Solution multiplicity and effects of data and eddy viscosity on Navier-Stokes solutions inferred by physics-informed neural networks

Understand

Physics-informed neural networks (PINNs) have emerged as a new simulation paradigm for fluid flows and are especially effective for inverse and hybrid problems.

• However, vanilla PINNs often fail in forward problems, especially at high Reynolds (Re) number flows.
• Herein, we study systematically the classical lid-driven cavity flow at $Re=2,000$, $3,000$ and $5,000$.
• We observe that vanilla PINNs obtain two classes of solutions, one class that agrees with direct numerical simulations (DNS), and another that is an unstable solution to the Navier-Stokes equations and not physically realizable.