Proceedings of International Conference on Applied Innovation in IT
2026/03/31, Volume 14, Issue 1, pp.177-183

Physics-Informed Neural Networks for Solving Partial Differential Equations: A Comparative Study with the Burgers’ Equation


Hassan Al-Mahdawi, Ghassan Khazal Ali, Anna Ivanovna Sidikova and Hassan Hadi Saleh


Abstract: Partial Differential Equations (PDE) are central to modelling phenomena of physical in engineering and science however up to now their mathematical solution has been elusive especially in high-dimensional domains with complex boundary conditions or nonlinear dynamics. Robust discretization techniques have been developed through the use of Finite Difference Method (FDM), Finite Element Method (FEM), and Spectral Methods but they face challenges of scalability, computational expense, and even problems associated with mesh-generation. Recently, Physics-Informed Neural Networks (PINNs) were proposed as a mesh-free method by which the governing physical law constraints can be imposed while training deep neural networks to approximate solutions of PDE imposing their initial and boundary conditions. This study will use the one-dimensional PDE for the viscous Burgers’ equation as the baseline problem. First, a review of traditional approaches is presented with an explicit enumeration of their strengths and weaknesses. A PINN architecture is then designed that leverages automatic differentiation for the residuals and composite loss functions to enforce physics constraints. Mathematical analyses benchmark PINNs against FDM in terms of accuracy and demonstrate comparable levels of accuracy with less dependency on discretization as well as delivering a much smoother solution. The study recapitulates that though training effort is substantial for PINNs, it has an enticing possibility to crack nonlinear-PDE in higher dimensions and imbalanced geometries, therefore making an up-to-date leap forward from standard numerical analysis.

Keywords: Physics-Informed Neural Networks (PINNs), Burgers’ Equation, Partial Differential Equations (PDEs), Finite Difference Method (FDM), Finite Element Method (FEM), Spectral Methods.

DOI: Under indexing

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