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At least 793 records · Page 44

Classical eikonal from Magnus expansion

In a classical scattering problem, the classical eikonal is defined as the generator of the canonical transformation that maps in-states to out-states. It can be regarded as the classical limit of the log of the quantum S-matrix. In a classical analog of the Born approximation in quantum mechanics, the classical eikonal admits an expansion in oriented tree graphs, where oriented edges denote retarded/advanced worldline propagators. The Magnus expansion, which takes the log of a time-ordered exponential integral, offers an efficient method to compute the coefficients of the tree graphs to all orders. We exploit a Hopf algebra structure behind the Magnus expansion to develop a fast algorithm which can compute the tree coefficients up to the 12th order (over half a million trees) in less than an hour. In a relativistic setting, our methods can be applied to the post-Minkowskian (PM) expansion for gravitational binaries in the worldline formalism. We demonstrate the methods by computing the 3PM eikonal and find agreement with previous results based on amplitude methods. Importantly, the Magnus expansion yields a finite eikonal, while the naïve eikonal based on the time-symmetric propagator is infrared-divergent from 3PM on.

Black Holes↗

Integrating quantum computing resources into scientific HPC ecosystems

Quantum Computing (QC) offers significant potential to enhance scientific discovery in fields such as quantum chemistry, optimization, and artificial intelligence. Yet QC faces challenges due to the noisy intermediate-scale quantum era’s inherent external noise issues. Here, this paper discusses the integration of QC as a computational accelerator within classical scientific high-performance computing (HPC) systems. By leveraging a broad spectrum of simulators and hardware technologies, we propose a hardware-agnostic framework for augmenting classical HPC with QC capabilities. Drawing on the HPC expertise of the Oak Ridge National Laboratory (ORNL) and the HPC lifecycle management of the Department of Energy (DOE), our approach focuses on the strategic incorporation of QC capabilities and acceleration into existing scientific HPC workflows. This includes detailed analyses, benchmarks, and code optimization driven by the needs of the DOE and ORNL missions. Our comprehensive framework integrates hardware, software, workflows, and user interfaces to foster a synergistic environment for quantum and classical computing research. This paper outlines plans to unlock new computational possibilities, driving forward scientific inquiry and innovation in a wide array of research domains.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Modeling of transient conduction in building envelope assemblies: A review

As buildings age, retrofits are becoming an increasingly important topic for the ever-growing and aging existing building stock. To compare designs or evaluate in-service building envelopes, thermal modeling is utilized to evaluate the thermal performance of envelope assemblies; however, it can be difficult to model the thermal performance of as-built assemblies due to degradation or missing documentation. To address this issue, inverse modeling can be applied to infer the properties of as-built envelope assemblies. This paper presents a review of the literature and published methods to model and infer the transient conductive performance of building envelopes. This review serves as a survey of existing transient conduction algorithms to evaluate performance, computational speed, and relevance for inverse modeling applications. In addition to the literature review, this work also evaluates the computational performance of the most prevalent transient conduction algorithms against the ASHRAE 1052RP toolkit to assess inverse modeling potential. This methodology serves as a foundation for future research to characterize the transient thermal performance of as-built building envelope assemblies.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

On the use of adjoints in the inversion of observed quasi-static deformation

An adjoint-based conjugate gradient algorithm provides an efficient means for imaging sources of deformation within the Earth, such as volume stresses associated with fluid flow in aquifers and reservoirs. For time intervals over which the overburden deforms elastically, one can calculate the gradient elements for a single model update using just two numerical simulations. The first is a forward run that is used to compute the residuals associated with the given iteration. The second simulation is to evaluate the application of the adjoint operator to the residuals. In this adjoint calculation, the residual displacements are applied as sources at the measurement locations, driving the deformation in the simulation. The volume stress on the source grid blocks, in response to the residual displacements, provide the gradient components. We apply this technique to satellite-based interferometric synthetic aperture radar (InSAR) line-of-sight displacements that were observed over an oil reservoir in California’s Central Valley. Furthermore, we find that the adjoint-based gradient estimates, requiring 18 CPU seconds, agree with conventional numerical calculations that take over 3700 CPU seconds to compute. Conjugate gradient algorithms utilizing the conventional approach and adjoint-based gradient computations give roughly the same reductions in misfit and similar final estimates of reservoir volume change.

58 GEOSCIENCES↗

Qutrit Randomized Benchmarking

Ternary quantum processors offer significant potential computational advantages over conventional qubit technologies, leveraging the encoding and processing of quantum information in qutrits (three-level systems). Therefore, to evaluate and compare the performance of such emerging quantum hardware it is essential to have robust benchmarking methods suitable for a higher-dimensional Hilbert space. We demonstrate extensions of industry standard randomized benchmarking (RB) protocols, developed and used extensively for qubits, suitable for ternary quantum logic. Using a superconducting five-qutrit processor, we find an average single-qutrit process infidelity of 3.8×10 -3 . Through interleaved RB, we characterize a few relevant gates, and employ simultaneous RB to fully characterize crosstalk errors. Finally, we apply cycle benchmarking to a two-qutrit CSUM gate and obtain a two-qutrit process fidelity of 0.85. Our results present and demonstrate RB-based tools to characterize the performance of a qutrit processor, and a general approach to diagnose control errors in future qudit hardware.

97 MATHEMATICS AND COMPUTING↗

Real-time Nonlinear Model Predictive Control (NMPC) Strategies using Physics-Based Models for Advanced Lithium-ion Battery Management System (BMS)

Optimal operation of lithium-ion batteries requires robust battery models for advanced battery management systems (ABMS). A nonlinear model predictive control strategy is proposed that directly employs the pseudo-two-dimensional (P2D) model for making predictions. Using robust and efficient model simulation algorithms developed previously, the computational time of the nonlinear model predictive control algorithm is quantified, and the ability to use such models for nonlinear model predictive control for ABMS is established.

25 ENERGY STORAGE↗

Quantum-Hardware Focused Application Performance Benchmarks (Final Technical Report)

Quantum computers promise to transform how we do scientific calculations. In this project, we benchmark different current quantum computers for solving chemistry problems and find ways to build noise-resilient implementations. We also use the characterization techniques developed to test ion trap quantum computers.

74 ATOMIC AND MOLECULAR PHYSICS↗

Adaptive Runtime Features For Distributed Graph Algorithms

Performance of distributed graph algorithms can benefit greatly by forming rapport between algorithmic abstraction and the underlying runtime system that is responsible for scheduling work and exchanging messages. However, due to their dynamic and irregular nature of computation, distributed graph algorithms written in different programming models impose varying degree of workload pressure on the runtime. To cope with such vastly different workload characteristics, a runtime has to make several trade-offs. One such trade-off arises, for example, when the runtime scheduler has to choose among alternatives such as whether to execute algorithmic work, or progress the network by probing network buffers, or throttle sending messages (termed flow control). This tradeoff decides between optimizing the throughput of a runtime scheduler by increasing the rate of execution of algorithmic work, and reducing the latency of the network messages. Another trade-off exists when a decision has to be made about when to send aggregated messages in buffers (message coalescing). This decision chooses between trading off latency for network bandwidth and vice versa. At any instant, such trade-offs emphasize either on improving the quantity of work being executed (by maximizing the scheduler throughput) or on improving the quality of work (by prioritizing better work). However, encoding static policies for different runtime features (such as flow control, coalescing) can prevent graph algorithms from achieving their full potential, thus can undermine the actual performance of a distributed graph algorithm . In this paper, we investigate runtime support for distributed graph algorithms in the context of two paradigms: variants of wellknown Bulk-Synchronous Parallel model and asynchronous programming model. We explore generic runtime features such as message coalescing (aggregation) and flow control and show that execution policies of these features need to be adjusted over time to make a positive impact on the execution time of a distributed graph algorithm. Since synchronous and asynchronous graph algorithms have different workload characteristics, not all of such runtime features may be good candidates for adaptation. Each of these algorithmic paradigms may require different set of features to be adapted over time. We demonstrate which set of feature(s) can be useful in each case to achieve the right balance of work in the runtime layer. Existing implementation of different graph algorithms can benefit from adapting dynamic policies in the underlying runtime.

Firoz, Jesun S.↗

Analog In-Memory Computing for the Synthetic Aperture Radar Polar Format Algorithm

As the utility of synthetic aperture radar (SAR) systems increases in autonomous vehicles, satellites, and other power- and space-constrained edge applications, there is a growing need for processors that can form SAR images at low power. In recent years, analog in-memory compute (AIMC) has shown immense promise for accelerating neural networks and other matrix-vector multiplication (MVM) heavy workloads at the edge. Here, in this work, we examine how the polar format algorithm (PFA), a popular SAR image formation algorithm, can be mapped to these AIMC systems. The PFA maps readily onto analog MVMs because it primarily consists of two linear operations: interpolation of frequency-domain data to a Cartesian grid, followed by a 2-D Fourier transform. This work presents two approaches to map the interpolation operation onto MVMs in analog hardware: a chirp transform and a modified form of sinc interpolation. These mappings introduce algorithmic errors, and their effect on the quality of SAR image formation is examined, both quantitatively and qualitatively. In addition, the impact of errors introduced by the analog hardware is explored to determine which approach is optimal under varying assumptions about the underlying analog memory devices and circuits.

Analog computing↗

Variable Time-Step Implementation for Rapid Quasi-Static Time-Series (QSTS) Simulations of Distributed PV

Distribution system analysis with high penetrations of distributed PV require quasi-static time-series (QSTS) analysis to model the variability introduced on the distribution system, but current QSTS algorithms are prohibitively burdensome and computationally intensive. This paper proposes a variable timestep algorithm to calculate the critical time periods when QSTS simulations should be solved at higher or lower time-resolution and to backtrack for any critical periods that were missed. This variable time-step solver is a new method of performing timeseries simulations with high accuracy while performing the simulation more than 50 times faster. The scalability of the algorithm is demonstrated using a real utility distribution system model with thousands of buses.

14 SOLAR ENERGY↗

Infinite quantum signal processing

Quantum signal processing (QSP) represents a real scalar polynomial of degree d using a product of unitary matrices of size 2 × 2 , parameterized by ( d + 1 ) real numbers called the phase factors. This innovative representation of polynomials has a wide range of applications in quantum computation. When the polynomial of interest is obtained by truncating an infinite polynomial series, a natural question is whether the phase factors have a well defined limit as the degree d → ∞ . While the phase factors are generally not unique, we find that there exists a consistent choice of parameterization so that the limit is well defined in the ℓ 1 space. This generalization of QSP, called the infinite quantum signal processing, can be used to represent a large class of non-polynomial functions. Our analysis reveals a surprising connection between the regularity of the target function and the decay properties of the phase factors. Our analysis also inspires a very simple and efficient algorithm to approximately compute the phase factors in the ℓ 1 space. The algorithm uses only double precision arithmetic operations, and provably converges when the ℓ 1 norm of the Chebyshev coefficients of the target function is upper bounded by a constant that is independent of d . This is also the first numerically stable algorithm for finding phase factors with provable performance guarantees in the limit d → ∞ .

Dong, Yulong [Department of Mathematics, Universit↗

ZFP: A compressed array representation for numerical computations

HPC trends favor algorithms and implementations that reduce data motion relative to FLOPS. We investigate the use of lossy compressed data arrays in place of traditional IEEE floating point arrays to store the primary data of calculations. Simulation is fundamentally an exercise in controlled approximation, and error introduced by finite-precision arithmetic (or lossy compression) is just one of several sources of error that need to be managed to ensure sufficient accuracy in a computed result. We describe ZFP, a compressed numerical format designed for in-memory storage of multidimensional arrays, and summarize theoretical results that demonstrate that the error of repeated lossy compression can be bounded and controlled. Furthermore, we establish a relationship between grid resolution and compression-induced errors and show that, contrary to conventional floating point, ZFP reduces finite-difference errors with finer grids. We present example calculations that demonstrate data reduction by 4x or more with negligible impact on solution accuracy. Our results further demonstrate several orders-of-magnitude increase in accuracy using ZFP over IEEE floating point and Posits for the same storage budget.

Lindstrom, Peter↗

A Learning-based Supervisory Control Architecture for Electric Vehicle Charging System Paired with Energy Storages

A Machine Learning-based predictive model is developed for optimal dispatching energy storage system integrated with Electric Vehicle battery charger. The model is effectively trained using transfer learning algorithm and successfully validated via measurement data to achieve high fidelity and accuracy. The study findings provide possibilities for future development of the presented approach to implement computational heavy predictive algorithms with multi-step predictions in emerging modular bidirectional charger topologies to realize vehicle-to-grid (V2G) technology. The online tuning can be explored using the new measurements obtained during the operation, henceforth, enhancing the controller performance for integrating multiple DERs into distribution power networks that shows huge interest for the utilities and regulatory agencies. Multiple operation scenatios have been evaluated and simulation results are discussed to verify intended performance of the proposed control solution.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Transport error estimation using residual Monte Carlo

The residual Monte Carlo (RMC) method is also known in the literature as sequential Monte Carlo and reduced-source Monte Carlo. Given a Monte Carlo method for solving a linear equation and an approximate solution to that system, the residual method enables use of essentially the same Monte Carlo algorithm to directly compute the additive error or “defect” associated with the approximate solution. As the size of the defect decreases relative to the size of the solution, the residual Monte Carlo method becomes increasingly efficient relative to the standard Monte Carlo (SMC) method. Here we present a new RMC algorithm for evaluating the space-angle error in S n radiation transport solutions, and provide computational examples demonstrating that it can be far more efficient than SMC for this purpose. Herein we also describe a particular pitfall that must be avoided if RMC is to be efficient, and explain why the performance of RMC can significantly differ between different transport problems and different quantities of interest for the same problem.

97 MATHEMATICS AND COMPUTING↗

Electron-Phonon Systems on a Universal Quantum Computer

We present an algorithm that extends existing quantum algorithms for simulating fermion systems in quantum chemistry and condensed matter physics to include bosons in general and phonons in particular. We introduce a qubit representation for the low-energy subspace of phonons which allows an efficient simulation of the evolution operator of the electron-phonon systems. As a consequence of the Nyquist-Shannon sampling theorem, the phonons are represented with exponential accuracy on a discretized Hilbert space with a size that increases linearly with the cutoff of the maximum phonon number. The additional number of qubits required by the presence of phonons scales linearly with the size of the system. The additional circuit depth is constant for systems with finite-range electron-phonon and phonon-phonon interactions and linear for long-range electron-phonon interactions. Our algorithm for a Holstein polaron problem was implemented on an Atos quantum learning machine quantum simulator employing the quantum phase estimation method. The energy and the phonon number distribution of the polaron state agree with exact diagonalization results for weak, intermediate, and strong electron-phonon coupling regimes.

97 MATHEMATICS AND COMPUTING↗

Accurate Consensus-based Distributed Averaging with Variable Time Delay in Support of Distributed Secondary Control Algorithms

We report that distributed secondary control has been widely used in hierarchical control structures, where multiple distributed generators (DGs) need to coordinate to regulate system voltage and frequency. In these systems, consensus algorithms determine the average of a group of dynamic states (e.g. voltages measured by a group of DGs). To be useful, consensus algorithms must be computationally efficient, stable and accurate. In practice, numerous practical implementation challenges significantly affect the consensus equilibrium. In this paper, we quantify the accuracy deviations of the distributed average observer algorithms proposed in the literature to demonstrate the problems with the state-of-the-art distributed averaging techniques. A novel approach is proposed that achieves accurate average tracking in the presence of time-varying communication delays among agents. In our implementation, time synchronization of all distributed controllers is enabled by a novel software platform, called Resilient Information Architecture Platform for the Smart Grid (RIAPS). The proposed distributed average observer is implemented on hardware controllers and its effectiveness is validated in a controller hardware-in-the-loop testbed.

24 POWER TRANSMISSION AND DISTRIBUTION↗