor molecules to determine the packing motif of a molecular crystal, but this simple approach can fail when neighbors are naively sampled isotropically around the crystal structure. To remedy this issue, here we propose an optimization algorithm, which rotates the molecular crystal structure to find representative molecules that inform the packing motif. We package this algorithm into an automated framework—Autopack—which both optimally rotates the crystal structure and labels the packing motif based on the appropriate neighboring molecules. In this work, we detail the Autopack framework and its performance, which shows improvements compared to previous state-of-the-art labeling methods, providing the first quantitative point of comparison for packing motif labeling algorithms. Furthermore, using Autopack (available at https://ipo.llnl.gov/technologies/software/autopack), we perform the first large-scale study of potential relationships between chemicals’ compositions and packing motifs, which shows that these relationships are more complex than previously hypothesized from studies that used only tens of polycyclic aromatic hydrocarbon molecules. Autopack’s capabilities help pose next steps for crystal engineering research focusing not only on a molecule’s adoption of a specific packing motif but also on new structure–property relationships.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Minimum feature size control in level set topology optimization via density fields

A level set topology optimization approach that uses an auxiliary density field to nucleate holes during the optimization process and achieves minimum feature size control in optimized designs is explored. The level set field determines the solid-void interface and the density field describes the distribution of a fictitious porous material using the solid isotropic material with penalization. These fields are governed by two sets of independent optimization variables which are initially coupled using a penalty for hole nucleation. The strength of the density field penalization and projection is gradually increased during the optimization process to promote a 0-1 density distribution. In addition, a second penalty regulates the evolution of the density field in the void phase. The treatment of the density field combined with the second penalty mitigate the appearance of small design features. The minimum feature size of optimized designs is controlled by the radius of the linear filter applied to the density optimization variables. The structural response is predicted by the extended finite element method, the sensitivities by the adjoint method, and the optimization variables are updated by a gradient-based optimization algorithm. Numerical examples investigate the robustness of this approach with respect to algorithmic parameters and mesh refinement. The results show the applicability of the combined density level set topology optimization approach for both optimal hole nucleation and for minimum feature size control in 2D and 3D. This comes, however, at the cost of a more complex problem formulation and additional computational cost due to an increased number of optimization variables.

42 ENGINEERING↗

The DESC stellarator code suite Part 3: Quasi-symmetry optimization

The DESC stellarator optimization code takes advantage of advanced numerical methods to search the full parameter space much faster than conventional tools. Only a single equilibrium solution is needed at each optimization step thanks to automatic differentiation, which efficiently provides exact derivative information. A Gauss–Newton trust-region optimization method uses second-order derivative information to take large steps in parameter space and converges rapidly. With just-in-time compilation and GPU portability, high-dimensional stellarator optimization runs take orders of magnitude less computation time with DESC compared to other approaches. This paper presents the theory of the DESC fixed-boundary local optimization algorithm along with demonstrations of how to easily implement it in the code. Example quasi-symmetry optimizations are shown and compared to results from conventional tools. Three different forms of quasi-symmetry objectives are available in DESC, and their relative advantages are discussed in detail. In the examples presented, the triple product formulation yields the best optimization results in terms of minimized computation time and particle transport. This paper concludes with an explanation of how the modular code suite can be extended to accommodate other types of optimization problems.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Electromagnetic Design Optimization Integrated with Mechanical Stress Analysis of PM-Assisted Synchronous Reluctance Machine Topologies Enabled with a Blend of Magnets

Permanent Magnet-Assisted Synchronous Reluctance Machines (PMASynRM) provide a low-cost alternative to Surface PM Machines due to the use of relatively lower grades of rare-earth (RE) or RE-free magnets, as the performance degradation due to weaker magnets is compensated by the presence of reluctance torque. However, the weaker magnets suffer from a high risk of demagnetization, leading to unreliable motor operation. Using a blend of RE and RE-free magnets has the potential to overcome this issue. This paper proposes to blend different grades of various rare-earth (RE) and rare-earth-free (RE-free) magnets in six different combinations and utilizes them in two-layer and three-layer U-shaped PMASynRM topologies with both eight-pole and six-pole variations. The rotor of the various designs is then optimized using a differential evolution (DE) based optimization algorithm to obtain low-cost designs with reduced RE magnet volume and minimum demagnetization risk. The optimization of each design is also integrated with the evaluation of mechanical stresses in the rotor laminations so as to maintain the stresses below the material yield strength. Furthermore, the various performance metrics, such as toque–speed/power–speed characteristics, demagnetization, and efficiency maps, are evaluated for each of the optimized and mechanically feasible designs. A quantitative comparison of the various optimized designs is also obtained to highlight the various trade-offs. The results indicate the feasibility of meeting the baseline torque requirement across the entire speed range, even with a 100% reduction in RE magnet volume and less than 5% demagnetization risk, while achieving a cost reduction exceeding 50%. Moreover, the two-layer, eight-pole designs exhibit relatively higher performance, whereas the three-layer, eight-pole designs are found to be the most economical option.

design optimization↗

Optimizing the shape of photometric redshift distributions with clustering cross-correlations

We present an optimization method for the assignment of photometric galaxies to a chosen set of redshift bins. This is achieved by combining simulated annealing, an optimization algorithm inspired by solid-state physics, with an unsupervised machine learning method, a self-organizing map (SOM) of the observed colours of galaxies. Starting with a sample of galaxies that is divided into redshift bins based on a photometric redshift point estimate, the simulated annealing algorithm repeatedly reassigns SOM-selected subsamples of galaxies, which are close in colour, to alternative redshift bins. We optimize the clustering cross-correlation signal between photometric galaxies and a reference sample of galaxies with well-calibrated redshifts. Depending on the effect on the clustering signal, the reassignment is either accepted or rejected. By dynamically increasing the resolution of the SOM, the algorithm eventually converges to a solution that minimizes the number of mismatched galaxies in each tomographic redshift bin and thus improves the compactness of their corresponding redshift distribution. This method is demonstrated on the synthetic Legacy Survey of Space and Time cosmoDC2 catalogue. We find a significant decrease in the fraction of catastrophic outliers in the redshift distribution in all tomographic bins, most notably in the highest redshift bin with a decrease in the outlier fraction from 57 percent to 16 percent.

79 ASTRONOMY AND ASTROPHYSICS↗

Integrated Transmission-Distribution Multi-Period Switching for Wildfire Risk Mitigation: Improving Speed and Scalability with Distributed Optimization: Preprint

With increasingly severe wildfire conditions driven by climate change, utilities must manage the risk of wildfire ignitions from electric power lines. During "public safety power shutoff'" events, utilities de-energize power lines to reduce wildfire ignition risk, which may result in load shedding. Distributed energy resources provide flexibility that can help support the system to reduce load shedding when lines are de-energized. We investigate a coordinated transmission-distribution optimization problem that balances wildfire risk mitigation and load shedding. We model distribution systems that include battery energy storage systems which may support loads when transmission lines are de-energized. This multi-period integrated transmission-distribution optimal switching problem jointly optimizes line switching decisions, the generators' setpoints, load shedding, and the batteries' states of charge, resulting in significant computational challenges. To improve scalability, we decompose the problem over both space and time and apply a distributed optimization algorithm. Using a large-scale synthetic California test case with realistic distribution models and real wildfire risk data, we show that distributed optimization can solve large-scale multi-period switching problems that are otherwise intractable for centralized solvers. We also discuss challenges and future directions for improving the distributed algorithm's convergence performance as the number of time periods increases.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Image Reconstruction from Sparse-view Data Acquired with Portable X-ray Devices

• Portable X-ray systems enable on-site 3D imaging for non-invasive inspection of suspicious packages and explosives. • Existing reconstruction algorithms (e.g., FDK or Feldkamp, Davis and Kress) require hundreds of projections over 360 degrees. • Sparse-view scan reduces scanning time and setup effort, making it ideal for field use in timecritical scenarios. • Existing reconstruction algorithms introduce severe artifacts when applied to sparse-view data. • We developed a total variation (TV)-based optimization algorithm for yielding 3D images from sparse-view data collected with our portable X-ray imaging system.

Xia, Dan [University of Chicago, Chicago, IL]↗