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On the coupled NBEM and FEM for a class of nonlinear exterior Dirichlet problem in R^(2.)

Science china mathematics 2004年第z1期47卷 181-189页

作者： wu zhengpeng, kang tong & yu dehaoinstitute of computational mathematics and scientific/engineering computing, {2. of mathematics and System sciences, chinese academy of sciences, beijing 100080, china Department of Applied mathematics, beijing Broadcasting Institute, beijing 10002., china Combinatorial and {12. mathematics Center, Pohang University of Science and Technology, Phoang 790-784, Republic of Korea chinese Acad Sci Acad Math & Syst Sci Inst Computat Math & Sci Engn Comp Beijing 100080 Peoples R China beijing Broadcasting Inst Dept Appl Math Beijing 100024 Peoples R China Pohang Univ Sci & Technol Combinatorial & Computat Math Ctr Phoang 790784 South Korea

In this paper, based on the natural boundary reduction advanced by Feng and yu, we couple the finite elementapproach with the natural boundary element method to study theweak solvability and Galerkin approximation of a class ofnonlinear exterior boundary value problems. The analysis is mainlybased on the variational formulation with *** provethe error estimate of the finite element solution and obtain theasymptotic rate of convergence. Finally, we also give anumerical example.

关键词： natural boundary integral method, finite element method, coupling method, error estimate.

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Brain-inspired artificial intelligence research: A review

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Science china(Technological sciences) 2024年第8期67卷 2282-2296页

作者： WANG GuoYin BAO HuaNan LIU Qun ZHOU TianGang wu Si HUANG TieJun yu ZhaoFei LU Cewu GONG YiHong ZHANG ZhaoXiang HE Sheng Chongqing Key Laboratory of computational Intelligence Chongqing University of Posts and TelecommunicationsChongqing 400065China Key Laboratory of Cyberspace Big Data Intelligent Security Chongqing University of Posts and TelecommunicationsChongqing 400065China College of Computer and Information Science Chongqing Normal UniversityChongqing 401331China State Key Laboratory of Brain and Cognitive Science Institute of BiophysicsChinese Academy of SciencesBeijing 100101China School of Psychological and Cognitive sciences Peking UniversityBeijing 100871China State Key Laboratory of Multimedia Information Processing School of Computer SciencePeking UniversityBeijing 100871China Department of Computer Science School of ElectronicsInformation and Electrical EngineeringShanghai Jiao Tong UniversityShanghai 200240China Faculty of Electronic and Information engineering Xi’an Jiaotong UniversityXi’an 710049China The Center for Research on Intelligent Perception and computing Institute of AutomationChinese Academy of SciencesBeijing 100190China Institute of Biophysics Chinese Academy of SciencesBeijing 100101China

Artificial intelligence(AI) systems surpass certain human intelligence abilities in a statistical sense as a whole, but are not yet the true realization of these human intelligence abilities and behaviors. There are differences, and even contradictions, between the cognition and behavior of AI systems and humans. With the goal of achieving general AI, this study contains a review of the role of cognitive science in inspiring the development of the three mainstream academic branches of AI based on the three-layer framework proposed by David Marr, and the limitations of the current development of AI are explored and analyzed. The differences and inconsistencies between the cognition mechanisms of the human brain and the computation mechanisms of AI systems are analyzed. They are found to be the cause of the differences and contradictions between the cognition and behavior of AI systems and humans. Additionally, eight important research directions and their scientific issues that need to focus on braininspired AI research are proposed: highly imitated bionic information processing, a large-scale deep learning model that balances structure and function, multi-granularity joint problem solving bidirectionally driven by data and knowledge, AI models that simulate specific brain structures, a collaborative processing mechanism with the physical separation of perceptual processing and interpretive analysis, embodied intelligence that integrates the brain cognitive mechanism and AI computation mechanisms,intelligence simulation from individual intelligence to group intelligence(social intelligence), and AI-assisted brain cognitive intelligence.

关键词： artificial intelligence cognitive science brain science intelligence science large language model

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