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At least 1,729 records · Page 96
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Diagnosing Barren Plateaus with Tools from Quantum Optimal Control

Variational Quantum Algorithms (VQAs) have received considerable attention due to their potential for achieving near-term quantum advantage. However, more work is needed to understand their scalability. One known scaling result for VQAs is barren plateaus, where certain circumstances lead to exponentially vanishing gradients. It is common folklore that problem-inspired ansatzes avoid barren plateaus, but in fact, very little is known about their gradient scaling. In this work we employ tools from quantum optimal control to develop a framework that can diagnose the presence or absence of barren plateaus for problem-inspired ansatzes. Such ansatzes include the Quantum Alternating Operator Ansatz (QAOA), the Hamiltonian Variational Ansatz (HVA), and others. With our framework, we prove that avoiding barren plateaus for these ansatzes is not always guaranteed. Specifically, we show that the gradient scaling of the VQA depends on the degree of controllability of the system, and hence can be diagnosed through the dynamical Lie algebra $\mathfrak{g}$ obtained from the generators of the ansatz. We analyze the existence of barren plateaus in QAOA and HVA ansatzes, and we highlight the role of the input state, as different initial states can lead to the presence or absence of barren plateaus. Taken together, our results provide a framework for trainability-aware ansatz design strategies that do not come at the cost of extra quantum resources. Moreover, we prove no-go results for obtaining ground states with variational ansatzes for controllable system such as spin glasses. Our work establishes a link between the existence of barren plateaus and the scaling of the dimension of $\mathfrak{g}$.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Optimization of the generator coordinate method with machine-learning techniques for nuclear spectra and neutrinoless double- β decay: Ridge regression for nuclei with axial deformation

The generator coordinate method (GCM) is an important tool of choice for modeling large-amplitude collective motion in atomic nuclei. The computational complexity of the GCM increases rapidly with the number of collective coordinates. It imposes a strong restriction on the applicability of the method. In this work, we propose a subspace-reduction algorithm that employs optimal statistical ML models as surrogates for exact quantum-number projection calculations for norm and Hamiltonian kernels. The model space of the original GCM is reduced to a subspace relevant for nuclear low energy spectra and the NME of ground state to ground state 0νββ decay based on the orthogonality condition (OC) and the energy-transition-orthogonality procedure (ENTROP), respectively. For simplicity, the polynomial ridge regression (RR) algorithm is used to learn the norm and Hamiltonian kernels of axially deformed configurations. The efficiency and accuracy of this algorithm are illustrated for 76 Ge and 76 Se by comparing results obtained using the optimal RR models to direct GCM calculations. The low-lying energy spectra of 76 Ge and 76 Se, as well as the 0νββ-decay NME between their ground states, are computed. Furthermore, the results show that the performance of the GCM+OC/ENTROP+RR is more robust than that of the GCM+RR alone, and the former can reproduce the results of the original GCM calculation accurately with a significantly reduced computational cost.

59 ≤ A ≤ 89↗
DOE OSTI2022

Evaluation of Optimal Net Load Management in Microgrids Using Hardware-in-the-Loop Simulation

This paper presents the performance evaluation of a net load management (NLM) engine that balances load and generation in an isolated community to power a critical facility after a grid interruption event (e.g., the loss of a large generation unit). This NLM engine is particularly important for microgrid systems because it provides a high-speed, cost-optimal control solution to coordinate grid-forming inverters and to dispatch grid-following inverters and deferrable loads in microgrid systems to enhance grid resilience and reliability. The NLM algorithm cost-optimally dispatches the grid-following inverters and deferrable loads based on the demanded power and load priorities, and the grid-forming inverters use droop control to form system voltages and share active and reactive power. A controller-hardware-in-the-loop platform is developed to evaluate the control performance of the NLM algorithm with two sequential contingency events of lost generation units. The experimental results indicate that the NLM engine can maintain system stability, achieve the targeted system voltage and frequency, and balance load and generation to serve the critical facility with improved system resilience and reliability.

grid-following inverter↗
DOE OSTI2022

Evaluation of Optimal Net Load Management in Microgrids Using Hardware-in-the-Loop Simulation

This presentation discusses the performance evaluation of a net load management (NLM) engine that balances load and generation in an isolated community to power a critical facility after a grid interruption event (e.g., the loss of a large generation unit). This NLM engine is particularly important for microgrid systems because it provides a high-speed, cost-optimal control solution to coordinate grid-forming inverters and to dispatch grid-following inverters and deferrable loads in microgrid systems to enhance grid resilience and reliability. The NLM algorithm cost-optimally dispatches the grid-following inverters and deferrable loads based on the demanded power and load priorities, and the grid-forming inverters use droop control to form system voltages and share active and reactive power. A controller-hardware-in-the-loop platform is developed to evaluate the control performance of the NLM algorithm with two sequential contingency events of lost generation units. The experimental results indicate that the NLM engine can maintain system stability, achieve the targeted system voltage and frequency, and balance load and generation to serve the critical facility with improved system resilience and reliability.

droop control↗
DOE OSTI2021

A primal–dual algorithm for risk minimization

In this paper, we develop an algorithm to efficiently solve risk-averse optimization problems posed in reflexive Banach space. Such problems often arise in many practical applications as, e.g., optimization problems constrained by partial differential equations with uncertain inputs. Unfortunately, for many popular risk models including the coherent risk measures, the resulting risk-averse objective function is nonsmooth. Here, this lack of differentiability complicates the numerical approximation of the objective function as well as the numerical solution of the optimization problem. To address these challenges, we propose a primal–dual algorithm for solving large-scale nonsmooth risk-averse optimization problems. This algorithm is motivated by the classical method of multipliers and by epigraphical regularization of risk measures. As a result, the algorithm solves a sequence of smooth optimization problems using derivative-based methods. We prove convergence of the algorithm even when the subproblems are solved inexactly and conclude with numerical examples demonstrating the efficiency of our method.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1989

Multiplier-continuation algorthms for constrained optimization

Several path following algorithms based on the combination of three smooth penalty functions, the quadratic penalty for equality constraints and the quadratic loss and log barrier for inequality constraints, their modern counterparts, augmented Lagrangian or multiplier methods, sequential quadratic programming, and predictor-corrector continuation are described. In the first phase of this methodology, one minimizes the unconstrained or linearly constrained penalty function or augmented Lagrangian. A homotopy path generated from the functions is then followed to optimality using efficient predictor-corrector continuation methods. The continuation steps are asymptotic to those taken by sequential quadratic programming which can be used in the final steps. Numerical test results show the method to be efficient, robust, and a competitive alternative to sequential quadratic programming.

Lundberg, Bruce N.↗
DOE OSTI2021

Sensor System and Observer Algorithm Co-Design For Modern Internal Combustion Engine Air Management Based on H2 Optimization

This paper outlines a novel sensor selection and observer design algorithm for linear time-invariant systems with both process and measurement noise based on H 2 optimization to optimize the tradeoff between the observer error and the number of required sensors. The optimization problem is relaxed to a sequence of convex optimization problems that minimize the cost function consisting of the H 2 norm of the observer error and the weighted l 1 norm of the observer gain. An LMI formulation allows for efficient solution via semi-definite programing. The approach is applied here, for the first time, to a turbo-charged spark-ignited engine using exhaust gas circulation to determine the optimal sensor sets for real-time intake manifold burnt gas mass fraction estimation. Simulation with the candidate estimator embedded in a high fidelity engine GT-Power model demonstrates that the optimal sensor sets selected using this algorithm have the best H 2 estimation performance. Sensor redundancy is also analyzed based on the algorithm results. This algorithm is applicable for any type of modern internal combustion engines to reduce system design time and experimental efforts typically required for selecting optimal sensor sets.

Zhang, Xu↗
NASA NTRS1990

Execution time supports for adaptive scientific algorithms on distributed memory machines

Optimizations are considered that are required for efficient execution of code segments that consists of loops over distributed data structures. The PARTI (Parallel Automated Runtime Toolkit at ICASE) execution time primitives are designed to carry out these optimizations and can be used to implement a wide range of scientific algorithms on distributed memory machines. These primitives allow the user to control array mappings in a way that gives an appearance of shared memory. Computations can be based on a global index set. Primitives are used to carry out gather and scatter operations on distributed arrays. Communications patterns are derived at runtime, and the appropriate send and receive messages are automatically generated.

Berryman, Harry↗
NASA NTRS1996

An Optimal Order Nonnested Mixed Multigrid Method for Generalized Stokes Problems

A multigrid algorithm is developed and analyzed for generalized Stokes problems discretized by various nonnested mixed finite elements within a unified framework. It is abstractly proved by an element-independent analysis that the multigrid algorithm converges with an optimal order if there exists a 'good' prolongation operator. A technique to construct a 'good' prolongation operator for nonnested multilevel finite element spaces is proposed. Its basic idea is to introduce a sequence of auxiliary nested multilevel finite element spaces and define a prolongation operator as a composite operator of two single grid level operators. This makes not only the construction of a prolongation operator much easier (the final explicit forms of such prolongation operators are fairly simple), but the verification of the approximate properties for prolongation operators is also simplified. Finally, as an application, the framework and technique is applied to seven typical nonnested mixed finite elements.

Deng, Qingping↗
NASA NTRS1997

Ocean Observations with EOS/MODIS: Algorithm Development and Post Launch Studies

Significant accomplishments made during the present reporting period are as follows: (1) We developed a new method for identifying the presence of absorbing aerosols and, simultaneously, performing atmospheric correction. The algorithm consists of optimizing the match between the top-of-atmosphere radiance spectrum and the result of models of both the ocean and aerosol optical properties; (2) We developed an algorithm for providing an accurate computation of the diffuse transmittance of the atmosphere given an aerosol model. A module for inclusion into the MODIS atmospheric-correction algorithm was completed; (3) We acquired reflectance data for oceanic whitecaps during a cruise on the RV Ka'imimoana in the Tropical Pacific (Manzanillo, Mexico to Honolulu, Hawaii). The reflectance spectrum of whitecaps was found to be similar to that for breaking waves in the surf zone measured by Frouin, Schwindling and Deschamps, however, the drop in augmented reflectance from 670 to 860 nm was not as great, and the magnitude of the augmented reflectance was significantly less than expected; and (4) We developed a method for the approximate correction for the effects of the MODIS polarization sensitivity. The correction, however, requires adequate characterization of the polarization sensitivity of MODIS prior to launch.

Gordon, Howard R.↗
DOE OSTI2024

Benchmarking Optimizers for Qumode State Preparation with Variational Quantum Algorithms

Quantum state preparation involves preparing a target state from an initial system, a process integral to applications such as quantum machine learning and solving systems of linear equations. Recently, there has been a growing interest in qumodes due to advancements in the field and their potential applications. However there is a notable gap in the literature specifically addressing this area. This paper aims to bridge this gap by providing performance benchmarks of various optimizers used in state preparation with Variational Quantum Algorithms. We conducted extensive testing across multiple scenarios, including different target states, both ideal and sampling simulations, and varying numbers of basis gate layers. Our evaluations offer insights into the complexity of learning each type of target state and demonstrate that some optimizers perform better than others in this context. Notably, the Powell optimizer was found to be exceptionally robust against sampling errors, making it a preferred choice in scenarios prone to such inaccuracies. Additionally, the Simultaneous Perturbation Stochastic Approximation optimizer was distinguished for its efficiency and ability to handle increased parameter dimensionality effectively.

Kan, Shuwen [Fordham University]↗
NASA NTRS1979

Improvement of scanning radiometer performance by digital reference averaging

Most radiometers utilize a calibration technique in which measurements of a known reference are subtracted from measurements of an unknown source so that common-mode bias errors are cancelled. When a radiometer is scanned over a varying scene, it produces a sequence of outputs, each being proportional to the difference between the reference and the corresponding input. A reference averaging technique is presented that employs a simple digital algorithm which exploits the asymmetry between the time-variable scene inputs and the nominally constant reference input by averaging many reference measurements to decrease the statistical uncertainty in the reference value. This algorithm is, therefore, optimized by an asymmetric chopping sequence in which the scene is viewed for more than one-half of the duty cycle (unlike the analog Dicke technique). Reference averaging algorithms are well within the capabilities of small microprocessors. Although this paper develops the technique for microwave radiometry, it may be beneficial for any system which measures a large number of unknowns relative to a known reference in the presence of slowly varying common-mode errors.

Bremer, J. C.↗
NASA NTRS2004

Applying a Genetic Algorithm to Reconfigurable Hardware

This paper investigates the feasibility of applying genetic algorithms to solve optimization problems that are implemented entirely in reconfgurable hardware. The paper highlights the pe$ormance/design space trade-offs that must be understood to effectively implement a standard genetic algorithm within a modem Field Programmable Gate Array, FPGA, reconfgurable hardware environment and presents a case-study where this stochastic search technique is applied to standard test-case problems taken from the technical literature. In this research, the targeted FPGA-based platform and high-level design environment was the Starbridge Hypercomputing platform, which incorporates multiple Xilinx Virtex II FPGAs, and the Viva TM graphical hardware description language.

Wells, B. Earl↗
DOE OSTI2023

Pressurized-Water Reactor Core Design Demonstration with Genetic Algorithm Based Multi-Objective Plant Fuel Reload Optimization Platform

LWRS M3 milestone report due September 15, 2023. This report summarizes development and demonstration activities of PRLO optimization platform built in Risk Analysis and Virtual ENviroment (RAVEN), specifically: (1) Improvement of multi-objective non-dominated sorting genetic algorithm II (NSGA-II) to handle large size of objectives and constraints, (2) Demonstration of pressurized water reactor core design with NSGA-II multi-objective optimization platform, and (3) Single-objective optimized core design including system analysis and fuel performance feedback.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2022

LINAC OPTICS OPTIMIZATION WITH MULTI-OBJECTIVE OPTIMIZATION

The beamline design of recirculating linacs requires special attention to avoid beam instabilities due to RF wakefields. A proposed high-energy, multi-pass energy recovery demonstration at CEBAF uses a low beam current. Stronger focusing at lower energies is necessary to avoid beam breakup(BBU) instabilities, even with this small beam current. The CEBAF linac optics optimization balances over-focusing at higher energies and beta excursions at lower energies. Using proper mathematical expressions, linac optics optimization can be achieved with evolutionary algorithms. Here, we present the optimization process of North Linac optics using multi-objective optimization.

Neththikumara, I.↗
NASA NTRS1988

Near-optimal output feedback regulation of ill-conditioned linear systems

A two-time scale approximation for the linear quadratic optimal output feedback regulator program is examined. Necessary conditions for optimality, as well as an algorithm for computing locally near-optimal gains are derived. If it is assumed that the slow and fast subsystem initial conditions are uniformly distributed, optimal gains for the two-time-scale problem provide a second-order approximation to optimal closed-loop performance in the unperturbed system. This is verified with a numerical example.

Moerder, Daniel D.↗
NASA NTRS1993

Rotor design optimization using a free wake analysis

The aim of this effort was to develop a comprehensive performance optimization capability for tiltrotor and helicopter blades. The analysis incorporates the validated EHPIC (Evaluation of Hover Performance using Influence Coefficients) model of helicopter rotor aerodynamics within a general linear/quadratic programming algorithm that allows optimization using a variety of objective functions involving the performance. The resulting computer code, EHPIC/HERO (HElicopter Rotor Optimization), improves upon several features of the previous EHPIC performance model and allows optimization utilizing a wide spectrum of design variables, including twist, chord, anhedral, and sweep. The new analysis supports optimization of a variety of objective functions, including weighted measures of rotor thrust, power, and propulsive efficiency. The fundamental strength of the approach is that an efficient search for improved versions of the baseline design can be carried out while retaining the demonstrated accuracy inherent in the EHPIC free wake/vortex lattice performance analysis. Sample problems are described that demonstrate the success of this approach for several representative rotor configurations in hover and axial flight. Features that were introduced to convert earlier demonstration versions of this analysis into a generally applicable tool for researchers and designers is also discussed.

Quackenbush, Todd R.↗
NASA NTRS1992

An analytic model for footprint dispersions and its application to mission design

This is the final report on our recent research activities that are complementary to those conducted by our colleagues, Professor Farrokh Mistree and students, in the context of the Taguchi method. We have studied the mathematical model that forms the basis of the Simulation and Optimization of Rocket Trajectories (SORT) program and developed an analytic method for determining mission reliability with a reduced number of flight simulations. This method can be incorporated in a design algorithm to mathematically optimize different performance measures of a mission, thus leading to a robust and easy-to-use methodology for mission planning and design.

Rao, J. R. Jagannatha↗