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Advanced Modeling and Simulation in Engineering Sciences
Fig. 14 | Advanced Modeling and Simulation in Engineering Sciences

Fig. 14

From: POD-Galerkin reduced order models and physics-informed neural networks for solving inverse problems for the Navier–Stokes equations

Fig. 14

The approximation of the physical viscosity by the PINN at each training epoch for the reduced setting \(N_u = N_p = N_S = 60\), Fig. 14a refers to the PINN based on the quadratic approximation of the convective term using a third order tensor and Fig. 14b corresponds to the PINN with the convective term being approximated as an output of the neural network (the approach adopted in this work). (a) The PINN with the convective term approximated as a quadratic product at the reduced level. (b) The PINN with the convective term approximated as an additional reduced output of the neural network

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