Fig. 3

The results of the POD-Galerkin PINN predictions for the 1st, 2nd and 3rd components of the velocity, pressure and convective reduced coefficients for the first numerical test. The plots compare the reduced coefficients with the \(L^2\) projection coefficients of the test velocity and pressure fields onto the corresponding POD modes. The red-dashed lines refers to the \(L^2\) projection coefficients, while the blue-dots correspond to the reduced coefficients obtained by the PINNs. The coefficients are plotted versus the physical viscosity values at which the test data was generated. (a) The first reduced coefficients for velocity, pressure and convective terms compared to the ones obtained by the \(L^2\) projection. (b) The second reduced coefficients for velocity, pressure and convective terms compared to the ones obtained by the \(L^2\) projection. (c) The third reduced coefficients for velocity, pressure and convective terms compared to the ones obtained by the \(L^2\) projection