2001
DOI: 10.1007/3-540-45718-6_20
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Solving Nonlinear Differential Equations by a Neural Network Method

Abstract: Abstract.In this paper we demonstrate a neural network method to solve nonlinear differential equations and its boundary conditions. The idea of our method is to incorporate knowledge about the differential equation and its boundary conditions into neural networks and the training sets. Hereby we obtain specifically structured neural networks. To solve the nonlinear differential equation and its boundary conditions we have to train all obtained neural networks simultaneously. This is realized by applying an ev… Show more

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Cited by 9 publications
(6 citation statements)
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References 7 publications
(8 reference statements)
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“…This was a key contribution since it allowed an exact value of the derivatives to be obtained with a small number of collocation points, and it has continued to be the employed technique since [23,51]. Some other authors opted to tune the parameters of the MLP using evolutionary algorithms instead, although this did not become a common practice [102].…”
Section: Physics-driven Neural Flow Solversmentioning
confidence: 99%
“…This was a key contribution since it allowed an exact value of the derivatives to be obtained with a small number of collocation points, and it has continued to be the employed technique since [23,51]. Some other authors opted to tune the parameters of the MLP using evolutionary algorithms instead, although this did not become a common practice [102].…”
Section: Physics-driven Neural Flow Solversmentioning
confidence: 99%
“…Les pmssances électriques évoluent aussi en parfaite correspondance avec la régulation de la tension (figure 74). -la méthode à base des réseaux de neurones (Neural Network) [ 17] et [ 18];…”
Section: Le Maintien De La Fréquenceunclassified
“…for conditions outside the range for which the network has been trained. Much research is being done on new types of neural networks that enable incorporating physics and are suitable for extrapolation (Aarts and Van der Veer, 2001;Van der Wielen et al, 2001). These new types of neural networks are still undergoing further investigation, however, and are not yet suitable for our analyses.…”
Section: Artificial Neural Networkmentioning
confidence: 99%