Neural network method for solving partial differential equations

Neural Processing Letters

Volumn 14, Issue 3, 2001, Pages 261-271

  Aarts, Lucie P ^a   Van Der Veer, Peter ^a  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Derivatives approximation; Differential equations; Evolutionary algorithms; Feedforward neural networks; Function approximation; Knowledge incorporation; Numerical solution methods; Partial differential equations; Simultaneously training

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; EVOLUTIONARY ALGORITHMS; FUNCTIONS; PARTIAL DIFFERENTIAL EQUATIONS;

DERIVATIVES APPROXIMATIONS;

FEEDFORWARD NEURAL NETWORKS;

EID: 0035575919     PISSN: 13704621     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1012784129883     Document Type: Article

References (13)

1. Approximations of functions by a multilayer perceptron: A new approach
2. On learning the derivatives of an unknown mapping with multilayer feedforward networks
3. A genetic algorithm for function optimization: A matlab implementation
4. Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks
5. Simultaneous approximations of multivariate functions and their derivatives by neural networks with one hidden layer
6. Hybrid modelling by integrating neural networks and numerical models
7. Evolving artificial neural networks