Author

Saima Noor

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Open access Sep 2026

Scientific machine learning meets semi-analytical computation: a hybrid NIM-PINN approach for nonlinear PDEs

In this paper, a hybrid semi-analytical–deep learning framework for the solution of nonlinear partial differential equations (PDEs) is proposed that integrates the New Iterative Method (NIM) with Physics-Informed Neural Networks (PINNs). Low–order NIM expansion provides an analytic baseline that meets the required init...

A. Alshehry, Saima Noor, Humaira Yasmin et al. · Scientific Reports · 0 citations

Open access Sep 2026

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 analytical approximation is generated by NI...

A. Alshehry, Saima Noor, Humaira Yasmin et al. · Scientific Reports · 0 citations

#diffusion models Open access Sep 2026

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 neural network learns only the residua...

A. Alshehry, Saima Noor, Humaira Yasmin et al. · Scientific Reports · 0 citations