Solving Partial Differential Equations with Bernstein Neural Networks

Abstract

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 presented for resolving PDEs based on the usage of Bernstein polynomial. Numerical experiments alongside comparisons show the fantastic capacity of the proposed techniques.