NEURAL-NETWORK-BASED APPROXIMATIONS FOR SOLVING PARTIAL-DIFFERENTIAL EQUATIONS

被引：313
|
作者：
DISSANAYAKE, MWMG
PHANTHIEN, N
机构：
[1] Department of Mechanical Engineering, The University of Sydney, Sydney, New South Wales
来源：
COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING | 1994年 / 10卷 / 03期
关键词：
D O I：
10.1002/cnm.1640100303
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
A numerical method, based on neural-network-based functions, for solving partial differential equations is reported in the paper. Using a 'universal approximator' based on a neural network and point collocation, the numerical problem of solving the partial differential equation is transformed to an unconstrained minimization problem. The method is extremely easy to implement and is suitable for obtaining an approximate solution in a short period of time. The technique is illustrated with the aid of two numerical examples.
引用
收藏
页码：195 / 201
页数：7
相关论文
共 50 条
  • [21] ITERATIVE METHOD FOR SOLVING NONLINEAR PARTIAL-DIFFERENTIAL EQUATIONS
    NEUBERGER, JW
    [J]. ADVANCES IN MATHEMATICS, 1976, 19 (02) : 245 - 265
  • [22] SOLVING PARTIAL-DIFFERENTIAL EQUATIONS USING RECURSIVE GRIDS
    KOZLOVSKY, G
    [J]. APPLIED NUMERICAL MATHEMATICS, 1994, 14 (1-3) : 165 - 181
  • [23] FULLY IMPLICIT ALGORITHMS FOR SOLVING PARTIAL-DIFFERENTIAL EQUATIONS
    PEPPER, DW
    HARRIS, SD
    [J]. JOURNAL OF FLUIDS ENGINEERING-TRANSACTIONS OF THE ASME, 1977, 99 (04): : 781 - 783
  • [24] UPPER SEMICONTINUITY OF ATTRACTORS FOR APPROXIMATIONS OF SEMIGROUPS AND PARTIAL-DIFFERENTIAL EQUATIONS
    HALE, JK
    LIN, XB
    RAUGEL, G
    [J]. MATHEMATICS OF COMPUTATION, 1988, 50 (181) : 89 - 123
  • [25] Transfer learning for deep neural network-based partial differential equations solving
    Xinhai Chen
    Chunye Gong
    Qian Wan
    Liang Deng
    Yunbo Wan
    Yang Liu
    Bo Chen
    Jie Liu
    [J]. Advances in Aerodynamics, 3
  • [26] Transfer learning for deep neural network-based partial differential equations solving
    Chen, Xinhai
    Gong, Chunye
    Wan, Qian
    Deng, Liang
    Wan, Yunbo
    Liu, Yang
    Chen, Bo
    Liu, Jie
    [J]. ADVANCES IN AERODYNAMICS, 2021, 3 (01)
  • [27] PARTIAL-DIFFERENTIAL EQUATIONS
    FOX, L
    [J]. COMPUTER JOURNAL, 1963, 6 (01): : 69 - &
  • [28] TECHNIQUE FOR SOLVING THE NONLINEAR PARTIAL-DIFFERENTIAL EQUATIONS OF TOKAMAK TRANSPORT
    KLEIN, HH
    BYRNE, RN
    [J]. JOURNAL OF COMPUTATIONAL PHYSICS, 1979, 33 (02) : 294 - 299
  • [29] HYBRID METHOD FOR SOLVING PARTIAL-DIFFERENTIAL EQUATIONS OF PARABOLIC TYPE
    PETROV, AA
    [J]. AUTOMATION AND REMOTE CONTROL, 1975, 36 (03) : 495 - 501
  • [30] THE USE OF SOLUTION ADAPTIVE GRIDS IN SOLVING PARTIAL-DIFFERENTIAL EQUATIONS
    ANDERSON, DA
    RAI, MM
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 1982, 10 : 317 - 338
12345