Physics Informed Neural Networks for the Unsteady Taylor Green Vortex with DeepXDE

The Taylor Green vortex is a classic benchmark for unsteady incompressible flows, but most existing physics-informed neural network (PINN) studies on this problem report only early time results or omit the pressure field entirely. We present a complete, step by step PINN simulation of the two-dimensional decaying vortex at Reynolds number 100 using the DeepXDE library. A fully connected network with four hidden layers of 128 neurons each is trained on 20,000 collocation points, 2,000 boundary points, and 2,000 initial points for 10,000 Adam iterations. The entire training takes about 13 minutes on a single GPU. Relative $L_2$ errors for the velocity components $u$ and $v$ increase from approximately 5% at $t = 0.25$ to 18% at $t = 1.0$. Vorticity fields are captured qualitatively, but peak values are smoothed over time. All visualisations contour plots, line cuts, three dimensional surfaces, and the loss history are generated automatically from the trained model. This work provides a reproducible benchmark for researchers developing or testing PINN methods for unsteady fluid dynamics, and it openly discusses both the successes and the persistent difficulties of the approach.