SETN '02 Proceedings of the Second Hellenic Conference on AI: Methods and Applications of Artificial Intelligence
Neural splines: exploiting parallelism for function approximation using modular neural networks
Neural, Parallel & Scientific Computations
IEEE Transactions on Neural Networks
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
A MLP solver for first and second order partial differential equations
ICANN'07 Proceedings of the 17th international conference on Artificial neural networks
Computers & Mathematics with Applications
IWANN'13 Proceedings of the 12th international conference on Artificial Neural Networks: advences in computational intelligence - Volume Part II
Comparison of artificial neural network architecture in solving ordinary differential equations
Advances in Artificial Neural Systems
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Partial differential equations (PDEs) with boundary conditions (Dirichlet or Neumann) defined on boundaries with simple geometry have been successfully treated using sigmoidal multilayer perceptrons in previous works. The article deals with the case of complex boundary geometry, where the boundary is determined by a number of points that belong to it and are closely located, so as to offer a reasonable representation. Two networks are employed: a multilayer perceptron and a radial basis function network. The later is used to account for the exact satisfaction of the boundary conditions. The method has been successfully tested on two-dimensional and three-dimensional PDEs and has yielded accurate results