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Space-time deep neural network approximations for high-dimensional partial differential equations

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arXiv 2020年

作者： Hornung, Fabian Jentzen, Arnulf Salimova, Diyora Faculty of Mathematics Karlsruhe Institute of Technology Germany China Institute for Analysis and Numerics Faculty of Mathematics and Computer Science University of Münster Germany Seminar for Applied Mathematics Department of Mathematics ETH Zurich Switzerland Department of Information Technology and Electrical Engineering ETH Zurich Switzerland Department for Applied Mathematics University of Freiburg Germany

It is one of the most challenging issues in applied mathematics to approximately solve high-dimensional partial differential equations (PDEs) and most of the numerical approximation methods for PDEs in the scientific literature suffer from the so-called curse of dimensionality in the sense that the number of computational operations employed in the corresponding approximation scheme to obtain an approximation precision Ε > 0 grows exponentially in the PDE dimension and/or the reciprocal of Ε. Recently, certain deep learning based methods for PDEs have been proposed and various numerical simulations for such methods suggest that deep artificial neural network (ANN) approximations might have the capacity to indeed overcome the curse of dimensionality in the sense that the number of real parameters used to describe the approximating deep ANNs grows at most polynomially in both the PDE dimension d ∈ N and the reciprocal of the prescribed approximation accuracy Ε > 0. There are now also a few rigorous mathematical results in the scientific literature which substantiate this conjecture by proving that deep ANNs overcome the curse of dimensionality in approximating solutions of PDEs. Each of these results establishes that deep ANNs overcome the curse of dimensionality in approximating suitable PDE solutions at a fixed time point T > 0 and on a compact cube [a, b]d in space but none of these results provides an answer to the question whether the entire PDE solution on [0, T] × [a, b]d can be approximated by deep ANNs without the curse of dimensionality. It is precisely the subject of this article to overcome this issue. More specifically, the main result of this work in particular proves for every a ∈ R, b ∈ (a, ∞) that solutions of certain Kolmogorov PDEs can be approximated by deep ANNs on the space-time region [0, T] × [a, b]d without the curse of dimensionality. Copyright © 2020, The Authors. All rights reserved.

关键词： Partial differential equations

Methods for pattern detection based on colour and size features in video streams

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Journal of Physics: Conference Series 2021年第1期1843卷

作者： Nguyen Cuong The V I Syryamkin Nguyen Trang Hoang Thuy Institute of Applied Mathematics and Computer Science Tomsk State University Tomsk Russia Faculty of Information technology Vietnam Maritime University Haiphong Vietnam

Detecting pattern in images plays a huge role in the field of computer vision. The article summarizes methods for detecting patterns by their properties, such as colours, shapes in images. And with video, the detection of patterns is also based on their movement. Human face recognition problem is also mentioned in the application of MTCNN network architecture and reconfiguring FaceNet to suit actual requirements. Test results are given and recommendations with data and program operating conditions are provided for the reference.

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Business model canvas should pay more attention to the software startup team

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arXiv 2021年

作者： Kemell, Kai-Kristian Elonen, Atte Suoranta, Mari Nguyen-Duc, Anh Garbajosa, Juan Chanin, Rafael Melegati, Jorge Rafiq, Usman Aldaeej, Abdullah Assyne, Nana Sales, Afonso Hyrynsalmi, Sami Risku, Juhani Edison, Henry Abrahamsson, Pekka Faculty of Information Technology University of Jyvaskyla Jyvaskyla Finland School of Business and Economics University of Jyväskylä Jyväskylä Finland Department of Business and IT University of Southeast Norway Bø Norway Universidad Politécnica de Madrid Madrid Spain School of Technology PUCRS Porto Alegre Brazil Faculty of Computer Science Free University of Bozen-Bolzano Bolzano Italy Department of Information Systems University of Maryland Baltimore Country Baltimore United States Department of Software Engineering LUT University Lahti Finland Lero NUI Galway Galway Ireland

Business Model Canvas (BMC) is a tool widely used to describe startup business models. Despite the various business aspects described, BMC pays a little emphasis on team-related factors. The importance of team-related factors in software development has been acknowledged widely in literature. While not as extensively studied, the importance of teams in software startups is also known in both literature and among practitioners. In this paper, we propose potential changes to BMC to have the tool better reflect the importance of the team, especially in a software startup environment. Based on a literature review, we identify various components related to the team, which we then further support with empirical data. We do so by means of a qualitative case study of five startups. Copyright © 2021, The Authors. All rights reserved.

关键词： Software design

Recognition of White-Cane Users from Surveillance Camera Images Based on Detection of Line Segments

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Recognition of White-Cane Users from Surveillance Camera Ima...

IEEE Global Conference on Life sciences and Technologies (LifeTech)

作者： Kazusa Sanada Hotaka Takizawa Mayumi Aoyagi Akihisa Ohya Makoto Kobayashi Department of Computer Science University of Tsukuba Tsukuba Japan Faculty of Engineering Information and Systems University of Tsukuba Tsukuba Japan Department of Special Needs Education Aichi University of Education Kariya Japan Faculty of Health Sciences Tsukuba University of Technology Tsukuba Japan

ISBN: (数字)9781728170633

ISBN: (纸本)9781728170640

Accidents caused by visually impaired individuals in public spaces are becoming social problems. In this study, we proposed a recognition method of white-cane users walking in public spaces on the basis of the video images obtained by surveillance cameras. The proposed method was applied to actual camera images, and experimental results were shown.

关键词： The visually impaired White cane Surveillance camera Line segment detection Line segment tracking Detective cameras open spaces Line sections Recognition (Psychology) Social Problems Line images Accidents Consumers

Machine learning for modelling unstructured grid data in computational physics: a review

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arXiv 2025年

作者： Cheng, Sibo Bocquet, Marc Ding, Weiping Finn, Tobias Sebastian Fu, Rui Fu, Jinlong Guo, Yike Johnson, Eleda Li, Siyi Liu, Che Moro, Eric Newton Pan, Jie Piggott, Matthew Quilodran, Cesar Sharma, Prakhar Wang, Kun Xiao, Dunhui Xue, Xiao Zeng, Yong Zhang, Mingrui Zhou, Hao Zhu, Kewei Arcucci, Rossella CEREA ENPC EDF R&D Institut Polytechnique de Paris Île-de-France France School of Artificial Intelligence and Computer Science Nantong University Jiangsu Nantong226019 China School of Mathematical Sciences Key Laboratory of Intelligent Computing and Applications Tongji University Shanghai200092 China School of Engineering and Materials Science Faculty of Science and Engineering Queen Mary University of London LondonE1 4NS United Kingdom Zienkiewicz Centre for Modelling Data and AI Faculty of Science and Engineering Swansea University SwanseaSA1 8EN United Kingdom Department of Computer Science and Engineering Hong Kong university of science and technology Hong Kong Department of Earth Science & Engineering Imperial College London LondonSW7 2AZ United Kingdom Tianjin Key Laboratory of Imaging and Sensing Microelectronics Technology School of Microelectronics Tianjin University Tianjin300072 China Centre for Health Informatics Cumming School of Medicine University of Calgary CalgaryABT2N 1N4 Canada Department of Community Health Sciences Cumming School of Medicine University of Calgary CalgaryABT2N 1N4 Canada Undaunted Grantham Institute for Climate Change and the Environment Imperial College London LondonSW7 2AZ United Kingdom Culham Campus AbingdonOX14 3DB United Kingdom Centre for Computational Science Department of Chemistry University College London LondonWC1E 6BT United Kingdom Concordia Institute for Information Systems Engineering Concordia University MontrealQCH3G 1M8 Canada School of Mechanical Medical and Process Engineering Faculty of Engineering Queensland University of Technology BrisbaneQLD Australia Department of Chemical Engineering University College London LondonWC1E 6BT United Kingdom

Unstructured grid data are essential for modelling complex geometries and dynamics in computational physics. Yet, their inherent irregularity presents significant challenges for conventional machine learning (ML) techniques. This paper provides a comprehensive review of advanced ML methodologies designed to handle unstructured grid data in high-dimensional dynamical systems. Key approaches discussed include graph neural networks, transformer models with spatial attention mechanisms, interpolation-integrated ML methods, and meshless techniques such as physics-informed neural networks. These methodologies have proven effective across diverse fields, including fluid dynamics and environmental simulations. This review is intended as a guidebook for computational scientists seeking to apply ML approaches to unstructured grid data in their domains, as well as for ML researchers looking to address challenges in computational physics. It places special focus on how ML methods can overcome the inherent limitations of traditional numerical techniques and, conversely, how insights from computational physics can inform ML development. To support benchmarking, this review also provides a summary of open-access datasets of unstructured grid data in computational physics. Finally, emerging directions such as generative models with unstructured data, reinforcement learning for mesh generation, and hybrid physics-data-driven paradigms are discussed to inspire future advancements in this evolving field. © 2025, CC BY-NC-SA.

关键词： Mesh generation

Human Cognition and Hyper Intelligence

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Human Cognition and Hyper Intelligence

IEEE International Symposium on Dependable, Autonomic and Secure Computing (DASC)

作者： D. Frank Hsu Mohammad Shehata Shao-Min Hung Shinsuke Shimojo Ryota Kanai Christina Schweikert Michael W. David Vincenzo Piuri Jianhua Ma Fordham University New York NY U.S.A. Division of Biology & Biological Engineering/Computation & Neural Systems California Institute of Technology Pasadena U.S.A. Araya Inc. Tokyo Japan Division of Computer Science Mathematics and Science St. John's University Queens New York U.S.A. School of Science & Technology Intelligence National Intelligence University Bethesda MD U.S.A. Università degli Studi di Milano Milano Italy Faculty of Computer and Information Sciences Hosei University Tokyo Japan

ISBN: (纸本)9781665421751

Human cognition is a complex neural process ranging from sensor-motor tasks to decision making. Hyper intelligence strives to accomplish complex tasks through creation or combination of diverse intelligent systems used by humans or machines based on a variety of methodologies, algorithms, and models in statistics, computation, and mathematics. In this paper, we give perspectives on various aspects of human cognition and hyper intelligence, as well as their relations, interactions, and causal effects. In particular, we focus on a diverse set of topics: cognitive process, functions of consciousness, model fusion, supply chain development, and convergence of technologies. Opportunities and challenges of this emerging field are also discussed. In addition, several issues for further investigation are suggested.

关键词： Hyper-intelligent systems Cognitive processes Computational modeling Supply chains Decision making Big Data Mathematical models

Emerging app issue identification via online joint sentiment-topic tracing

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arXiv 2020年

作者： Gao, Cuiyun Zeng, Jichuan Wen, Zhiyuan Lo, David Xia, Xin King, Irwin Lyu, Michael R. Department of Computer Science and Engineering Chinese University of Hong Kong Shatin Hong Kong Department of Computing Hong Kong Polytechnic university Kowloon Hong Kong School of Information Systems Singapore Management University Singapore Faculty of Information Technology Monash University Australia

Millions of mobile apps are available in app stores, such as Apple’s App Store and Google Play. For a mobile app, it would be increasingly challenging to stand out from the enormous competitors and become prevalent among users. Good user experience and well-designed functionalities are the keys to a successful app. To achieve this, popular apps usually schedule their updates frequently. If we can capture the critical app issues faced by users in a timely and accurate manner, developers can make timely updates, and good user experience can be ensured. There exist prior studies on analyzing reviews for detecting emerging app issues. These studies are usually based on topic modeling or clustering techniques. However, the short-length characteristics and sentiment of user reviews have not been considered. In this paper, we propose a novel emerging issue detection approach named MERIT to take into consideration the two aforementioned characteristics. Specifically, we propose an Adaptive Online Biterm Sentiment-Topic (AOBST) model for jointly modeling topics and corresponding sentiments that takes into consideration app versions. Based on the AOBST model, we infer the topics negatively reflected in user reviews for one app version, and automatically interpret the meaning of the topics with most relevant phrases and sentences. Experiments on popular apps from Google Play and Apple’s App Store demonstrate the effectiveness of MERIT in identifying emerging app issues, improving the state-of-the-art method by 22.3% in terms of F1-score. In terms of efficiency, MERIT can return results within acceptable time. Copyright © 2020, The Authors. All rights reserved.

关键词： User profile

Application of artificial intelligence techniques for automated detection of myocardial infarction: A review

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arXiv 2021年

作者： Joloudari, Javad Hassannataj Mojrian, Sanaz Nodehi, Issa Mashmool, Amir Zadegan, Zeynab Kiani Shirkharkolaie, Sahar Khanjani Alizadehsani, Roohallah Tamadon, Tahereh Khosravi, Samiyeh Kohnehshari, Mitra Akbari Hassannatajjeloudari, Edris Sharifrazi, Danial Mosavi, Amir Loh, Hui Wen Tan, Ru-San Rajendra Acharya, U. Department of Computer Engineering Faculty of Engineering University of Birjand Birjand Iran Department of Information Technology Engineering Mazandaran University of Science and Technology Babol Iran Department of Computer Engineering University of Qom Qom Iran Italy Institute for Intelligent Systems Research and Innovation Deakin University GeelongVIC3216 Australia Computer Engineering Department Engineering Faculty Bu-Ali Sina University Hamedan Iran Department of Nursing School of Nursing and Allied Medical Sciences Maragheh Faculty of Medical Sciences Maragheh Iran Department of Computer Engineering Shiraz Branch Islamic Azad University Shiraz Iran Faculty of Informatics Obuda University Budapest Hungary School of Science and Technology Singapore University of Social Sciences Singapore Department of Cardiology National Heart Centre Singapore Singapore Ngee Ann Polytechnic Singapore599489 Singapore Dept. of Biomedical Informatics and Medical Engineering Asia University Taichung Taiwan

Myocardial infarction (MI) results in heart muscle injury due to receiving insufficient blood flow. MI is the most common cause of mortality in middle-aged and elderly individuals around the world. To diagnose MI, clinicians need to interpret electrocardiography (ECG) signals, which requires expertise and is subject to observer bias. Artificial intelligence-based methods can be utilized to screen for or diagnose MI automatically using ECG signals. In this work, we conducted a comprehensive assessment of artificial intelligence-based approaches for MI detection based on ECG as well as other biophysical signals, including machine learning (ML) and deep learning (DL) models. The performance of traditional ML methods relies on handcrafted features and manual selection of ECG signals, whereas DL models can automate these tasks. The review observed that deep convolutional neural networks (DCNNs) yielded excellent classification performance for MI diagnosis, which explains why they have become prevalent in recent years. To our knowledge, this is the first comprehensive survey of artificial intelligence techniques employed for MI diagnosis using ECG and other biophysical signals. © 2021, CC BY-SA.

关键词： Deep neural networks

Dual-channel hypergraph networks in the time–frequency domain for learning advanced spatiotemporal dependencies in multivariate time series

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Neurocomputing 2025年 648卷

作者： Ziwei Chen Jianjian Jiang Xiangmin Luo Fangyuan Lei Xiaochen Yuan Jin Zhan Guangdong Provincial Key Laboratory of Intellectual Property and Big Data Guangdong Polytechnic Normal University Guangzhou 510665 China College of Electronic and Information Engineering Guangdong Polytechnic Normal University Guangzhou 510665 China Faculty of Applied Sciences Macao Polytechnic University 999078 Macao Special Administrative Region of China School of Computer Science Guangdong Polytechnic Normal University Guangzhou 510665 China

Multivariate time series play a crucial role in applications such as human activity recognition and fault diagnosis, where capturing spatiotemporal dependencies is paramount. While recent methods have leveraged graph neural networks (GNNs) or hybrid models that integrate convolutional neural networks (CNNs) and long short-term memory (LSTM) networks to learn these dependencies, two significant challenges remain: First, previous research has neglected the dynamic dependencies and overall correlations among multivariate time series, which are crucial for comprehensive data utilization. Second, when processing both temporal and spatial dimensional information, how to effectively integrate higher-order information while avoiding complexity issues in model design and implementation remains a challenge. To address these challenges, we propose a Dual-channel Temporal–Spatial Hypergraph Network (DTSHN) classification framework based on the time–frequency domain. Specifically, our DTSHN is a time–frequency domain dual-channel interactive learning model that enhances the utilization and diversity of time series data. To capture higher-order relationships among signals, we design a dynamic hypergraph structure learning module and construct temporal and spatial hypergraph structures in the time–frequency domain. Additionally, we propose a temporal–spatial hypergraph network module to learn temporal correlations and spatial dependencies within time series. Furthermore, to address the feature consistency issue in the time–frequency domain under the dual-channel paradigm, we introduce a time–frequency contrastive learning strategy to enable the model to learn effective feature representations across both domains. The experimental results show that our proposed model achieves 96.77%, 94.33% and 97.57% optimal accuracy in HAR, FM and PS datasets, respectively. In addition, we have reduced the FLOPs by 19.8% compared to other optimal models.

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