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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Quantum algorithms from fluctuation theorems: Thermal-state preparation

Fluctuation theorems provide a correspondence between properties of quantum systems in thermal equilibrium and a work distribution arising in a non-equilibrium process that connects two quantum systems with Hamiltonians H 0 and H 1 = H 0 + V. Building upon these theorems, we present a quantum algorithm to prepare a purification of the thermal state of H 1 at inverse temperature β ≥ 0 starting from a purification of the thermal state of H 0 . The complexity of the quantum algorithm, given by the number of uses of certain unitaries, is $\mathcal{O}$ (e β(ΔA - w l )/2 ), where ΔA is the free-energy difference between H 1 and H 0 , and w l is a work cutoff that depends on the properties of the work distribution and the approximation error ϵ > 0. If the non-equilibrium process is trivial, this complexity is exponential i β∥V∥, where ∥V∥ is the spectral norm of V. This represents a significant improvement of prior quantum algorithms that have complexity exponential in β∥H 1 ∥ in the regime where ∥V∥$\ll$ ∥H 1 ∥. The dependence of the complexity in ϵ varies according to the structure of the quantum systems. It can be exponential in 1/ϵ in general, but we show it to be sublinear in 1/ϵ if H 0 and H 1 commute, or polynomial in 1/ϵ if H 0 and H 1 are local spin systems. The possibility of applying a unitary that drives the system out of equilibrium allows one to increase the value of w l and improve the complexity even further. To this end, we analyze the complexity for preparing the thermal state of the transverse field Ising model using different non-equilibrium unitary processes and see significant complexity improvements.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Real-Time Krylov Theory for Quantum Computing Algorithms

Quantum computers provide new avenues to access ground and excited state properties of systems otherwise difficult to simulate on classical hardware. New approaches using subspaces generated by real-time evolution have shown efficiency in extracting eigenstate information, but the full capabilities of such approaches are still not understood. In recent work, we developed the variational quantum phase estimation (VQPE) method, a compact and efficient real-time algorithm to extract eigenvalues on quantum hardware. Here we build on that work by theoretically and numerically exploring a generalized Krylov scheme where the Krylov subspace is constructed through a parametrized real-time evolution, which applies to the VQPE algorithm as well as others. We establish an error bound that justifies the fast convergence of our spectral approximation. We also derive how the overlap with high energy eigenstates becomes suppressed from real-time subspace diagonalization and we visualize the process that shows the signature phase cancellations at specific eigenenergies. We investigate various algorithm implementations and consider performance when stochasticity is added to the target Hamiltonian in the form of spectral statistics. To demonstrate the practicality of such real-time evolution, we discuss its application to fundamental problems in quantum computation such as electronic structure predictions for strongly correlated systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Encoding trade-offs and design toolkits in quantum algorithms for discrete optimization: coloring, routing, scheduling, and other problems

Challenging combinatorial optimization problems are ubiquitous in science and engineering. Several quantum methods for optimization have recently been developed, in different settings including both exact and approximate solvers. Addressing this field of research, this manuscript has three distinct purposes. First, we present an intuitive method for synthesizing and analyzing discrete (i.e., integer-based) optimization problems, wherein the problem and corresponding algorithmic primitives are expressed using a discrete quantum intermediate representation (DQIR) that is encoding-independent. This compact representation often allows for more efficient problem compilation, automated analyses of different encoding choices, easier interpretability, more complex runtime procedures, and richer programmability, as compared to previous approaches, which we demonstrate with a number of examples. Second, we perform numerical studies comparing several qubit encodings; the results exhibit a number of preliminary trends that help guide the choice of encoding for a particular set of hardware and a particular problem and algorithm. Our study includes problems related to graph coloring, the traveling salesperson problem, factory/machine scheduling, financial portfolio rebalancing, and integer linear programming. Third, we design low-depth graph-derived partial mixers (GDPMs) up to 16-level quantum variables, demonstrating that compact (binary) encodings are more amenable to QAOA than previously understood. We expect this toolkit of programming abstractions and low-level building blocks to aid in designing quantum algorithms for discrete combinatorial problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Variational Quantum Algorithms for Semidefinite Programming

A semidefinite program (SDP) is a particular kind of convex optimization problem with applications in operations research, combinatorial optimization, quantum information science, and beyond. In this work, we propose variational quantum algorithms for approximately solving SDPs. For one class of SDPs, we provide a rigorous analysis of their convergence to approximate locally optimal solutions, under the assumption that they are weakly constrained (i.e., N$\gg$M, where N is the dimension of the input matrices and M is the number of constraints). We also provide algorithms for a more general class of SDPs that requires fewer assumptions. Finally, we numerically simulate our quantum algorithms for applications such as MaxCut, and the results of these simulations provide evidence that convergence still occurs in noisy settings.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

HamLib: A library of Hamiltonians for benchmarking quantum algorithms and hardware

In order to characterize and benchmark computational hardware, software, and algorithms, it is essential to have many problem instances on-hand. This is no less true for quantum computation, where a large collection of real-world problem instances would allow for benchmarking studies that in turn help to improve both algorithms and hardware designs. To this end, here we present a large dataset of qubit-based quantum Hamiltonians. The dataset, called HamLib (for Hamiltonian Library), is freely available online and contains problem sizes ranging from 2 to 1000 qubits. HamLib includes problem instances of the Heisenberg model, Fermi-Hubbard model, Bose-Hubbard model, molecular electronic structure, molecular vibrational structure, MaxCut, Max- k -SAT, Max- k -Cut, QMaxCut, and the traveling salesperson problem. The goals of this effort are (a) to save researchers time by eliminating the need to prepare problem instances and map them to qubit representations, (b) to allow for more thorough tests of new algorithms and hardware, and (c) to allow for reproducibility and standardization across research studies.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Well-Balanced, Conservative Finite Difference Algorithm for Atmospheric Flows

The numerical simulation of meso-, convective-, and microscale atmospheric flows requires the solution of the Euler or the Navier-Stokes equations. Nonhydrostatic weather prediction algorithms often solve the equations in terms of derived quantities such as Exner pressure and potential temperature (and are thus not conservative) and/or as perturbations to the hydrostatically balanced equilibrium state. This paper presents a well-balanced, conservative finite difference formulation for the Euler equations with a gravitational source term, where the governing equations are solved as conservation laws for mass, momentum, and energy. Preservation of the hydrostatic balance to machine precision by the discretized equations is essential because atmospheric phenomena are often small perturbations to this balance. The proposed algorithm uses the weighted essentially nonoscillatory and compact-reconstruction weighted essentially nonoscillatory schemes for spatial discretization that yields high-order accurate solutions for smooth flows and is essentially nonoscillatory across strong gradients; however, the well-balanced formulation may be used with other conservative finite difference methods. The performance of the algorithm is demonstrated on test problems as well as benchmark atmospheric flow problems, and the results are verified with those in the literature.

Ghosh, Debojyoti↗
DOE OSTI2019

Do Epistemic Uncertainties Allow for Replacing Microstructural Experiments with Reconstruction Algorithms?

A novel problem in computational materials modeling is addressed: “Are the computational microstructure reconstruction techniques reliable enough to replace experiments?” Here, “reliable” computations are associated with producing “expected” reconstructions that are adequately close to the experimental data. The output of computational techniques can deviate from the experimental measurements because of the epistemic uncertainties in the algorithms. In this work, an analytical formulation for quantification of epistemic uncertainties in a microstructure reconstruction algorithm based on Markov random field is presented. The method is used to predict the large-scale spatial distribution of a microstructure given an experimental input measured over a small spatial domain. However, small variations are observed on the microstructural features of the synthesized samples due to the Markov random field algorithm. The proposed analytical technique aims to quantify these uncertainties and estimate their propagation to the macroscale material properties to provide a significant understanding on how reliable it is to replace the experiments with the Markov random field model to predict microstructural maps over large spatial domains.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

CLUE: A Fast Parallel Clustering Algorithm for High Granularity Calorimeters in High-Energy Physics

One of the challenges of high granularity calorimeters, such as that to be built to cover the endcap region in the CMS Phase-2 Upgrade for HL-LHC, is that the large number of channels causes a surge in the computing load when clustering numerous digitized energy deposits (hits) in the reconstruction stage. In this article, we propose a fast and fully parallelizable density-based clustering algorithm, optimized for high-occupancy scenarios, where the number of clusters is much larger than the average number of hits in a cluster. The algorithm uses a grid spatial index for fast querying of neighbors and its timing scales linearly with the number of hits within the range considered. We also show a comparison of the performance on CPU and GPU implementations, demonstrating the power of algorithmic parallelization in the coming era of heterogeneous computing in high-energy physics.

Rovere, Marco↗
DOE OSTI2024

Assessment of Envelope- and Machine Learning-Based Electrical Fault Type Detection Algorithms for Electrical Distribution Grids

This study introduces envelope- and machine learning (ML)-based electrical fault type detection algorithms for electrical distribution grids, advancing beyond traditional logic-based methods. The proposed detection model involves three stages: anomaly area detection, ML-based fault presence detection, and ML-based fault type detection. Initially, an envelope-based detector identifying the anomaly region was improved to handle noisier power grid signals from meters. The second stage acts as a switch, detecting the presence of a fault among four classes: normal, motor, switching, and fault. Finally, if a fault is detected, the third stage identifies specific fault types. This study explored various feature extraction methods and evaluated different ML algorithms to maximize prediction accuracy. The performance of the proposed algorithms is tested in an emulated software–hardware electrical grid testbed using different sample rate meters/relays, such as SEL735, SEL421, SEL734, SEL700GT, and SEL351S near and far from an inverter-based photovoltaic array farm. The performance outcomes demonstrate the proposed model’s robustness and accuracy under realistic conditions.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Optimal Operation of PV Sources in DC Grids for Improving Technical, Economical, and Environmental Conditions by Using Vortex Search Algorithm and a Matrix Hourly Power Flow

This document presents a master–slave methodology for solving the problem of optimal operation of photovoltaic (PV) distributed generators (DGs) in direct current (DC) networks. This problem was modeled using a nonlinear programming model (NLP) that considers the minimization of three different objective functions in a daily operation of the system. The first one corresponds to the minimization of the total operational cost of the system, including the energy purchasing cost to the conventional generators and maintenance costs of the PV sources; the second objective function corresponds to the reduction of the energy losses associated with the transport of energy in the network, and the third objective function is related to the minimization of the total emissions of CO2 by the conventional generators installed on the DC grid. The minimization of these objective functions is achieved by using a master–slave optimization approach through the application of the Vortex Search algorithm combined with a matrix hourly power flow. To evaluate the effectiveness and robustness of the proposed approach, two test scenarios were used, which correspond to a grid-connected and a standalone network located in two different regions of Colombia. The grid-connected system emulates the behavior of the solar resource and power demand of the city of Medellín-Antioquia, and the standalone network corresponds to an adaptation of the generation and demand curves for the municipality of Capurganá-Choco. A numerical comparison was performed with four optimization methodologies reported in the literature: particle swarm optimization, multiverse optimizer, crow search algorithm, and salp swarm algorithm. The results obtained demonstrate that the proposed optimization approach achieved excellent solutions in terms of response quality, repeatability, and processing times.

14 SOLAR ENERGY↗
DOE OSTI2021

Displacement Analysis of Geothermal Field Based on PSInSAR And SOM Clustering Algorithms A Case Study of Brady Field, Nevada—USA

The availability of free and high temporal resolution satellite data and advanced SAR techniques allows us to analyze ground displacement cost-effectively. Our aim was to properly define subsidence and uplift areas to delineate a geothermal field and perform time-series analysis to identify temporal trends. A Persistent Scatterer Interferometry (PSI) algorithm was used to estimate vertical displacement in the Brady geothermal field located in Nevada by analyzing 70 Sentinel-1A Synthetic-Aperture Radar (SAR) images, between January 2017 and December 2019. To classify zones affected by displacement, an unsupervised Self-Organizing Map (SOM) algorithm was applied to classify points based on their behavior in time, and those clusters were used to determine subsidence, uplift, and stable regions automatically. Finally, time-series analysis was applied to the clustered data to understand the inflection dates. The maximum subsidence is –19 mm/yr with an average value of –6 mm/yr within the geothermal field. The maximum uplift is 14 mm/yr with an average value of 4 mm/yr within the geothermal field. The uplift occurred on the NE of the field, where the injection wells are located. On the other hand, subsidence is concentrated on the SW of the field where the production wells are located. The coupling of the PSInSAR and the SOM algorithms was shown to be effective in analyzing the direction and pattern of the displacements observed in the field.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2013

Indoor Localization Algorithms for an Ambulatory Human Operated 3D Mobile Mapping System

Indoor localization and mapping is an important problem with many applications such as emergency response, architectural modeling, and historical preservation. In this paper, we develop an automatic, off-line pipeline for metrically accurate, GPS-denied, indoor 3D mobile mapping using a human-mounted backpack system consisting of a variety of sensors. There are three novel contributions in our proposed mapping approach. First, we present an algorithm which automatically detects loop closure constraints from an occupancy grid map. In doing so, we ensure that constraints are detected only in locations that are well conditioned for scan matching. Secondly, we address the problem of scan matching with poor initial condition by presenting an outlier-resistant, genetic scan matching algorithm that accurately matches scans despite a poor initial condition. Third, we present two metrics based on the amount and complexity of overlapping geometry in order to vet the estimated loop closure constraints. By doing so, we automatically prevent erroneous loop closures from degrading the accuracy of the reconstructed trajectory. The proposed algorithms are experimentally verified using both controlled and real-world data. The end-to-end system performance is evaluated using 100 surveyed control points in an office environment and obtains a mean accuracy of 10 cm. Experimental results are also shown on three additional datasets from real world environments including a 1500 meter trajectory in a warehouse sized retail shopping center.

Corso, N↗
DOE OSTI2017

Assessment of canopy chlorophyll content retrieval in maize and soybean: Implications of hysteresis on the development of generic algorithms

Here, canopy chlorophyll content (Chl) closely relates to plant photosynthetic capacity, nitrogen status and productivity. The goal of this study is to develop remote sensing techniques for accurate estimation of canopy Chl during the entire growing season without re-parameterization of algorithms for two contrasting crop species, maize and soybean. These two crops represent different biochemical mechanisms of photosynthesis, leaf structure and canopy architecture. The relationships between canopy Chl and reflectance, collected at close range and resampled to bands of the Multi Spectral Instrument (MSI) aboard Sentinel-2, were analyzed in samples taken across the entirety of the growing seasons in three irrigated and rainfed sites located in eastern Nebraska between 2001 and 2005. Crop phenology was a factor strongly influencing the reflectance of both maize and soybean. Substantial hysteresis of the reflectance vs. canopy Chl relationship existed between the vegetative and reproductive stages. The effect of the hysteresis on vegetation indices (VI), applied for canopy Chl estimation, depended on the bands used and their formulation. The hysteresis greatly affected the accuracy of canopy Chl estimation by widely-used VIs with near infrared (NIR) and red reflectance (e.g., normalized difference vegetation index (NDVI), enhanced vegetation index (EVI) and simple ratio (SR)). VIs that use red edge and NIR bands (e.g., red edge chlorophyll index (CIred edge), red edge NDVI and the MERIS terrestrial chlorophyll index (MTCI)) were minimally affected by crop phenology (i.e., they exhibited little hysteresis) and were able to accurately estimate canopy Chl in two crops without algorithm re-parameterization and, thus, were found to be the best candidates for generic algorithms to estimate crop Chl using the surface reflectance products of MSI Sentinel-2.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Vehicle Position Detection Based on Machine Learning Algorithms in Dynamic Wireless Charging

Dynamic wireless charging (DWC) has emerged as a viable approach to mitigate range anxiety by ensuring continuous and uninterrupted charging for electric vehicles in motion. DWC systems rely on the length of the transmitter, which can be categorized into long-track transmitters and segmented coil arrays. The segmented coil array, favored for its heightened efficiency and reduced electromagnetic interference, stands out as the preferred option. However, in such DWC systems, the need arises to detect the vehicle’s position, specifically to activate the transmitter coils aligned with the receiver pad and de-energize uncoupled transmitter coils. This paper introduces various machine learning algorithms for precise vehicle position determination, accommodating diverse ground clearances of electric vehicles and various speeds. Through testing eight different machine learning algorithms and comparing the results, the random forest algorithm emerged as superior, displaying the lowest error in predicting the actual position.

47 OTHER INSTRUMENTATION↗
DOE OSTI2018

A Machine Learning-Genetic Algorithm (ML-GA) Approach for Rapid Optimization Using High-Performance Computing

A Machine Learning-Genetic Algorithm (ML-GA) approach was developed to virtually discover optimum designs using training data generated from multi-dimensional simulations. Machine learning (ML) presents a pathway to transform complex physical processes that occur in a combustion engine into compact informational processes. In the present work, a total of over 2000 sector-mesh computational fluid dynamics (CFD) simulations of a heavy-duty engine were performed. These were run concurrently on a supercomputer to reduce overall turnaround time. The engine being optimized was run on a low-octane (RON70) gasoline fuel under partially premixed compression ignition (PPCI) mode. A total of nine input parameters were varied, and the CFD simulation cases were generated by randomly sampling points from this nine-dimensional input space. These input parameters included fuel injection strategy, injector design, and various in-cylinder flow and thermodynamic conditions at intake valve closure (IVC). The outputs (targets) of interest from these simulations included five metrics related to engine performance and emissions. Over 2000 samples generated from CFD were then used to train an ML model that could predict these five targets based on the nine input features. A robust super learner approach was employed to build the ML model, where results from a collection of different ML algorithms were pooled together. Thereafter, a stochastic global optimization genetic algorithm (GA) was used, with the ML model as the objective function, to optimize the input parameters based on a merit function so as to minimize fuel consumption while satisfying CO and NOx emissions constraints. The optimized configuration from ML-GA was found to be very close to that obtained from a sequentially performed CFD-GA approach, where a CFD simulation served as the objective function. In addition, the overall turnaround time was (at least) 75% lower with the ML-GA approach, as the training data was generated from concurrent CFD simulations and employing the ML model as the objective function significantly accelerated the GA optimization. Finally, this study demonstrates the potential of ML-GA and high-performance computing (HPC) to reduce the number of CFD simulations to be performed for optimization problems without loss in accuracy, thereby providing significant cost savings compared to traditional approaches.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Evaluation of cloud height, optical thickness, and phase retrievals from the CHROMA algorithm applied to Sentinel-3 OLCI data

We previously developed the Cloud Height Retrieval from O 2 Molecular Absorption (CHROMA) algorithm for the Ocean Color Instrument (OCI) on the new NASA Plankton, Aerosol, Cloud, ocean Ecosystem (PACE) mission. Here, we apply CHROMA to observations from the Ocean Land Colour Instrument (OLCI) to guide expectations for PACE, as it will take some time to obtain large-scale validation data for OCI. We use cloud top height (CTH), phase, and (for liquid clouds) cloud optical thickness (COT) data from the ground-based Atmospheric Radiation Measurement (ARM) network to evaluate the OLCI retrievals. We found that OLCI and Moderate Resolution Imaging Spectroradiometer (MODIS) CTH compare similarly well to the ARM reference. OLCI has a tendency to underestimate CTH as CTH increases, and algorithm assumptions about cloud geometric thickness may contribute to this. ARM COT from multifilter shadowband radiometers (MFRSR) and Sun photometers are well-correlated with one another, albeit with a roughly 30 % offset on average; OLCI and MODIS COT agree more closely with the MFRSR data. OLCI retrieval uncertainty estimates show skill at telling low-uncertainty cases from high-uncertainty ones, although CTH uncertainties are underestimated. Additionally, we compare the OLCI data to satellite retrievals based on thermal infrared measurements from MODIS and Sea and Land Surface Temperature Radiometer (SLSTR) data. Differences are broadly consistent with physical expectations based on the A-band vs. thermal techniques, although one key challenge in such aggregated comparisons is different cloud masking sensitivities and algorithm failure rates meaning additional sampling differences are introduced. We conclude by discussing the transition to and possible enhancements for PACE OCI.

Sayer, Andrew M. [Univ. of Maryland Baltimore Coun↗
DOE OSTI2026

A Novel Segmentation Algorithm for the ARM User Facility All-Sky Imagers Using Machine Learning Applications

Cloud cover plays a pivotal role in modulating the Earth's energy budget through the reflection of incoming solar radiation and the trapping of outgoing longwave radiation. Ground-based all-sky imagers offer an objective assessment of cloud cover that can be used to estimate solar irradiance, classify cloud types, track cloud movement, and serve as a benchmark 10 for the evaluation of satellite and reanalysis data products. The Atmospheric Radiation Measurement (ARM) user facility has utilized all-sky imagers for more than 25 years to monitor cloud cover and augment its comprehensive suite of atmospheric measurements. Following the retirement of its Total Sky Imager (TSI), ARM recently deployed the TSI’s successor, the All Sky Imager (ASI-16 camera systems). To provide a smooth transition and continuity to the vast amount of knowledge gathered by the TSI over the years, while addressing typical deployment issues, we developed a novel pixel segmentation algorithm, 15 the ASI Sky Cover (ASISKYCOVER). ASISKYCOVER builds on the different strengths and properties of the TSI processing algorithm while integrating machine learning techniques, ensuring data validity and accuracy across diverse atmospheric conditions. It enhances cloud cover characterization with new features such as artifact detection and uncertainty quantification. ASISKYCOVER also includes cloud cover estimates for near-zenith (narrow field-of-view) and reduces susceptibility to false detections. This study introduces ASISKYCOVER, details its algorithm framework, and demonstrates its capabilities using a 20 year-long dataset from the ARM Southern Great Plains site. Comparisons with co-located TSI data and other ARM measurements, such as zenith-pointing radars and lidars, are presented, underscoring the ASISKYCOVER’s potential to improve cloud cover analyses and data evaluation efforts, as well as to be integrated into higher-level data products that synergize instrument suites to generate new and insightful information

Silber, Israel↗
DOE OSTI2016

GFIT2: an experimental algorithm for vertical profile retrieval from near-IR spectra

An algorithm for retrieval of vertical profiles from ground-based spectra in the near IR is described and tested. Known as GFIT2, the algorithm is primarily intended for CO 2 , and is used exclusively for CO 2 in this paper. Retrieval of CO 2 vertical profiles from ground-based spectra is theoretically possible, would be very beneficial for carbon cycle studies and the validation of satellite measurements, and has been the focus of much research in recent years. GFIT2 is tested by application both to synthetic spectra and to measurements at two Total Carbon Column Observing Network (TCCON) sites. We demonstrate that there are approximately 3° of freedom for the CO 2 profile, and the algorithm performs as expected on synthetic spectra. We show that the accuracy of retrievals of CO 2 from measurements in the 1.61 μ (6220 cm -1 ) spectral band is limited by small uncertainties in calculation of the atmospheric spectrum. We investigate several techniques to minimize the effect of these uncertainties in calculation of the spectrum. These techniques are somewhat effective but to date have not been demonstrated to produce CO 2 profile retrievals with sufficient precision for applications to carbon dynamics. As a result, we finish by discussing ongoing research which may allow CO 2 profile retrievals with sufficient accuracy to significantly improve the scientific value of the measurements from that achieved with column retrievals.

54 ENVIRONMENTAL SCIENCES↗