PINN implementation for the Taylor

Title	PINN implementation for the Taylor–Green vortex
Authors	A. A. Podgornov¹, E. A. Kaledina¹ ¹National Research Mordovia State University
Annotation	A physically-informed neural network for the numerical solution of the Navier–Stokes equations for an incompressible fluid in a two-dimensional setting has been implemented. Using the classical Taylor–Green vortex as an example, the accuracy and stability of the method are assessed for various levels of input data noise, and a comparison with the finite difference method is made.
Keywords	Physics-informed neural network, Navier–Stokes equations, Taylor–Green vortex.
Citation	Podgornov A. A., Kaledina E. A. ''PINN implementation for the Taylor–Green vortex'' [Electronic resource]. Mathematical modeling, numerical methods, and software systems: Collection of materials from the 12th All‑Russian Scientific Youth School‑Seminar named after E. V. Voskresensky (Saransk, July 21–24, 2026). - pp. 184-188. Available at: https://conf.svmo.ru/files/2026/papers/paper101.pdf. - Date of access: 25.09.2026.