Solving Partial Differential Equations with Bernstein Neural Networks [chapter]

Sina Razvarz, Raheleh Jafari, Alexander Gegov
2018 Advances in Intelligent Systems and Computing  
In this paper, a neural network-based procedure is suggested to produce estimated solutions (controllers) for the second-order nonlinear partial differential equations (PDEs). This concept is laid down so as to produce a prevalent approximation on the basis of the learning method which is at par with quasi-Newton rule. The proposed neural network contains the regularizing parameters (weights and biases), that can be utilized for making the error function least. Besides, an advanced technique is
more » ... presented for resolving PDEs based on the usage of Bernstein polynomial. Numerical experiments alongside comparisons show the fantastic capacity of the proposed techniques.
doi:10.1007/978-3-319-97982-3_5 fatcat:3lnvpo6oabeupaoifyhrzuwxuy