Sensor placement study for estimation of Reynolds number in flow past a circular cylinder using an Inverse Physics-Informed Neural Network

Determining an unknown flow parameter from a limited number of experimental measurement data is an essential requirement for many engineering problems. Inverse physics-informed neural network (I-PINN) provide a mesh-free way unlike the usual adjoint- or conjugategradient-based methods by adding the unknown parameter as a trainable one along with other weights of the neural network during the training phase. In this paper, we study the effective sensor placement for a flow past a circular cylinder to recover the Reynolds number (𝑅𝑒) of the flow. We consider five zones in the flow independently and try to recover the 𝑅𝑒 from synthetic data obtained from the validated forward PINN. In the first of three sweeps, the near-, mid-, and far-wake zones recover 𝑅𝑒 to within 9.9–21.6% error whereas the shear-layer zone stays in a tighter 28.2–31.7% error band. The upstream zone which samples the near uniform free stream values comes out to be the ineffective almost every time at 46.3–54.1%. The two repeat sweeps shift these errors, but the wake zones stay the most accurate in all three. We also see that more sensors do not translate into better accuracy in any zone, which implies that sensor location matters more than sensor count for recovering 𝑅𝑒.