Azzh Saad Alshehry

A novel new iterative method–physics-informed neural networks approach for accurate and efficient solutions of nonlinear damped Burgers’ equations

In this work, a hybrid semi-analytical and deep learning framework is proposed for solving nonlinear damped Burgers equations by combining the New Iterative Method (NIM) with Physics-Informed Neural Networks (PINNs). The developed methodology consists of the use of NIM to build a...

Novel analysis of physics-informed neural networks for solving Cahn-Allen, FitzHugh-Nagumo and Fisher–KPP Models

This paper presents a hybrid semi-analytical/deep-learning framework for nonlinear PDEs, combining the New Iterative Method (NIM) with Physics-Informed Neural Networks (PINNs). A truncated NIM series provides a closed-form baseline satisfying the initial condition exactly, while...

A hybrid semi-analytical and neural network approach for solving nonlinear Kolmogorov and Rosenau-Hyman equations

This paper presents a hybrid semi-analytical and physics-informed neural network framework for solving linear and nonlinear partial differential equations. The proposed approach combines the New Iterative Method (NIM) with Physics-Informed Neural Networks (PINNs): a low-order ana...