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Multilayer perceptrons and radial basis function neural network methods for the solution of differential equations: a survey. (English) Zbl 1236.65107
Summary: Since neural networks have universal approximation capabilities, therefore it is possible to postulate them as solutions for given differential equations that define unsupervised errors. In this paper, we present a wide survey and classification of different Multilayer Perceptron (MLP) and Radial Basis Function (RBF) neural network techniques, which are used for solving differential equations of various kinds. Our main purpose is to provide a synthesis of the published research works in this area and stimulate further research interest and effort in the identified topics. Here, we describe the crux of various research articles published by numerous researchers, mostly within the last 10 years to get a better knowledge about the present scenario.

MSC:
65L99 Numerical methods for ordinary differential equations
68T05 Learning and adaptive systems in artificial intelligence
34-04 Software, source code, etc. for problems pertaining to ordinary differential equations
35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations
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