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RKDG Methods with Multi-resolution WENO Limiters for Solving Steady-State Problems on Triangular Meshes

Communications on applied Mathematics and Computation 2024年第3期6卷 1575-1599页

作者： Jun Zhu Chi-Wang Shu Jianxian Qiu State Key Laboratory of Mechanics and Control of Mechanical Structures and Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles(NUAA) MIITNanjing University of Aeronautics and AstronauticsNanjing 210016JiangsuChina Division of Applied Mathematics Brown UniversityProvidenceRI 02912USA School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific ComputingXiamen UniversityXiamen 361005FujianChina

In this paper, we design high-order Runge-Kutta discontinuous Galerkin (RKDG) methods with multi-resolution weighted essentially non-oscillatory (multi-resolution WENO) limiters to compute compressible steady-state problems on triangular meshes. A troubled cell indicator extended from structured meshes to unstructured meshes is constructed to identify triangular cells in which the application of the limiting procedures is required. In such troubled cells, the multi-resolution WENO limiting methods are used to the hierarchical L^(2) projection polynomial sequence of the DG solution. Through using the RKDG methods with multi-resolution WENO limiters, the optimal high-order accuracy can be gradually reduced to first-order in the triangular troubled cells, so that the shock wave oscillations can be well suppressed. In steady-state simulations on triangular meshes, the numerical residual converges to near machine zero. The proposed spatial reconstruction methods enhance the robustness of classical DG methods on triangular meshes. The good results of these RKDG methods with multi-resolution WENO limiters are verified by a series of two-dimensional steady-state problems.

关键词： RKDG method Steady-state problem Multi-resolution WENO limiter Triangular mesh Machine zero

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Who Should I Trust? A Visual Analytics Approach for Comparing Net Load Forecasting Models

Who Should I Trust? A Visual Analytics Approach for Comparin...

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2025 IEEE PES Grid Edge Technologies Conference and Exposition, Grid Edge 2025

作者： Bhattacharjee, Kaustav Kundu, Soumya Chakraborty, Indrasis Dasgupta, Aritra New Jersey Institute of Technology Department of Data Science United States Pacific Northwest National Laboratory Optimization and Control Group United States Lawrence Livermore National Laboratory Center for Applied Scientific Computing United States

ISBN: (纸本)9798350352528

Net load forecasting is crucial for energy planning and facilitating informed decision-making regarding trade and load distributions. However, evaluating forecasting models' performance against benchmark models remains challenging, thereby impeding experts' trust in the model's performance. In this context, there is a demand for technological interventions that allow scientists to compare models across various timeframes and solar penetration levels. This paper introduces a visual analytics-based application designed to compare the performance of deep-learning-based net load forecasting models with other models for probabilistic net load forecasting. This application employs carefully selected visual analytic interventions, enabling users to discern differences in model performance across different solar penetration levels, dataset resolutions, and hours of the day over multiple months. We also present observations made using our application through a case study, demonstrating the effectiveness of visualizations in aiding scientists in making informed decisions and enhancing trust in net load forecasting models. © 2025 IEEE.

关键词： AI/ML net load forecasting visual analytics

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Forte: An Interactive Visual Analytic Tool for Trust-Augmented Net Load Forecasting

Forte: An Interactive Visual Analytic Tool for Trust-Augment...

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2024 IEEE Power and Energy Society Innovative Smart Grid Technologies Conference, ISGT 2024

ISBN: (纸本)9798350313604

Accurate net load forecasting is vital for energy planning, aiding decisions on trade and load distribution. However, assessing the performance of forecasting models across diverse input variables, like temperature and humidity, remains challenging, particularly for eliciting a high degree of trust in the model outcomes. In this context, there is a growing need for data-driven technological interventions to aid scientists in comprehending how models react to both noisy and clean input variables, thus shedding light on complex behaviors and fostering confidence in the outcomes. In this paper, we present Forte, a visual analytics-based application to explore deep probabilistic net load forecasting models across various input variables and understand the error rates for different scenarios. With carefully designed visual interventions, this web-based interface empowers scientists to derive insights about model performance by simulating diverse scenarios, facilitating an informed decision-making process. We discuss observations made using Forte and demonstrate the effectiveness of visualization techniques to provide valuable insights into the correlation between weather inputs and net load forecasts, ultimately advancing grid capabilities by improving trust in forecasting models. © 2024 IEEE.

关键词： Decision making

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What Does ChatGPT Say:The DAO from Algorithmic Intelligence to Linguistic Intelligence

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IEEE/CAA Journal of Automatica Sinica 2023年第3期10卷 575-579页

作者： Fei-Yue Wang Qinghai Miao Xuan Li Xingxia Wang Yilun Lin School of Artificial Intelligence University of Chinese Academy of SciencesBeijing 100049China State Key Laboratory for Management and Control of Complex Systems Chinese Academy of SciencesBeijing 100190China Virtual Reality Fundamental Research Laboratory Department of Mathematics and TheoriesPeng Cheng LaboratoryShenzhen 518000China Urban Computing Lab Department of Applied ResearchShanghai AI LaboratoryShanghai 200232China IEEE

THE well-known ancient Chinese philosopher Lao Tzu(老子)or Laozi(6th~4th century BC during the Spring and Autumn period)started his classic Tao Teh Ching《道德经》or Dao De Jing(see Fig.1)with six Chinese characters:"道(Dao)可(Ke)道(Dao)非(Fei)常(Chang)道(Dao)",which has been traditionally interpreted as“道可道,非常道”or"The Dao that can be spoken is not the eternal Dao".

关键词： DAO Intelligence Spring

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A Fixed-Point Fast Sweeping WENO Method with Inverse Lax-Wendroff Boundary Treatment for Steady State of Hyperbolic Conservation Laws

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Communications on applied Mathematics and Computation 2023年第1期5卷 403-427页

作者： Liang Li Jun Zhu Chi-Wang Shu Yong-Tao Zhang Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles(NUAA) MIITNanjing University of Aeronautics and AstronauticsNanjing 210016JiangsuChina State Key Laboratory of Mechanics and Control of Mechanical Structures and Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles(NUAA) MIITNanjing University of Aeronautics and AstronauticsNanjing 210016JiangsuChina Division of Applied Mathematics Brown UniversityProvidenceRI 02912USA Department of Applied and Computational Mathematics and Statistics University of Notre DameNotre DameIN 46556USA

Fixed-point fast sweeping WENO methods are a class of efficient high-order numerical methods to solve steady-state solutions of hyperbolic partial differential equations(PDEs).The Gauss-Seidel iterations and alternating sweeping strategy are used to cover characteristics of hyperbolic PDEs in each sweeping order to achieve fast convergence rate to steady-state solutions.A nice property of fixed-point fast sweeping WENO methods which distinguishes them from other fast sweeping methods is that they are explicit and do not require inverse operation of nonlinear local ***,they are easy to be applied to a general hyperbolic *** deal with the difficulties associated with numerical boundary treatment when high-order finite difference methods on a Cartesian mesh are used to solve hyperbolic PDEs on complex domains,inverse Lax-Wendroff(ILW)procedures were developed as a very effective approach in the *** this paper,we combine a fifthorder fixed-point fast sweeping WENO method with an ILW procedure to solve steadystate solution of hyperbolic conservation laws on complex computing *** experiments are performed to test the method in solving various problems including the cases with the physical boundary not aligned with the *** results show highorder accuracy and good performance of the ***,the method is compared with the popular third-order total variation diminishing Runge-Kutta(TVD-RK3)time-marching method for steady-state *** examples show that for most of examples,the fixed-point fast sweeping method saves more than half CPU time costs than TVD-RK3 to converge to steady-state solutions.

关键词： Fixed-point fast sweeping methods Multi-resolution WENO schemes Steady state ILW procedure Convergence

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Classification of Attention Performance Post-Longitudinal tDCS via Functional Connectivity and Machine Learning Methods 9

Classification of Attention Performance Post-Longitudinal tD...

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9th IEEE International Conference for Convergence in Technology, I2CT 2024

作者： Rao, Akash K. Menon, Vishnu K. Bhavsar, Arnav Chowdhury, Shubhajit Roy Negi, Ramsingh Dutt, Varun Indian Institute of Technology Mandi Applied Cognitive Science Laboratory Mandi India Indian Institute of Technology Mandi School of Computing And Electrical Engineering Mandi India Institute of Nuclear Medicine And Allied Sciences Cognitive Control And Machine Learning Group Delhi India

ISBN: (纸本)9798350394474

Attention is the brain's mechanism for selectively processing specific stimuli while filtering out irrelevant information. Characterizing changes in attention following long-term interventions (such as transcranial direct current stimulation (tDCS)) has seldom been emphasized in the literature. To classify attention performance post-tDCS, this study uses functional connectivity and machine learning algorithms. Fifty individuals were split into experimental and control conditions. On Day 1, EEG data was obtained as subjects executed an attention task. From Day 2 through Day 8, the experimental group was administered 1mA tDCS, while the control group received sham tDCS. On Day 10, subjects repeated the task mentioned on Day 1. Functional connectivity metrics were used to classify attention performance using various machine learning methods. Results revealed that combining the Adaboost model and recursive feature elimination yielded a classification accuracy of 91.84%. We discuss the implications of our results in developing neurofeedback frameworks to assess attention. © 2024 IEEE.

关键词： Electroencephalography

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A Neurobehavioral Evaluation of the Efficacy of 1mA Longitudinal, Anodal TDCS on Multitasking and Transfer Performance

A Neurobehavioral Evaluation of the Efficacy of 1mA Longitud...

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2024 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2024

作者： Rao, Akash K Uttrani, Shashank Shah, Darshil Menon, Vishnu K Bhavsar, Arnav Roy Chowdhury, Shubhajit Negi, Ramsingh Dutt, Varun Manipal Academy of Higher Education India Indian Institute of Technology Applied Cognitive Science Laboratory Mandi India School of Computing and Electrical Engineering Indian Institute of Technology Mandi India Cognitive Control and Machine Learning Group The Institute of Nuclear Medicine and Allied Sciences Defence Research and Development Organization India

ISBN: (纸本)9781665410205

Multitasking requires rapid switching of attention and cognitive resources between different tasks in a dynamic environment, relying on cognitive processes, such as working memory, executive control, and selective attention. Although studies have investigated the efficacy of various neurobehavioral interventions in improving multitasking capabilities, the effects of longitudinal anodal transcranial direct current stimulation (tDCS) in enhancing multitasking performance have not been investigated. This research investigated the efficacy of 1mA anodal tDCS administered longitudinally on multitasking performance. 42 participants were randomly and equally divided into the experimental and placebo control conditions in this study conducted for 10 days. All participants executed two multitasking tasks on day 1 and received 1mA anodal/placebo tDCS during task training from day 2 to day 8. Various behavioral and neurophysiological measures have been measured. The findings revealed that tDCS had the propensity to augment multitasking capabilities in the trained task but had limited transfer capabilities. EEG-based brain connectivity analysis also revealed the formation of network hubs in the prefrontal and frontal regions, indicating enhanced cortical activation in the beta band. We intend to use these findings to design interventional frameworks to enhance multitasking performance using tDCS. © 2024 IEEE.

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Who Should I Trust? A Visual Analytics Approach for Comparing Net Load Forecasting Models

Who Should I Trust? A Visual Analytics Approach for Comparin...

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Grid Edge Technologies Conference & Exposition (Grid Edge), IEEE PES

作者： Kaustav Bhattacharjee Soumya Kundu Indrasis Chakraborty Aritra Dasgupta Department of Data Science New Jersey Institute of Technology USA Optimization and Control Group Pacific Northwest National Laboratory USA Center for Applied Scientific Computing Lawrence Livermore National Laboratory USA

ISBN: (数字)9798350352528

ISBN: (纸本)9798350352535

关键词： Analytical models Load forecasting Biological system modeling Visual analytics Decision making Predictive models Data models Planning Forecasting Load modeling

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Forte: An Interactive Visual Analytic Tool for Trust-Augmented Net Load Forecasting

Forte: An Interactive Visual Analytic Tool for Trust-Augment...

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Innovative Smart Grid Technologies (ISGT)

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Who should I trust? A Visual Analytics Approach for Comparing Net Load Forecasting Models

arXiv

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arXiv 2024年

作者： Bhattacharjee, Kaustav Kundu, Soumya Chakraborty, Indrasis Dasgupta, Aritra Department of Data Science New Jersey Institute of Technology United States Optimization and Control Group Pacific Northwest National Laboratory United States Center for Applied Scientific Computing Lawrence Livermore National Laboratory United States

关键词： Visual analytics

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