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At least 73 records · Page 4

MULTILEVEL ACCELERATION OF STOCHASTIC COLLOCATION METHODS FOR PDE WITH RANDOM INPUT DATA

Stochastic Collocation (SC) methods for stochastic partial differential equa- tions (SPDEs) suffer from the curse of dimensionality, whereby increases in the stochastic dimension cause an explosion of computational effort. To combat these challenges, multilevel approximation methods seek to decrease computational complexity by balancing spatial and stochastic discretization errors. As a form of variance reduction, multilevel techniques have been successfully applied to Monte Carlo (MC) methods, but may be extended to accelerate other methods for SPDEs in which the stochastic and spatial degrees of freedom are de- coupled. This article presents general convergence and computational complexity analysis of a multilevel method for SPDEs, demonstrating its advantages with regard to standard, single level approximation. The numerical results will highlight conditions under which multilevel sparse grid SC is preferable to the more traditional MC and SC approaches.

Webster, Clayton G↗

A Highly Efficient Control Framework for Centralized Residential Charging Coordination of Large Electric Vehicle Populations

The potential for widespread adoption of plug-in electric vehicles (PEVs) brings with it the potential for negative impacts on the electric grid from electric vehicle charging. Uncoordinated PEV charging may increase electricity demand during peak hours, which could create concerns for the grid as the number of PEVs increases. Therefore, it is important to coordinate charging to alleviate potential negative impacts. Centralized charging coordination is preferred by grid operator over distributed control strategies because it can systematically allocate energy across a large population of PEVs and achieve global coordination benefits. However, centralized methods presented in the literature to date require prohibitively expensive computational resources and lack realistic PEV charging models. As a result, they cannot achieve the efficiency and accuracy required to implement charging coordination in the real world. This paper introduces a highly efficient receding horizon control framework that enables dynamic charging coordination for large PEV populations. A two-stage hierarchical optimization routine is proposed that aggregates individual PEV charging flexibility to reduce the computational complexity of the optimization process. The control framework is based on high-fidelity, validated charging system models and charging behavior models derived from a real-world data set of residential charging activities collected from thousands of charging stations over multiple years. Case studies illustrate that the proposed charging control framework is capable of effectively coordinating the charging of millions of PEVs using a standard desktop computer.

30 DIRECT ENERGY CONVERSION↗

Information Gain Based Dimensionality Selection for Classifying Text Documents

Selecting the optimal dimensions for various knowledge extraction applications is an essential component of data mining. Dimensionality selection techniques are utilized in classification applications to increase the classification accuracy and reduce the computational complexity. In text classification, where the dimensionality of the dataset is extremely high, dimensionality selection is even more important. This paper presents a novel, genetic algorithm based methodology, for dimensionality selection in text mining applications that utilizes information gain. The presented methodology uses information gain of each dimension to change the mutation probability of chromosomes dynamically. Since the information gain is calculated a priori, the computational complexity is not affected. The presented method was tested on a specific text classification problem and compared with conventional genetic algorithm based dimensionality selection. The results show an improvement of 3% in the true positives and 1.6% in the true negatives over conventional dimensionality selection methods.

97 MATHEMATICS AND COMPUTING↗

Development of a Kalman filter estimator for simulation and control of particulate matter distribution of a diesel catalyzed particulate filter

The knowledge of the temperature and particulate matter mass distribution is essential for monitoring the performance and durability of a catalyzed particulate filter. A catalyzed particulate filter model was developed, and it showed capability to accurately predict temperature and particulate matter mass distribution and pressure drop across the catalyzed particulate filter. However, the high-fidelity model is computationally demanding. Therefore, a reduced order multi-zone particulate filter model was developed to reduce computational complexity with an acceptable level of accuracy. In order to develop a reduced order model, a parametric study was carried out to determine the number of zones necessary for aftertreatment control applications. The catalyzed particulate filter model was further reduced by carrying out a sensitivity study of the selected model assumptions. The reduced order multi-zone particulate filter model with 5 × 5 zones was selected to develop a catalyzed particulate filter state estimator considering its computational time and accuracy. Next, a Kalman filter–based catalyzed particulate filter estimator was developed to estimate unknown states of the catalyzed particulate filter such as temperature and particulate matter mass distribution and pressure drop (Δ P) using the sensor inputs to the engine electronic control unit and the reduced order multi-zone particulate filter model. A diesel oxidation catalyst estimator was also integrated with the catalyzed particulate filter estimator in order to provide estimates of diesel oxidation catalyst outlet concentrations of NO 2 and hydrocarbons and inlet temperature for the catalyzed particulate filter estimator. The combined diesel oxidation catalyst–catalyzed particulate filter estimator was validated for an active regeneration experiment. The validation results for catalyzed particulate filter temperature distribution showed that the root mean square temperature error by using the diesel oxidation catalyst–catalyzed particulate filter estimator is within 3.2 °C compared to the experimental data. Similarly, the Δ P estimator closely simulated the measured total Δ P and the estimated cake pressure drop error is within 0.2 kPa compared to the high-fidelity catalyzed particulate filter model.

Engineering↗

Optimum Full Information, Unlimited Complexity, Invariant and Minimax Clock Skew and Offset Estimators for IEEE 1588

This paper presents the problem of clock skew and offset estimation for the IEEE 1588 precision time protocol. Built on the classical two-way message exchange scheme, IEEE 1588 is a prominent synchronization protocol for packet switched networks. Because of the presence of random queuing delays in a packet switched network, the joint recovery of clock skew and offset from the received packet timestamps can be viewed as a statistical estimation problem. Recently, assuming perfect clock skew information, minimax optimum clock offset estimators were developed for IEEE 1588. Building on this work, we first develop joint optimum invariant clock skew and offset estimators for IEEE 1588 for known queuing delay statistics and unlimited computational complexity. We then show the developed estimators are minimax optimum, i.e., these estimators minimize the maximum skew normalized mean square estimation error over all possible values of the unknown parameters. Minimax optimum estimators that utilize information from past timestamps to improve accuracy are also introduced. The developed optimum estimators provide useful fundamental limits for evaluating the performance of clock skew and offset estimation schemes. These performance limits can aid system designers to develop algorithms with the desired computational complexity that achieve performance close to the performance of the optimum estimators. If a designer finds an approach with a complexity they find acceptable and which provides performance close to the optimum performance, they can use it and know they have near optimum performance. This is precisely the approach used in communications when comparing to capacity.

Cellular networks↗

The black hole interior from non-isometric codes and complexity

Quantum error correction has given us a natural language for the emergence of spacetime, but the black hole interior poses a challenge for this framework: at late times the apparent number of interior degrees of freedom in effective field theory can vastly exceed the true number of fundamental degrees of freedom, so there can be no isometric (i.e. inner-product preserving) encoding of the former into the latter. In this paper we explain how quantum error correction nonetheless can be used to explain the emergence of the black hole interior, via the idea of “non-isometric codes protected by computational complexity”. We show that many previous ideas, such as the existence of a large number of “null states”, a breakdown of effective field theory for operations of exponential complexity, the quantum extremal surface calculation of the Page curve, post-selection, “state-dependent/state-specific” operator reconstruction, and the “simple entropy” approach to complexity coarse-graining, all fit naturally into this framework, and we illustrate all of these phenomena simultaneously in a soluble model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Discrete models of fluids: spatial averaging, closure and model reduction

We consider semidiscrete ODE models of single-phase fluids and two-fluid mixtures. In the presence of multiple fine-scale heterogeneities, the size of these ODE systems can be very large. Spatial averaging is then a useful tool for reducing computational complexity of the problem. The averages satisfy exact balance equations of mass, momentum, and energy. These equations do not form a satisfactory continuum model because evaluation of stress and heat flux requires solving the underlying ODEs. To produce continuum equations that can be simulated without resolving microscale dynamics, we recently proposed a closure method based on the use of regularized deconvolution. Here we continue the investigation of deconvolution closure with the long term objective of developing consistent computational upscaling for multiphase particle methods. The structure of the fine-scale particle solvers is reminiscent of molecular dynamics. For this reason we use nonlinear averaging introduced for atomistic systems by Noll, Hardy, and Murdoch-Bedeaux. We also consider a simpler linear averaging originally developed in large eddy simulation of turbulence. We present several simple but representative examples of spatially averaged ODEs, where the closure error can be analyzed. Based on this analysis we suggest a general strategy for reducing the relative error of approximate closure. For problems with periodic highly oscillatory material parameters we propose a spectral boosting technique that augments the standard deconvolution and helps to correctly account for dispersion effects. We also conduct several numerical experiments, one of which is a complete mesoscale simulation of a stratified two-fluid flow in a channel. In this simulation, the operation count per coarse time step scales sublinearly with the number of particles.

Multiscale modeling, discrete models, fluid flow↗

Experimental Setup and Learning-Based AI Model for Developing Accurate PV Inverter Models

The integration of power electronics-based interfaces presents challenges due to the absence of detailed models and the high computational complexity. Generic models used in system studies lack accuracy in capturing converter dynamics. This paper proposes a data-driven approach developed from experimental setup data. This approach enhances accuracy in photovoltaic inverter modeling. We used two types of PV inverters in the experiment. The recorded experimental data undergo processing through a machine learning model. Results from the model trained through machine learning is also presented.

artificial intelligence↗

High Performance Computing Based Parallel HIearchical Modal Association Clustering (HPAR HMAC)

For many applications, clustering is a crucial step in order to gain insight into the makeup of a dataset. The best approach to a given problem often depends on a variety of factors, such as the size of the dataset, time restrictions, and soft clustering requirements. The HMAC algorithm seeks to combine the strengths of 2 particular clustering approaches: model-based and linkage-based clustering. One particular weakness of HMAC is its computational complexity. HMAC is not practical for mega-scale data clustering. For high-definition imagery, a user would have to wait months or years for a result; for a 16-megapixel image, the estimated runtime skyrockets to over a decade! To improve the execution time of HMAC, it is reasonable to consider an multi-core implementation that utilizes available system resources. An existing imple-mentation (Ray and Cheng 2014) divides the dataset into N partitions - one for each thread prior to executing the HMAC algorithm. This implementation benefits from 2 types of optimization: parallelization and divide-and-conquer. By running each partition in parallel, the program is able to accelerate computation by utilizing more system resources. Although the parallel implementation provides considerable improvement over the serial HMAC, it still suffers from poor computational complexity, O(N2). Once the maximum number of cores on a system is exhausted, the program exhibits slower behavior. We now consider a modification to HMAC that involves a recursive partitioning scheme. Our modification aims to exploit divide-and-conquer benefits seen by the parallel HMAC implementation. At each level in the recursion tree, partitions are divided into 2 sub-partitions until a threshold size is reached. When the partition can no longer be divided without falling below threshold size, the base HMAC algorithm is applied. This results in a significant speedup over the parallel HMAC.

Patlolla, Dilip R↗

State-Constrained Grid-Forming Inverter Control for Robust Operation of AC Microgrids

The control of grid-forming inverters has become an important problem to achieve high efficiency, reliability, and resilience of the future power grid. The distributed control that utilizes a sparse communication network has been proposed for AC microgrids, in which each DG only has access to the information of a small number of its neighboring DGs, reducing the computational complexity and improving the resiliency to faults and unknown parameters. However, these approaches have not provided a clear analysis of the coupling between active/reactive power injections and the voltage magnitude/frequency or a distributed updating law with a solid theoretical foundation. Additionally, in the existing approaches, tracking the references from the secondary control may violate operational constraints.

Xu, Ying↗

Editorial: Edge computation and digital distribution networks

The development of digital technologies is penetrating all areas of energy revolution. Based on the in-depth integration of advanced digital technologies, distribution networks are gradually transforming into digital distribution networks (DDNs) with tremendous changes from the structure to the operation mode. DDNs is the digitalized appearance of the physical distribution network, in which ubiquitous connections and massive data are the basic characteristics (Huo et al., 2022). It is an important task to utilize the massive data and propose novel operation modes to construct more efficient and intelligent distribution networks (Jian et al., 2022). Among the advanced digital technologies in DDNs, edge computing has received wide attention (Zhao et al., 2022). It has superior performance in local sensing and intelligent computation, which can effectively relieve huge communication pressure. However, the limited computing resources and the complex computing tasks at the edge side significantly challenge the collaboration of distribution network regulation and advanced digital technologies (Hu et al., 2022). It is necessary to find out proper methods to utilize advanced digital technology to construct DDNs. This Research Topic is organized to introduce the recent progress in the construction, operation and advanced computational methods for DDNs. Finally, seven papers have been accepted, which can be sorted into the following three categories: 1) Evolution and technical features of DDNs, 2) Intelligent operation control of DDNs, 3) Advanced simulation for large-scale DDNs. The three sections below respectively introduce the major research and contributions of the papers covered in each category.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Accelerating network layouts using graph neural networks

Graph layout algorithms used in network visualization represent the first and the most widely used tool to unveil the inner structure and the behavior of complex networks. Current network visualization software relies on the force-directed layout (FDL) algorithm, whose high computational complexity makes the visualization of large real networks computationally prohibitive and traps large graphs into high energy configurations, resulting in hard-to-interpret “hairball” layouts. Here we use Graph Neural Networks (GNN) to accelerate FDL, showing that deep learning can address both limitations of FDL: it offers a 10 to 100 fold improvement in speed while also yielding layouts which are more informative. We analytically derive the speedup offered by GNN, relating it to the number of outliers in the eigenspectrum of the adjacency matrix, predicting that GNNs are particularly effective for networks with communities and local regularities. Finally, we use GNN to generate a three-dimensional layout of the Internet, and introduce additional measures to assess the layout quality and its interpretability, exploring the algorithm’s ability to separate communities and the link-length distribution. The novel use of deep neural networks can help accelerate other network-based optimization problems as well, with applications from reaction-diffusion systems to epidemics.

97 MATHEMATICS AND COMPUTING↗

A Conceptual Architecture for a Quantum-HPC Middleware

Abstract-Quantum computing promises potential for science and industry by solving certain computationally complex problems faster than classical computers. Quantum computing systems evolved from coupled to classical computing nodes (HPC). With the increasing monolithic systems towards modular architectures comprising multiple quantum processing units (QPUs) scale, middleware systems that facilitate the efficient coupling of quantum-classical computing are becoming critical. Through an in-depth analysis of quantum applications, integration patterns and systems, we identified a gap in understanding Quantum HPC middleware systems. We present a conceptual middleware to facilitate reasoning about quantum-classical integration and serve as the basis for a future middleware system. An essential contribution of this paper lies in leveraging well-established high performance computing abstractions for managing workloads, tasks, and resources to integrate quantum computing into HPC systems seamlessly

97 MATHEMATICS AND COMPUTING↗

ANALYSIS OF VARIANCE-BASED MIXED MULTISCALE FINITE ELEMENT METHOD AND APPLICATIONS IN STOCHASTIC TWO-PHASE FLOWS

The stochastic partial differential systems have been widely used to model physical processes, where the inputs involve large uncertainties. Flows in random and heterogeneous porous media is one of the cases where the random inputs (e.g., permeability) are often modeled as a stochastic field with high-dimensional random parameters. To treat the high dimensionality and heterogeneity efficiently, model reduction is employed in both stochastic space and physical space. An analysis of variance (ANOVA)-based mixed multiscale finite element method MsFEM) is developed to decompose the high-dimensional stochastic problem into a set of lower-dimensional stochastic subproblems, which require much less computational complexity and significantly reduce the computational cost in stochastic space, and the mixed MsFEM can capture the heterogeneities on a coarse grid to greatly reduce the computational cost in the spatial domain. In addition, to enhance the efficiency of the traditional ANOVA method, an adaptive ANOVA method based on a new adaptive criterion is developed, where the most active dimensions can be selected to greatly reduce the computational cost before conducting ANOVA decomposition. This novel adaptive criterion is based on variance-decomposition method coupled with sparse-grid probabilistic collocation method or multilevel Monte Carlo method. The advantage of this adaptive criterion lies in its much lower computational overhead for identifying the active dimensions and interactions. A number of numerical examples in two-phase stochastic flows are presented and demonstrate the accuracy and performance of the adaptive ANOVA-based mixed Ms-FEM.

Wei, Jia↗