计算机科学 ›› 2022, Vol. 49 ›› Issue (4): 254-262.doi: 10.11896/jsjkx.210500158

• 人工智能 • 上一篇    下一篇

基于物理信息的神经网络:最新进展与展望

李野, 陈松灿   

  1. 南京航空航天大学计算机科学与技术学院/人工智能学院 南京 211106
  • 收稿日期:2021-05-22 修回日期:2021-10-19 发布日期:2022-04-01
  • 通讯作者: 李野(yeli20@nuaa.edu.cn)
  • 基金资助:
    南京航空航天大学新教师工作启动基金(90YAH20131); 中央高校基本科研业务费(NJ2020023)

Physics-informed Neural Networks:Recent Advances and Prospects

LI Ye, CHEN Song-can   

  1. College of Computer Science and Technology/Artificial Intelligence, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China
  • Received:2021-05-22 Revised:2021-10-19 Published:2022-04-01
  • About author:LI Ye,born in 1989,Ph.D,lecturer,is a member of China Computer Federation.His main research interests include machine learning and numerical solutions for partial differential equations.
  • Supported by:
    This work was supported by the Start-up Fund of Nanjing University of Aeronautics and Astronautics(90YAH20131) and Fundamental Research Funds for the Central Universities(NJ2020023).

摘要: 基于物理信息的神经网络(Physics-informed Neural Networks,PINN),是一类用于解决有监督学习任务的神经网络,它不仅尽力遵循训练数据样本的分布规律,而且遵守由偏微分方程描述的物理定律。与纯数据驱动的神经网络学习相比,PINN在训练过程中施加了物理信息约束,因此能用更少的数据样本学习得到更具泛化能力的模型。近年来,PINN已逐渐成为机器学习和计算数学交叉学科的研究热点,并在理论和应用方面都获得了相对深入的研究,取得了可观的进展。但PINN独特的网络结构在实际应用中也存在训练缓慢甚至不收敛、精度低等问题。文中在总结当前PINN研究的基础上,对其网络/体系设计及其在流体力学等多个领域中的应用进行了探究,并展望了进一步的研究方向。

关键词: 机器学习, 偏微分方程, 人工智能, 神经网络, 物理模型

Abstract: Physical-informed neural networks (PINN) are a class of neural networks used to solve supervised learning tasks.They not only try to follow the distribution law of the training data, but also follow the physical laws described by partial diffe-rential equations.Compared with pure data-driven neural networks, PINN imposes physical information constraints during the training process, so that more generalized models can be acquired with fewer training data.In recent years, PINN has gradually become a research hotspot in the interdisciplinary field of machine learning and computational mathematics, and has obtained relatively in-depth research in both theory and application, and has made considerable progress.However, due to the unique network structure of PINN, there are some problems such as slow training or even non-convergence and low precision in practical application.On the basis of summarizing the current research of PINN, this paper explores the network/system design and its application in many fields such as fluid mechanics, and looks forward to the further research directions.

Key words: Artificial intelligence, Machine learning, Neural network, Partial differential equations, Physical model

中图分类号: 

  • TP183
[1] KRIZHEVSKY A,SUTSKEVER I,HINTON G E.ImageNet classification with deep convolutional neural networks[J].Communications of the ACM,2017,60(6):84-90.
[2] LI H.Deep learning for natural language processing:advantages and challenges[J].National Science Review,2018,5(1):24-26.
[3] LAKE B M,SALAKHUTDINOV R,TENENBAUM J B.Human-level concept learning through probabilistic program induction[J].Science,2015,350(6266):1332-1338.
[4] ALIPANAHI B,DELONG A,WEIRAUCH M T,et al.Predicting the sequence specificities of DNA-and RNA-binding proteins by deep learning[J].Nature Biotechnology,2015,33(8):831-838.
[5] TEMAM R.Navier-Stokes equations:theory and numericalanalysis[M].American Mathematical Society,2001.
[6] TAFLOVE A,HAGNESS S C.Computational electrodynamics:the finite-difference time-domain method[M].Artech House,2005.
[7] BEREZIN F A,SHUBIN M.The Schrödinger Equation[M].Springer Science & Business Media,2012.
[8] AMES W F.Numerical methods for partial differential equations[M].Academic Press,2014.
[9] LAGARIS I E,LIKAS A,FOTIADIS D I.Artificial neural networks for solving ordinary and partial differential equations[J].IEEE Transactions on Neural Networks,1998,9(5):987-1000.
[10] PSICHOGIOS D C,UNGAR L H.A hybrid neural network-first principles approach to process modeling[J].AIChE Jour-nal,1992,38(10):1499-1511.
[11] LAGARIS I E,LIKAS A C,PAPAGEORGIOU D G.Neural-network methods for boundary value problems with irregular boundaries[J].IEEE Transactions on Neural Networks,2000,11(5):1041-1049.
[12] RAISSI M,PERDIKARIS P,KARNIADAKIS G E.Physics informed deep learning (part I):Data-driven solutions of nonli-near partial diffe-rential equations[J].arXiv:1711.10561,2017.
[13] RAISSI M,PERDIKARIS P,KARNIADAKIS G E.Physics informed deep learning (part II):Data-driven discovery of nonli-near partial differential equations[J].arXiv:1711.10566,2017.
[14] RAISSI M,PERDIKARIS P,KARNIADAKIS G E.Physics-informed neural networks:A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations[J].Journal of Computational Physics,2019,378:686-707.
[15] BAKER N,ALEXANDER F,BREMER T,et al.Workshop report on basic research needs for scientific machine learning:Core technologies for artificial intelligence[R].USDOE Office of Science (SC),Washington,DC(United States),2019.
[16] BAYDIN A G,PEARLMUTTER B A,RADUL A A,et al.Automatic differentiation in machine learning:a survey[J].Journal of Machine Learning Research,2018,18:1-43.
[17] LU L,MENG X,MAO Z,et al.DeepXDE:A deep learning library for solving differential equations[J].SIAM Review,2021,63(1):208-228.
[18] WANG J X,WU J,LING J,et al.A comprehensive physics-informed machine learning framework for predictive turbulence modeling[J].arXiv:1701.07102,2017.
[19] ZHU Y,ZABARAS N.Bayesian deep convolutional encoder-decoder networks for surrogate modeling and uncertainty quantification[J].Journal of Computational Physics,2018,366:415-447.
[20] HAGGE T,STINIS P,YEUNG E,et al.Solving differentialequations with unknown constitutive relations as recurrent neural networks[J].arXiv:1710.02242,2017.
[21] HAN J,JENTZEN A,WEINAN E.Solving high-dimensionalpartial differential equations using deep learning[J].Procee-dings of the National Academy of Sciences,2018,115(34):8505-8510.
[22] TRIPATHY R K,BILIONIS I.Deep UQ:Learning deep neural network surrogate models for high dimensional uncertainty quantification[J].Journal of Computational Physics,2018,375:565-588.
[23] VLACHAS P R,BYEON W,WAN Z Y,et al.Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks[J/OL].Proceedings of the Royal Society A:Mathematical,Physical and Engineering Sciences,2018,474(2213).https://doi.org/10.1098/rspa.2017.0844.
[24] PARISH E J,DURAISAMY K.A paradigm for data-driven predictive modeling using field inversion and machine learning[J].Journal of Computational Physics,2016,305:758-774.
[25] DURAISAMY K,ZHANG Z J,SINGH A P.New approaches in turbulence and transition modeling using data-driven techniques[C]//53rd AIAA Aerospace Sciences Meeting.Kissimmee,Florida,2015:1284.
[26] LING J,KURZAWSKI A,TEMPLETON J.Reynolds averaged turbulence modelling using deep neural networks with embedded invariance[J].Journal of Fluid Mechanics,2016,807:155-166.
[27] ZHANG Z J,DURAISAMY K.Machine learning methods for data-driven turbulence modeling[C/OL]//22nd AIAA Computational Fluid Dynamics Conference.2015:2460.
[28] MILANO M,KOUMOUTSAKOS P.Neural network modeling for near wall turbulent flow[J].Journal of Computational Phy-sics,2002,182(1):1-26.
[29] PERDIKARIS P,VENTURI D,KARNIADAKIS G E.Multifidelity information fusion algorithms for high-dimensional systems and massive data sets[J].SIAM Journal on Scientific Computing,2016,38(4):B521-B538.
[30] RICO-MARTINEZ R,ANDERSON J S,KEVREKIDIS I G.Continuous-time nonlinear signal processing:a neural network based approach for gray box identification[C]//Proceedings of IEEE Workshop on Neural Networks for Signal Processing.IEEE,1994:596-605.
[31] LING J,TEMPLETON J.Evaluation of machine learning algorithms for prediction of regions of high Reynolds averaged Na-vier-Stokes uncertainty[J/OL].Physics of Fluids,2015,27(8).https://doi.org/10.1063/1.4927765.
[32] YANG X,ZAFAR S,WANG J X,et al.Predictive large-eddy-simulation wall modeling via physics-informed neural networks[J/OL].Physical Review Fluids,2019,4(3).https://doi.org/10.1103/PhysRevFluids.4.034602.
[33] PANG G,D’ELIA M,PARKS M,et al.nPINNs:nonlocal Phy-sics-Informed Neural Networks for a parametrized nonlocal universal Laplacian operator.Algorithms and Applications[J/OL].Journal of Computational Physics,2020,422.https://doi.org/10.1016/j.jcp.2020.109760.
[34] PANG G,LU L,KARNIADAKIS G E.fPINNs:Fractionalphysics-informed neural networks[J].SIAM Journal on Scien-tific Computing,2019,41(4):A2603-A2626.
[35] SONG F,PANGE G,MENEVEAU C,et al.Fractional physical-inform neural networks (fPINNs) for turbulent flows[C]//Annual Meeting of the APS Division of Fluid Dynamics.2019:23-26.
[36] MENG X,LI Z,ZHANG D,et al.PPINN:Parareal physics-informed neural network for time-dependent PDEs[J/OL].Computer Methods in Applied Mechanics and Engineering,2020,370.https://doi.org/10.1016/j.cma.2020.113250.
[37] JAGTAP A D,KHARAZMI E,KARNIADAKIS G E.Conservative physics-informed neural networks on discrete domains for conservation laws:applications to forward and inverse problems[J/OL].Computer Methods in Applied Mechanics and Engineering,2020,365.https://doi.org/10.1016/j.cma.2020.113028.
[38] DWIVEDI V,PARASHAR N,SRINIVASAN B.Distributedphysics informed neural network for data-efficient solution to partial differential equations[J].arXiv:1907.08967,2019.
[39] YANG L,MENG X,KARNIADAKIS G E.B-PINNs:Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data[J/OL].Journal of Computational Physics,2021,425.https://doi.org/10.1016/j.jcp.2020.109913.
[40] KHARAZMI E,ZHANG Z,KARNIADAKIS G E.Variational physics-informed neural networks for solving partial differential equations[J].arXiv:1912.00873,2019.
[41] JAGTAP A D,KARNIADAKIS G E.Extended physics-in-formed neural networks (XPINNs):a generalized space-time domain decomposition based deep learning framework for nonli-near partial differential equations[J].Communications in Computational Physics,2020,28(5):2002-2041.
[42] MISHRA S,MOLINARO R.Estimates on the generalization error of physics-informed neural networks (PINNs) for approximating PDEs[J].arXiv:2006.16144,2020.
[43] MISHRA S,MOLINARO R.Estimates on the generalization error of physics-informed neural networks (PINNs) for approximating PDEs II:a class of inverse problems[J].arXiv:2007.01138,2020.
[44] WANG S,TENG Y,PERDIKARIS P.Understanding and mitigating gradient pathologies in physics-informed neural networks[J].arXiv:2001.04536,2020.
[45] WANG S,YU X,PERDIKARIS P.When and why PINNs fail to train:A neural tangent kernel perspective[J].arXiv:2007.14527,2020.
[46] WANG S,WANG H,PERDIKARIS P.On the eigenvector bias of Fourier feature networks:from regression to solving multi-scale PDEs with physics-informed neural networks[J].arXiv:2012.10047,2020.
[47] JAGTAP A D,KAWAGUCHI K,KARNIADAKIS G E.Adaptive activation functions accelerate convergence in deep and physics-informed neural networks[J/OL].Journal of Computational Physics,2020,404.https://doi.org/10.1016/j.jcp.2019.109136.
[48] JAGTAP A D,KAWAGUCHI K,KARNIADAKIS G E.Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks[J/OL].Proceedings of the Royal Society A,2020,476(2239).http://doi.org/10.1098/rspa.2020.0334. [49] RAISSI M,YAZDANI A,KARNIADAKIS G E.Hidden fluid mechanics:Learning velocity and pressure fields from flow visua-lizations[J].Science,2020,367(6481):1026-1030.
[50] JIN X,CAI S,LI H,et al.NSFnets (Navier-Stokes flow nets):Physics-informed neural networks for the incompressible Na-vier-Stokes equations[J/OL].Journal of Computational Physics,2021,426.https://doi.org/10.1016/j.jcp.2020.109951.
[51] MAO Z,JAGTAP A D,KARNIADAKIS G E.Physics-informed neural networks for high-speed flows[J/OL].Computer Me-thods in Applied Mechanics and Engineering,2020,360.https://doi.org/10.1016/j.cma.2019.112789.
[52] GUO H,ZHUANG X,LIANG D,et al.Stochastic groundwater flow analysis in heterogeneous aquifer with modified neural architecture search (NAS) based physics-informed neural networks using transfer learning[J].arXiv:2010.12344,2020.
[53] SAHLI COSTABAL F,YANG Y,PERDIKARIS P,et al.Phy-sics-informed neural networks for cardiac activation mapping[J].Frontiers in Physics,2020,8:42.
[54] FANG Z,ZHAN J.Deep physical informed neural networks for metamaterial design[J].IEEE Access,2019,8:24506-24513.
[55] CHEN Y,LU L,KARNIADAKIS G E,et al.Physics-informed neural networks for inverse problems in nano-optics and metamaterials[J].Optics express,2020,28(8):11618-11633.
[56] SHUKLA K,DI LEONI P C,BLACKSHIRE J,et al.Physics-informed neural network for ultrasound nondestructive quantification of surface breaking cracks[J].Journal of Nondestructive Evaluation,2020,39(3):1-20.
[57] MISYRIS G S,VENZKE A,CHATZIVASILEIADIS S.Phy-sics-informed neural networks for power systems[C]//2020 IEEE Power & Energy Society General Meeting (PESGM).IEEE,2020:1-5.
[58] STIASNY J,MISYRIS G S,CHATZIVASILEIADIS S.Physics-informed neural networks for non-linear system identification applied to power system dynamics[J].arXiv:2004.04026,2020.
[59] WANG C,BENTIVEGNA E,ZHOU W,et al.Physics-informed neural network super resolution for advection-diffusion models[J].arXiv:2011.02519,2020.
[60] NASCIMENTO R G,FRICKE K,VIANA F A C.A tutorial on solving ordinary differential equations using Python and hybrid physics-informed neural network[J/OL].Engineering Applications of Artificial Intelligence,2020,96.https://doi.org/10.1016/j.engappai.2020.103996.
[61] HENNIGH O,NARASIMHAN S,NABIAN M A,et al.Anend-to-end AI-driven simulation framework[EB/OL].Workshop:Machine Learning and the Physical Sciences,the 34th Conference on Neural Information Processing Systems,2020.https://ml4physicalsciences.github.io/2020/.
[62] HENNIGH O,NARASIMHAN S,NABIAN M A,et al.NVIDIA SimNetTM:an AI-accelerated multi-physics simulation framework[C]//International Conference on Computational Science.Cham:Springer,2021:447-461.
[63] YANG L,ZHANG D,KARNIADAKIS G E.Physics-informed generative adversarial networks for stochastic differential equations[J].SIAM Journal on Scientific Computing,2020,42(1):A292-A317.
[64] NABIAN M A,MEIDANI H.A deep neural network surrogate for high-dimensional random partial differential equations[J].arXiv:1806.02957,2018.
[65] ZHANG D,GUO L,KARNIADAKIS G E.Learning in modal space:Solving time-dependent stochastic PDEs using physics-informed neural networks[J].SIAM Journal on Scientific Computing,2020,42(2):A639-A665.
[66] ZHANG D,LU L,GUO L,et al.Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems[J/OL].Journal of Computational Physics,2019,397.https://doi.org/10.1016/j.jcp.2019.07.048.
[67] RAHAMAN N,BARATIN A,ARPIT D,et al.On the spectral bias of neural networks[C]//International Conference on Machine Learning.PMLR,2019:5301-5310.
[68] RONEN B,JACOBS D,KASTEN Y,et al.The convergence rate of neural networks for learned functions of different frequencies[J].Advances in Neural Information Processing Systems,2019,32:4761-4771.
[69] ZHANG T,DEY B,KAKKAR P,et al.Frequency-compensated PINNs for fluid-dynamic design problems[J].arXiv:2011.01456,2020.
[70] SHIN Y,DARBON J,KARNIADAKIS G E.On the conver-gence and generalization of physics informed neural networks[J].arXiv:2004.01806,2020.
[71] FUKS O,TCHELEPI H A.Limitations of physics informed machine learning for nonlinear two-phase transport in porous media[J].Journal of Machine Learning for Modeling and Computing,2020,1(1):19-37.
[72] ZHU Y,ZABARAS N,KOUTSOURELAKIS P S,et al.Phy-sics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data[J].Journal of Computational Physics,2019,394:56-81.
[73] RAISSI M,KARNIADAKIS G E.Hidden physics models:Machine learning of nonlinear partial differential equations[J].Journal of Computational Physics,2018,357:125-141.
[74] RAISSI M.Deep hidden physics models:Deep learning of nonlinear partial differential equations[J].The Journal of Machine Learning Research,2018,19(1):932-955.
[75] JACOT A,GABRIEL F,HONGLER C.Neural tangent kernel:convergence and generalization in neural networks[C]//Proceedings of the 32nd International Conference on Neural Information Processing Systems.2018:8580-8589.
[76] ARORA S,DU S,HU W,et al.On exact computation with an infinitely wide neural net[C]//Proceedings of the 33rd International Conference on Neural Information Processing Systems.2019:8141-8150.
[77] JI W,QIU W,SHI Z,et al.Stiff-PINN:physics-informed neural network for stiff chemical kinetics[J].arXiv:2011.04520,2020.
[78] WIGHT C L,ZHAO J.Solving Allen-Cahn and Cahn-Hilliardequations using the adaptive physics-informed neural networks[J].arXiv:2007.04542,2020.
[79] MCCLENNY L,BRAGA-NETO U.Self-adaptive physics-in-formed neural networks using a soft attention mechanism[J].arXiv:2009.04544,2020.
[80] YU C C,TANG Y C,LIU B D.An adaptive activation function for multilayer feedforward neural networks[C]//2002 IEEE Region 10 Conference on Computers,Communications,Control and Power Engineering.IEEE,2002,1:645-650.
[81] QIAN S,LIU H,LIU C,et al.Adaptive activation functions in convolutional neural networks[J].Neurocomputing,2018,272:204-212.
[82] ZOBEIRY N,HUMFELD K D.A physics-informed machinelearning approach for solving heat transfer equation in advanced manufacturing and engineering applications[J].arXiv:2010.02011,2020.
[83] ALBER M,TEPOLE A B,CANNON W R,et al.Integratingmachine learning and multiscale modeling-perspectives,challenges,and opportunities in the biological,biomedical,and behavioral sciences[J].NPJ Digital Medicine,2019,2(1):1-11.
[84] PENG G C Y,ALBER M,TEPOLE A B,et al.Multiscale mo-deling meets machine learning:What can we learn?[J].Archives of Computational Methods in Engineering,2020:1-21.
[85] CAI S,MAO Z,WANG et al.Physics-informed neural networks (PINNs) for fluid mechanics:A review[J].arXiv:2105.09506,2021.
[86] ANDERSON J D,WENDT J.Computational fluid dynamics[M].New York:McGraw-Hill,1995.
[87] RAISSI M,WANG Z,TRIANTAFYLLOU M S,et al.Deeplearning of vortex induced vibrations[J].arXiv:1808.08952,2018.
[88] SUN L,GAO H,PAN S,et al.Surrogate modeling for fluidflows based on physics-constrained deep learning without simulation data[J/OL].Computer Methods in Applied Mechanics and Engineering,2020,361.https://doi.org/10.1016/j.cma.2019.112732.
[89] WESSELS H,WEIßENFELS C,WRIGGERS P.The neuralparticle method-An updated Lagrangian physics informed ne-ural network for computational fluid dynamics[J/OL].Compu-ter Methods in Applied Mechanics and Engineering,2020,368.https://doi.org/10.1016/j.cma.2020.113127.
[90] MEHTA P P,PANG G,SONG F,et al.Discovering a universal variable-order fractional model for turbulent Couette flow using a physics-informed neural network[J].Fractional Calculus and Applied Analysis,2019,22(6):1675-1688.
[91] TARTAKOVSKY A M,MARRERO C O,PERDIKARIS P,et al.Physics-informed deep neural networks for learning parameters and constitutive relationships in subsurface flow problems [J/OL].Water Resources Research,2020,56(5).https://doi.org/10.1029/2019WR026731.
[92] HE Q Z,BARAJAS-SOLANO D,TARTAKOVSKY G,et al.Physics-informed neural networks for multiphysics data assimilation with application to subsurface transport[J/OL].Advances in Water Resources,2020,141.https://doi.org/10.1016/j.advwatres.2020.103610.
[93] KISSAS G,YANG Y,HWUANG E,et al.Machine learning in cardiovascular flows modeling:Predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks[J/OL].Computer Methods in Applied Mechanics and Engineering,2020,358.https://doi.org/10.1016/j.cma.2019.112623.
[94] LIU D,WANG Y.Multi-fidelity physics-constrained neural net-work and its application in materials modeling[J/OL].Journal of Mechanical Design,2019,141(12).https://doi.org/10.1115/1.4044400.
[95] ZHANG E,YIN M,KARNIADAKIS G E.Physics-informedneural networks for nonhomogeneous material identification in elasticity imaging[J].arXiv:2009.04525,2020.
[96] ZHU Q,LIU Z,YAN J.Machine learning for metal additive manufacturing:predicting temperature and melt pool fluid dynamics using physics-informed neural networks[J].Computational Mechanics,2021,67(2):619-635.
[97] DOURADO A,VIANA F A C.Physics-informed neural networks for missing physics estimation in cumulative damage models:a case study in corrosion fatigue[J/OL].Journal of Computing and Information Science in Engineering,2020,20(6).https://doi.org/10.1115/1.4047173.
[98] YUCESAN Y A,VIANA F A C.A physics-informed neural network for wind turbine main bearing fatigue[J].International Journal of Prognostics and Health Management,2020,11(1):17.
[99] GOSWAMI S,ANITESCU C,CHAKRABORTY S,et al.Transfer learning enhanced physics informed neural network for phase-field modeling of fracture[J/OL].Theoretical and Applied Fracture Mechanics,2020,106.https://doi.org/10.1016/j.tafmec.2019.102447.
[100] TAO F,LIU X,DU H,et al.Physics-informed artificial neural network approach for axial compression buckling analysis of thin-walled cylinder[J].AIAA Journal,2020,58(6):2737-2747.
[101] MISHRA S,MOLINARO R.Physics Informed Neural Net-works for Simulating Radiative Transfer[J].arXiv:2009.13291,2020.
[102] KADEETHUM T,JØRGENSEN T M,NICK H M.Physics-informed neural networks for solving nonlinear diffusivity and Biot’s equations[J/OL].PloS ONE,2020,15(5).https://doi.org/10.1371/journal.pone.0232683.
[103] LIU M,LIANG L,SUN W.A generic physics-informed neural network-based constitutive model for soft biological tissues[J/OL].Computer Methods in Applied Mechanics and Engineering,2020,372.https://doi.org/10.1016/j.cma.2020.113402.
[104] WANG R,MADDIX D,FALOUTSOS C,et al.Bridging phy-sics-based and data-driven modeling for learning dynamical systems[J].arXiv:2011.10616,2020.
[1] 冷典典, 杜鹏, 陈建廷, 向阳.
面向自动化集装箱码头的AGV行驶时间估计
Automated Container Terminal Oriented Travel Time Estimation of AGV
计算机科学, 2022, 49(9): 208-214. https://doi.org/10.11896/jsjkx.210700028
[2] 宁晗阳, 马苗, 杨波, 刘士昌.
密码学智能化研究进展与分析
Research Progress and Analysis on Intelligent Cryptology
计算机科学, 2022, 49(9): 288-296. https://doi.org/10.11896/jsjkx.220300053
[3] 周芳泉, 成卫青.
基于全局增强图神经网络的序列推荐
Sequence Recommendation Based on Global Enhanced Graph Neural Network
计算机科学, 2022, 49(9): 55-63. https://doi.org/10.11896/jsjkx.210700085
[4] 周乐员, 张剑华, 袁甜甜, 陈胜勇.
多层注意力机制融合的序列到序列中国连续手语识别和翻译
Sequence-to-Sequence Chinese Continuous Sign Language Recognition and Translation with Multi- layer Attention Mechanism Fusion
计算机科学, 2022, 49(9): 155-161. https://doi.org/10.11896/jsjkx.210800026
[5] 何强, 尹震宇, 黄敏, 王兴伟, 王源田, 崔硕, 赵勇.
基于大数据的进化网络影响力分析研究综述
Survey of Influence Analysis of Evolutionary Network Based on Big Data
计算机科学, 2022, 49(8): 1-11. https://doi.org/10.11896/jsjkx.210700240
[6] 李瑶, 李涛, 李埼钒, 梁家瑞, Ibegbu Nnamdi JULIAN, 陈俊杰, 郭浩.
基于多尺度的稀疏脑功能超网络构建及多特征融合分类研究
Construction and Multi-feature Fusion Classification Research Based on Multi-scale Sparse Brain Functional Hyper-network
计算机科学, 2022, 49(8): 257-266. https://doi.org/10.11896/jsjkx.210600094
[7] 李宗民, 张玉鹏, 刘玉杰, 李华.
基于可变形图卷积的点云表征学习
Deformable Graph Convolutional Networks Based Point Cloud Representation Learning
计算机科学, 2022, 49(8): 273-278. https://doi.org/10.11896/jsjkx.210900023
[8] 郝志荣, 陈龙, 黄嘉成.
面向文本分类的类别区分式通用对抗攻击方法
Class Discriminative Universal Adversarial Attack for Text Classification
计算机科学, 2022, 49(8): 323-329. https://doi.org/10.11896/jsjkx.220200077
[9] 张光华, 高天娇, 陈振国, 于乃文.
基于N-Gram静态分析技术的恶意软件分类研究
Study on Malware Classification Based on N-Gram Static Analysis Technology
计算机科学, 2022, 49(8): 336-343. https://doi.org/10.11896/jsjkx.210900203
[10] 王润安, 邹兆年.
基于物理操作级模型的查询执行时间预测方法
Query Performance Prediction Based on Physical Operation-level Models
计算机科学, 2022, 49(8): 49-55. https://doi.org/10.11896/jsjkx.210700074
[11] 陈泳全, 姜瑛.
基于卷积神经网络的APP用户行为分析方法
Analysis Method of APP User Behavior Based on Convolutional Neural Network
计算机科学, 2022, 49(8): 78-85. https://doi.org/10.11896/jsjkx.210700121
[12] 朱承璋, 黄嘉儿, 肖亚龙, 王晗, 邹北骥.
基于注意力机制的医学影像深度哈希检索算法
Deep Hash Retrieval Algorithm for Medical Images Based on Attention Mechanism
计算机科学, 2022, 49(8): 113-119. https://doi.org/10.11896/jsjkx.210700153
[13] 檀莹莹, 王俊丽, 张超波.
基于图卷积神经网络的文本分类方法研究综述
Review of Text Classification Methods Based on Graph Convolutional Network
计算机科学, 2022, 49(8): 205-216. https://doi.org/10.11896/jsjkx.210800064
[14] 闫佳丹, 贾彩燕.
基于双图神经网络信息融合的文本分类方法
Text Classification Method Based on Information Fusion of Dual-graph Neural Network
计算机科学, 2022, 49(8): 230-236. https://doi.org/10.11896/jsjkx.210600042
[15] 金方焱, 王秀利.
融合RACNN和BiLSTM的金融领域事件隐式因果关系抽取
Implicit Causality Extraction of Financial Events Integrating RACNN and BiLSTM
计算机科学, 2022, 49(7): 179-186. https://doi.org/10.11896/jsjkx.210500190
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!