Development and optimization of physics-informed neural networks for solving partial differential equations
Year: 2025
Type: preprint
Abstract: This work compares the advantages and limitations of the Finite Difference Method with Physics-Informed Neural Networks, showing where each can best be applied for different problem scenarios. Analysis on the L2 relative error based on one-dimensional and two-dimensional Poisson equations suggests that FDM gives far more accurate results with a relative error of 7.26 x 10-8 and 2.21 x 10-4, respectively, in comparison with PINNs, with an error of 5.63 x 10-6 and 6.01 x 10-3 accordingly. Besides forward problems, PINN is realized also for forward-inverse problems which reflect its ability to predict source term after its sufficient training. Visualization of the solution underlines different methodologies adopted by FDM and PINNs, yielding useful insights into their performance and applicability.
Source: arXiv (Cornell University)
Institutions: New Uzbekistan University, Suleyman Demirel University
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4407207819