Physics Informed Neural Network Based Deep Adaptive Sampling Technique for Partial Differential Equations Solving

In recent times, the Deep Neural Network (DNN) has attained high attention to solve the engineering issue. In this research, proposed a Physics Informed Neural Network (PINNs) based Deep Adaptive Sampling (DAS) technique is proposed to solve the Partial Differential Equations (PDEs). The DNN is used for approximate solution of PDEs and deep generative methods are used for generation of gathering points for refining training set. Process of DAS method has two phases such as PDEs solving through reducing residual loss in gathering points in training set and producing training set for enhancing an accuracy of present approximation solution. The performance of proposed technique is evaluated in terms of linear and non-linear problems with training time and error. The methods used fsor comparing the proposed technique are Residual-based Adaptive Refinement (RAR) technique for huge dimension issues, DSA-R, DAS-G and uniform sampling technique. The proposed DAS technique showed effective performance in training time and minimization of error than uniform sampling techniques.