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Results for “algorithmic efficiency”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

A Novel Protection Scheme for Unbalanced Faults in Inverter Dominated Networks: A Computationally Efficient Algorithm for Entry-Level Relays

Microgrids are now a common practice in distribution systems to increase resilience and reliability. However, microgrid protection remains a critical challenge, considering its requirement to operate in both grid connected and islanded, and the variability in fault characteristics under each mode of operation. This paper presents unbalanced power (S unb ) based fault detection algorithm, which considers local voltage and current unbalances to determine faults in the system. S unb is a computationally efficient fault detection algorithm that is suitable for implementation in the programmable logic of entry level protective relays. In addition, the difference in current and voltage unbalance (D n ) is used to determine the fault type. The proposed method demonstrates high sensitivity and selectivity for line-to-ground (LG), line-to-line (LL), and double line-to-ground (LLG) faults, representing the most common faults in distribution systems. It also allows relay coordination with upstream and downstream protection devices in both island and grid connected operation, while preserving grading margins. The same pickup and time multiplier settings of a particular relay for both modes of operation eliminates the need for adaptive settings, which rely on communication networks. Validation was performed with a hardware-in-the-loop (HIL) setup using Typhoon HIL real time simulator interfaced with three entry-level, SEL 751 relays. Results confirmed the algorithm’s ability to discriminate fault conditions, and determine the fault type under both operating modes, maintain fast detection times, and ensure proper protection coordination.

fault classification↗
DOE OSTI2024

Lax-Oleinik-Type Formulas and Efficient Algorithms for Certain High-Dimensional Optimal Control Problems

Two of the main challenges in optimal control are solving problems with state-dependent running costs and developing efficient numerical solvers that are computationally tractable in high dimension. In this paper, we provide analytical solutions to certain optimal control problems whose running cost depends on the state variable and with constraints on the control. We also provide Lax-Oleinik-type representation formulas for the corresponding Hamilton-Jacobi partial differential equations with state-dependent Hamiltonians. Additionally, we present an efficient, grid-free numerical solver based on our representation formulas, which is shown to scale linearly with the state dimension, and thus, to overcome the curse of dimensionality. Using existing optimization methods and the min-plus technique, we extend our numerical solvers to address more general classes of convex and nonconvex initial costs. We demonstrate the capabilities of our numerical solvers using implementations on a central processing unit (CPU) and a field-programmable gate array (FPGA). In several cases, our FPGA implementation obtains over a 10 times speedup compared to the CPU, which demonstrates the promising performance boosts FPGAs can achieve. Furthermore, our numerical results show that our solvers have the potential to serve as a building block for solving broader classes of high-dimensional optimal control problems in real-time.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Sequential Kalman tuning of the t -preconditioned Crank-Nicolson algorithm: efficient, adaptive and gradient-free inference for Bayesian inverse problems

Ensemble Kalman Inversion (EKI) has been proposed as an efficient method for the approximate solution of Bayesian inverse problems with expensive forward models. However, when applied to the Bayesian inverse problem EKI is only exact in the regime of Gaussian target measures and linear forward models. Here, in this work we propose embedding EKI and Flow Annealed Kalman Inversion, its normalizing flow (NF) preconditioned variant, within a Bayesian annealing scheme as part of an adaptive implementation of the t-preconditioned Crank-Nicolson (tpCN) sampler. The tpCN sampler differs from standard pCN in that its proposal is reversible with respect to the multivariate t-distribution. The more flexible tail behaviour allows for better adaptation to sampling from non-Gaussian targets. Within our Sequential Kalman Tuning (SKT) adaptation scheme, EKI is used to initialize and precondition the tpCN sampler for each annealed target. The subsequent tpCN iterations ensure particles are correctly distributed according to each annealed target, avoiding the accumulation of errors that would otherwise impact EKI. We demonstrate the performance of SKT for tpCN on three challenging numerical benchmarks, showing significant improvements in the rate of convergence compared to adaptation within standard SMC with importance weighted resampling at each temperature level, and compared to similar adaptive implementations of standard pCN. The SKT scheme applied to tpCN offers an efficient, practical solution for solving the Bayesian inverse problem when gradients of the forward model are not available. Code implementing the SKT schemes for tpCN is available at https://github.com/RichardGrumitt/KalmanMC.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Compute-Efficient Deep Learning: Algorithmic Trends and Opportunities

Although deep learning has made great progress in recent years, the exploding economic and environmental costs of training neural networks are becoming unsustainable. To address this problem, there has been a great deal of research on algorithmically-efficient deep learning, which seeks to reduce training costs not at the hardware or implementation level, but through changes in the semantics of the training program. In this paper, we present a structured and comprehensive overview of the research in this field. First, we formalize the algorithmic speedup problem, then we use fundamental building blocks of algorithmically efficient training to develop a taxonomy. Our taxonomy highlights commonalities of seemingly disparate methods and reveals current research gaps. Next, we present evaluation best practices to enable comprehensive, fair, and reliable comparisons of speedup techniques. To further aid research and applications, we discuss common bottlenecks in the training pipeline (illustrated via experiments) and offer taxonomic mitigation strategies for them. Finally, we highlight some unsolved research challenges and present promising future directions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Efficient numerical algorithm for multi-level ionization of high-atomic-number gases

An efficient numerical algorithm for laser driven multi-level ionization of high-atomic-number gases is proposed and implemented in an electromagnetic particle-in-cell code SPACE. The algorithm is based on analytical solutions to the system of differential equations describing ionization evolution. Using analytical solutions resolves the multiscale issue of ionization due to different characteristic time scales of ionization processes and the main code time step. Algorithm efficiency and memory requirements are significantly improved by using a locally reduced system of differential equations. The algorithm also assigns proper orbital quantum numbers and their projections to ionization states. The algorithm is verified and validated using experimental data.

Cheng, A. (ORCID:000000021945282X)↗
DOE OSTI2024

Towards provably efficient quantum algorithms for large-scale machine-learning models

Large machine learning models are revolutionary technologies of artificial intelligence whose bottlenecks include huge computational expenses, power, and time used both in the pre-training and fine-tuning process. In this work, we show that fault-tolerant quantum computing could possibly provide provably efficient resolutions for generic (stochastic) gradient descent algorithms, scaling as $\mathcal{O}$(T 2 x polylog($n$)), where n is the size of the models and T is the number of iterations in the training, as long as the models are both sufficiently dissipative and sparse, with small learning rates. Based on earlier efficient quantum algorithms for dissipative differential equations, we find and prove that similar algorithms work for (stochastic) gradient descent, the primary algorithm for machine learning. In practice, we benchmark instances of large machine learning models from 7 million to 103 million parameters. We find that, in the context of sparse training, a quantum enhancement is possible at the early stage of learning after model pruning, motivating a sparse parameter download and re-upload scheme. Our work shows solidly that fault-tolerant quantum algorithms could potentially contribute to most state-of-the-art, large-scale machine-learning problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

An Efficient Numerical Algorithm for Solving Coupled Time-Dependent Ginzburg-Landau Equation for Superconductivity and Elasticity

A decoupled finite element algorithm is developed for simulating the vortex dynamics on an elastic superconductor which couples the time-dependent Ginzburg- Landau equation with the complex-valued superconducting order parameter and the vector-valued magnetic potential, and the elasticity equation. We present an iterative algorithm for the decoupled system arising from the time and spatial discretization using a combination of preconditioner, algebraic multigrid method (AMG) and preconditioned conjugate gradient method (PCG). The iterative algorithm allows us to perform large-scale three-dimensional simulations of mesoscale pattern formation during superconducting phase transitions with arbitrary elastic boundary conditions. Here, the performance and efficiency of the algorithm are numerically verified by several benchmark problems, exhibiting up to two orders of magnitude improvement depending on the scale of discrete system compared to the exact solver.

Efficiency↗
DOE OSTI2024

Demonstration of the rodeo algorithm on a quantum computer

The rodeo algorithm is an efficient algorithm for eigenstate preparation and eigenvalue estimation for any observable on a quantum computer. This makes it a promising tool for studying the spectrum and structure of atomic nuclei as well as other fields of quantum many-body physics. The only requirement is that the initial state has sufficient overlap probability with the desired eigenstate. While it is exponentially faster than well-known algorithms such as phase estimation and adiabatic evolution for eigenstate preparation, it has yet to be implemented on an actual quantum device. In this work, we apply the rodeo algorithm to determine the energy levels of a random one-qubit Hamiltonian, resulting in a relative error of 0.08% using mid-circuit measurements on the IBM Q device Casablanca. This surpasses the accuracy of directly-prepared eigenvector expectation values using the same quantum device. We take advantage of the high-accuracy energy determination and use the Hellmann-Feynman theorem to compute eigenvector expectation values for a different random one-qubit observable. For the Hellmann-Feynman calculations, we find a relative error of 0.7%. Here, we conclude by discussing possible future applications of the rodeo algorithm for multi-qubit Hamiltonians.

algorithm↗
DOE OSTI2024

Retrieving Top-k Hyperedge Triplets: Models and Applications

Complex systems frequently exhibit multi-way, rather than pairwise, interactions. These group interactions can- not be faithfully modeled as collections of pairwise interactions using graphs and instead require hypergraphs. However, methods that analyze hypergraphs directly, rather than via lossy graph reductions, remain limited. Hypergraph motifs hold promise in this regard, as motif patterns serve as building blocks for larger group interactions which are inexpressible by graphs. Recent work has focused on categorizing and counting hypergraph motifs based on the existence of nodes in hyperedge intersection regions. Here, we argue that the relative sizes of hyperedge inter- sections within motifs contain varied and valuable information. We propose a suite of efficient algorithms for finding top-k triplets of hyperedges based on optimizing the sizes of these intersection patterns. This formulation uncovers interesting local patterns of interaction, finding hyperedge triplets that either (1) are the least similar with each other, (2) have the highest pairwise but not groupwise correlation, or (3) are the most similar with each other. We formalize this as a combinatorial optimization problem and design efficient algorithms based on filtering hyperedges. Our comprehensive experimental evaluation shows that the resulting hyperedge triplets yield insightful information on real-world hypergraphs. Our approach is also orders of magnitude faster than a naive baseline implementation.

hypergraphs, motifs, Combinatorial Algorithms↗
DOE OSTI2025

A High-Efficiency Delayed Update Algorithm for Evaluating Slater Determinants in Quantum Monte Carlo

For quantum Monte Carlo simulations of molecular systems or supercells with thousands of electrons, matrix operations related to Slater determinants lead the computational cost. McDaniel et al. [J. Chem. Phys. 2017, 147, 174107] proposed a delayed update algorithm to increase computational efficiency by using matrix–matrix multiplication when updating the inverse matrices of Slater determinants. However, preparing intermediate matrices for applying the Sherman–Morrison–Woodbury formula remained a bottleneck. Here, in this work, we introduce an improved algorithm for CPUs and GPUs that (1) reduces this bottleneck by iteratively updating the intermediate matrices and (2) is efficient at any acceptance ratio, with no cost for rejected moves on CPUs and minimal cost on GPUs. We show the full scheme of integrating the delayed update algorithm into a single-electron move. The high efficiency of our algorithm is demonstrated on CPUs and GPUs for a 512 atom/6144 valence electron calculation, with 12× and 2× overall speed-up compared to traditional rank-1 update schemes in diffusion quantum Monte Carlo, respectively.

Luo, Ye [Argonne National Laboratory (ANL), Argonn↗
DOE OSTI2024

Extracting and Interpreting Electrochemical Impedance Spectra (EIS) from Physics-Based Models of Lithium-Ion Batteries

This paper implements a highly efficient algorithm to extract electrochemical impedance spectra (EIS) from physics-based battery models (e.g., a P2D model). The mathematical approach is different from how EIS is practiced experimentally. Experimentally, the voltage (current) is harmonically perturbed over a wide range of frequencies and the amplitude and phase shift of the corresponding current (voltage) is measured. The experimental approach can be implemented in simulation software, but is computationally expensive. The approach here is to determine locally linear state-space models from the full physical model. The four Jacobian matrices that are the basis of the state-space models can be derived by numerical differentiation of the physical model. The EIS is then extracted from the state-space model using computationally efficient matrix-manipulation techniques. The algorithm can evaluate the full EIS at an instant in time during a transient, independent of whether the battery is in a stationary state. The approach is also able to separate the full-cell impedance to evaluate partial EIS, such as for a battery anode alone. Although such partial EIS is difficult to measure experimentally, the partial EIS provides valuable insights in interpreting the full-cell EIS.

25 ENERGY STORAGE↗
DOE OSTI2025

Robust A-Optimal Experimental Design for Sensor Placement in Bayesian Linear Inverse Problems

Optimal design of experiments for Bayesian inverse problems has recently gained wide popularity and attracted much attention, especially in the computational science and Bayesian inversion communities. An optimal design maximizes a predefined utility function that is formulated in terms of the elements of an inverse problem, an example being optimal sensor placement for parameter identification. The state-of-the-art algorithmic approaches following this simple formulation generally overlook misspecification of the elements of the inverse problem, such as the prior or the measurement uncertainties. This work presents an efficient algorithmic approach for designing optimal experimental design schemes for Bayesian linear inverse problems such that the optimal design is robust to misspecification of elements of the inverse problem. Specifically, we consider a worst-case scenario approach for the uncertain or misspecified parameters, formulate robust objectives, and propose an algorithmic approach for optimizing such objectives. Furthermore, both relaxation and stochastic solution approaches are discussed with detailed analysis and insight into the interpretation of the problem and the proposed algorithmic approach. Extensive numerical experiments to validate and analyze the proposed approach are carried out for sensor placement in a parameter identification problem.

Bayesian inverse problems↗
DOE OSTI2024

Assessing decision boundaries under uncertainty

In order to make design decisions, engineers may seek to identify regions of the design domain that are acceptable in a computationally efficient manner. A design is typically considered acceptable if its reliability with respect to parametric uncertainty exceeds the designer’s desired level of confidence. Despite major advancements in reliability estimation and in design classification via decision boundary estimation, the current literature still lacks a design classification strategy that incorporates parametric uncertainty and desired design confidence. To address this gap, this paper offers a novel interpretation of the acceptance region by defining the decision boundary as the hypersurface which isolates the designs that exceed a user-defined level of confidence given parametric uncertainty. This work addresses the construction of this novel decision boundary using computationally efficient algorithms that were developed for reliability analysis and decision boundary estimation. The approach proposed in this paper is verified on two physical examples from structural and thermal analysis using Support Vector Machines and Efficient Global Optimization-based contour estimation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

The Feasibility of Incorporating a 3D Velocity Model Into Earthquake Location Around Salt Lake City, UT Using a Physics Informed Neural Network

Earthquake location algorithms typically require travel time calculation. Doing this calculation in 3D, despite advances in algorithm efficiency and computational power, can still be prohibitively expensive in terms of resources and storage. Implementation of high-resolution 3D models in routine earthquake location would be a significant step forward in most of the world. Machine learning algorithms have potential to act as substitutes for travel time calculation algorithms or stored travel time tables. We investigate EikoNet - a physics informed neural network machine learning model that estimates travel times very quickly and comes with negligible memory-overhead. Specifically, we apply EikoNet to the Wasatch Fault Community Velocity Model (WFCVM), a highly detailed and complex 3D velocity model of the Salt Lake City, UT region. While routine locations in the area and studies of the 2020 Magna, UT earthquake sequence used a 1D velocity model, a 3D model may help better our understanding the structure of the major fault in the region. Our primary goal was to test the speed, memory requirements, and accuracy of EikoNet compared to a reference eikonal solver. We find that while the EikoNet is exceedingly fast and requires little memory overhead, achieving acceptable accuracy in estimated travel times is difficult and requires extensive computational resources.

58 GEOSCIENCES↗