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Discovering Physics-Informed Neural Networks Model for Solving Partial Differential Equations through Evolutionary Computation

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arXiv 2024年

作者： Zhang, Bo Yang, Chao National Engineering Laboratory for Big Data Analysis and Applications Peking University Beijing100871 China School of Mathematical Sciences Peking University Beijing100871 China PKU Changsha Institute for Computing and Digital Economy Changsha410205 China

In recent years, the researches about solving partial differential equations (PDEs) based on artificial neural network have attracted considerable attention. In these researches, the neural network models are usually designed depend on human experience or trial and error. Despite the emergence of several model searching methods, these methods primarily concentrate on optimizing the hyperparameters of fully connected neural network model based on the framework of physics-informed neural networks (PINNs), and the corresponding search spaces are relatively restricted, thereby limiting the exploration of superior models. This article proposes an evolutionary computation method aimed at discovering the PINNs model with higher approximation accuracy and faster convergence rate. In addition to searching the numbers of layers and neurons per hidden layer, this method concurrently explores the optimal shortcut connections between the layers and the novel parametric activation functions expressed by the binary trees. In evolution, the strategy about dynamic population size and training epochs (DPSTE) is adopted, which significantly increases the number of models to be explored and facilitates the discovery of models with fast convergence rate. In experiments, the performance of different models that are searched through Bayesian optimization, random search and evolution is compared in solving Klein-Gordon, Burgers, and Lamé equations. The experimental results affirm that the models discovered by the proposed evolutionary computation method generally exhibit superior approximation accuracy and convergence rate, and these models also show commendable generalization performance with respect to the source term, initial and boundary conditions, equation coefficient and computational domain. The corresponding code is available at https://***/MathBon/Discover-PINNs-Model. Copyright © 2024, The Authors. All rights reserved.

关键词： Neural network models

Power Grid Critical State Search Based on Improved Particle Swarm Optimization 6th

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Power Grid Critical State Search Based on Improved Particle ...

6th International Conference on Advanced Intelligent Systems and Informatics, AISI 2020

作者： Luo, Jie Deng, Hui-Qiong Li, Qin-Bin Zheng, Rong-Jin Li, Pei-Qiang Chang, Kuo-Chi School of Information Science and Engineering Fujian University of Technology Fuzhou350108 China Fujian Provincial University Engineering Research Center of Smart Grid Simulation Analysis and Integrated Control Fuzhou350108 China Fujian Provincial Key Laboratory of Big Data Mining and Applications Fujian University of Technology Fuzhou China College of Mechanical and Electrical Engineering National Taipei University of Technology Taipei Taiwan

ISBN: (纸本)9783030586683

This article proposes a method to find the closest critical initial running state of power grid, aiming at the possible chain reaction failure caused by branch fault in power system. First of all, assuming the initial failure of power grid, considering the specific performance of relay protection, analyze the critical state of the branch in cascading trip in detail, the electrical distance between the current running state and the interlocking fault expressed in the form of nodal injection power is given. Secondly, on the basic of the relationship between the nodal injections power and the system safety, a safety level model that the system will not trigger cascading failures is established. Finally, the improved simplified mean particle swarm optimization algorithm is used to solve the model, and an example is analyzed on IEEE-14 node system. An example shows the effectiveness and feasibility of the proposed method, which provides a reference for further prevention of cascading trip accidents. © 2021, The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Outages

Finding Simplex Items in data Streams 39

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Finding Simplex Items in Data Streams

39th IEEE International Conference on data engineering, ICDE 2023

作者： Fan, Zhuochen Guo, Jiarui Li, Xiaodong Yang, Tong Zhao, Yikai Wu, Yuhan Cui, Bin Xu, Yanwei Uhlig, Steve Zhang, Gong Peking University School of Computer Science National Engineering Laboratory for Big Data Analysis Technology and Application Beijing China Peng Cheng Laboratory Shenzhen China Central Research Institute 2012 Labs Huawei Technologies Co. Ltd. Theory Lab Hong Kong Queen Mary University of London School of Electronic Engineering and Computer Science London United Kingdom

ISBN: (纸本)9798350322279

In this paper, we propose a new type of item in data streams, called simplex items. Simplex items have frequencies in consecutive p windows that can be approximated by a polynomial of degree at most k, where k = 0, 1, 2. These low-order representable simplex items have a wide range of potential applications. For example, when k = 1, we can leverage these items whose frequency has obvious linear increase or decrease to speed up the running time of a class of machine learning models and detect network attacks such as distributed denial-of-service (DDoS), etc. To find k-degree simplex items in real time, we propose a novel sketch, namely X-Sketch, to accurately record simplex items in a compact space. The key idea of X-Sketch is to effectively filter out non-simplex items with less memory overhead, and then monitor the remaining potential simplex items and keep those items with more consecutive windows. We conduct extensive experiments, and the experimental results show that the F1 Score of X-Sketch is on average 68.6%, 57.9%, and 42.2% higher than the baseline solution for k = 0, 1, 2, respectively. Finally, we also provide a case study that applies X-Sketch to "accelerate"the two machine learning models through end-to-end experiments. We have released our source code at GitHub. © 2023 IEEE.

关键词： Denial-of-service attack

PrompTHis: Visualizing the Process and Influence of Prompt Editing during Text-to-Image Creation

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arXiv 2024年

作者： Guo, Yuhan Shao, Hanning Liu, Can Xu, Kai Yuan, Xiaoru Key Laboratory of Machine Perception Ministry of Education School of AI Peking University China National Engineering Laboratory for Big Data Analysis and Application Peking University China University of Nottingham United Kingdom

Generative text-to-image models, which allow users to create appealing images through a text prompt, have seen a dramatic increase in popularity in recent years. However, most users have a limited understanding of how such models work and it often requires many trials and errors to achieve satisfactory results. The prompt history contains a wealth of information that could provide users with insights into what have been explored and how the prompt changes impact the output image, yet little research attention has been paid to the visual analysis of such process to support users. We propose the Image Variant Graph, a novel visual representation designed to support comparing prompt-image pairs and exploring the editing history. The Image Variant Graph models prompt differences as edges between corresponding images and presents the distances between images through projection. Based on the graph, we developed the PrompTHis system through co-design with artists. Besides Image Variant Graph, PrompTHis also incorporates a detailed prompt-image history and a navigation mini-map. Based on the review and analysis of the prompting history, users can better understand the impact of prompt changes and have a more effective control of image generation. A quantitative user study with eleven amateur participants and qualitative interviews with five professionals and one amateur user were conducted to evaluate the effectiveness of PrompTHis. The results demonstrate PrompTHis can help users review the prompt history, make sense of the model, and plan their creative process. © 2024, CC BY.

关键词： Image analysis

Accelerating Scalable Graph Neural Network Inference with Node-Adaptive Propagation

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Accelerating Scalable Graph Neural Network Inference with No...

International Conference on data engineering

作者： Xinyi Gao Wentao Zhang Junliang Yu Yingxia Shao Quoc Viet Hung Nguyen Bin Cui Hongzhi Yin The University of Queensland Brisbane Australia Peking University Beijing China National Engineering Laboratory for Big Data Analysis and Applications Beijing China Beijing University of Posts and Telecommunications Beijing China Griffith University Gold Coast Australia

ISBN: (数字)9798350317152

ISBN: (纸本)9798350317169

Graph neural networks (GNNs) have exhibited exceptional efficacy in a diverse array of applications. However, the sheer size of large-scale graphs presents a significant challenge to real-time inference with GNNs. Although existing Scalable GNNs leverage linear propagation to preprocess the features and accelerate the training and inference procedure, these methods still suffer from scalability issues when making inferences on unseen nodes, as the feature preprocessing requires the graph to be known and fixed. To further accelerate Scalable GNNs inference in this inductive setting, we propose an online propagation framework and two novel node-adaptive propagation methods that can customize the optimal propagation depth for each node based on its topological information and thereby avoid redundant feature propagation. The trade-off between accuracy and latency can be flexibly managed through simple hyper-parameters to accommodate various latency constraints. Moreover, to compensate for the inference accuracy loss caused by the potential early termination of propagation, we further propose Inception Distillation to exploit the multi-scale receptive field information within graphs. The rigorous and comprehensive experimental study on public datasets with varying scales and characteristics demonstrates that the proposed inference acceleration framework outperforms existing state-of-the-art graph inference acceleration methods in terms of accuracy and efficiency. Particularly, the superiority of our approach is notable on datasets with larger scales, yielding a $75\times$ inference speedup on the largest Ogbn-products dataset.

关键词： Training Accuracy Scalability Redundancy Propagation losses data engineering Real-time systems

Accelerating Scalable Graph Neural Network Inference with Node-Adaptive Propagation

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arXiv 2023年

作者： Gao, Xinyi Zhang, Wentao Yu, Junliang Shao, Yingxia Nguyen, Quoc Viet Hung Cui, Bin Yin, Hongzhi The University of Queensland Brisbane Australia Peking University Beijing China National Engineering Laboratory for Big Data Analysis and Applications Beijing China Beijing University of Posts and Telecommunications Beijing China Griffith University Gold Coast Australia

Graph neural networks (GNNs) have exhibited exceptional efficacy in a diverse array of applications. However, the sheer size of large-scale graphs presents a significant challenge to real-time inference with GNNs. Although existing Scalable GNNs leverage linear propagation to preprocess the features and accelerate the training and inference procedure, these methods still suffer from scalability issues when making inferences on unseen nodes, as the feature preprocessing requires the graph to be known and fixed. To further accelerate Scalable GNNs inference in this inductive setting, we propose an online propagation framework and two novel node-adaptive propagation methods that can customize the optimal propagation depth for each node based on its topological information and thereby avoid redundant feature propagation. The trade-off between accuracy and latency can be flexibly managed through simple hyper-parameters to accommodate various latency constraints. Moreover, to compensate for the inference accuracy loss caused by the potential early termination of propagation, we further propose Inception Distillation to exploit the multi-scale receptive field information within graphs. The rigorous and comprehensive experimental study on public datasets with varying scales and characteristics demonstrates that the proposed inference acceleration framework outperforms existing state-of-the-art graph inference acceleration methods in terms of accuracy and efficiency. Particularly, the superiority of our approach is notable on datasets with larger scales, yielding a 75× inference speedup on the largest Ogbn-products dataset. Copyright © 2023, The Authors. All rights reserved.

关键词： Graph neural networks

SHE: A Generic Framework for data Stream Mining over Sliding Windows 22

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SHE: A Generic Framework for Data Stream Mining over Sliding...

Proceedings of the 51st International Conference on Parallel Processing

作者： Yuhan Wu Zhuochen Fan Qilong Shi Yixin Zhang Tong Yang Cheng Chen Zheng Zhong Junnan Li Ariel Shtul Yaofeng Tu School of Computer Science and National Engineering Laboratory for Big Data Analysis Technology and Application Peking University China and PCL Research Center of Networks and Communications Peng Cheng Laboratory China School of Computer Science and National Engineering Laboratory for Big Data Analysis Technology and Application Peking University China National University of Defense Technology China Redis Labs Israel ZTE Corporation China

ISBN: (纸本)9781450397339

1data stream mining over a sliding window is a fundamental problem in many applications, such as financial data trackers, intrusion detection and QoS. To meet the demand for high throughput of high speed data streams, sliding window algorithms turn to hardware platforms including FPGA/ASIC and programmable switches. These hardware platforms have three constraints for algorithms running on, which are 1) small memory usage 2) single stage memory access and 3) limited concurrent memory access. Algorithms perfectly fit in with these constraints will enable a highest utilization of these hardware platforms. However, no existing sliding window algorithm is specifically designed for hardware platforms. In this paper, we propose the Sliding Hardware Estimator (SHE), which is a generic framework that extends existing fixed window algorithms to sliding windows on hardware platforms. The key idea of SHE is that, during insertions we approximately delete out-dated information with little time and space overhead, while during queries we design sophisticated techniques to minimize error. We have fully implemented our SHE on FPGA, achieving a throughput of 544 Mips. We apply SHE to four typical data stream mining tasks. Experimental results show that, when compared with the state-of-the-art which cannot be implemented in hardware, SHE reduces the error by up to 100 times in membership queries. All related source codes are released at Github.

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K-Core Decomposition on Super Large Graphs with Limited Resources

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arXiv 2021年

作者： Gao, Shicheng Xu, Jie Li, Xiaosen Fu, Fangcheng Zhang, Wentao Ouyang, Wen Tao, Yangyu Cui, Bin School of Electronic and Computer Engineering Shenzhen Graduate School Peking University China Tencent Inc. China Center for Data Science Peking University National Engineering Laboratory for Big Data Analysis and Applications China School of CS Key Laboratory of High Confidence Software Technologies Peking University China Institute of Computational Social Science Peking University Qingdao China

K-core decomposition is a commonly used metric to analyze graph structure or study the relative importance of nodes in complex graphs. Recent years have seen rapid growth in the scale of the graph, especially in industrial settings. For example, our industrial partner runs popular social applications with billions of users and is able to gather a rich set of user data. As a result, applying K-core decomposition on large graphs has attracted more and more attention from academics and the industry. A simple but effective method to deal with large graphs is to train them in the distributed settings, and some distributed K-core decomposition algorithms are also proposed. Despite their effectiveness, we experimentally and theoretically observe that these algorithms consume too many resources and become unstable on super-large-scale graphs, especially when the given resources are limited. In this paper, we deal with those super-large-scale graphs and propose a divide-and-conquer strategy on top of the distributed K-core decomposition algorithm. We evaluate our approach on three large graphs. The experimental results show that the consumption of resources can be significantly reduced, and the calculation on large-scale graphs becomes more stable than the existing methods. For example, the distributed K-core decomposition algorithm can scale to a large graph with 136 billion edges without losing correctness with our divide-and-conquer technique. Copyright © 2021, The Authors. All rights reserved.

关键词： Graphic methods

A-Map: Interactive Visual Exploration of Intercity Accessibility Dynamics Based on Railway Network data

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A-Map: Interactive Visual Exploration of Intercity Accessibi...

Pacific (formerly Asia-Pacific APVIS) Visualization Symposium

作者： Kaichen Nie Hanning Shao Yuchu Luo Min Tian Hao Wu Wei Zeng Xin Fu Xiaoru Yuan Key Laboratory of Machine Perception (Ministry of Education) School of AI Peking University Hong Kong University of Science and Technology Guangzhou Chang’an University National Engineering Laboratory for Big Data Analysis and Application Peking University

ISBN: (数字)9798350393804

ISBN: (纸本)9798350393811

Railway transportation is closely linked to everyday lives while also aiding domain experts in analyzing national or regional development. However, discrepancies between travel time reduced by railways and actual distance pose challenges in visualizing the accessibility. Existing methods either struggle to simultaneously depict the accessibility relationships among all cities or disregard genuine geographical positions, leading to spatial cognitive confusion. In this work, we propose a novel approach to balance between the geographical positions and travel time between cities. We construct linear cartograms to represent accessibility while preserving better local railway network structures compared with existing methods. We further propose the A-Map system, enabling users to interactively explore the extensive development of China’s railway system over decades. We validate the effectiveness of our proposed layout algorithm from qualitative metric evaluation and illustrate the applicability of our system with results.

关键词： Measurement Visualization Heuristic algorithms Urban areas Layout Transportation data visualization