Complete flow characterization from snapshot PIV, fast probes and physics-informed neural networks

Abstract

Physics-informed neural networks (PINNs) are function approximators that can incorporate physics laws during training. In recent years, PINNs have been shown to be capable of reconstructing fluid behavior using constraints based on the Navier–Stokes equations and field data. On the downside, the lack of time resolution in a wide range of experimental applications severely limits the applicability of PINNs. We propose a novel methodology based on feeding PINNs with time-resolved fields estimated from non-time-resolved field measurements (e.g. particle image velocimetry) and time-resolved pointprobe measurements (e.g. hot-wires). First, the dimensionality of the problem is reduced by using as a target the temporal modes from a truncated proper orthogonal decomposition (POD) of the velocity fields. Then, using a multilayer perceptron (MLP), a correspondence is established between probe data and the POD time coefficients of the velocity fields. The estimated fields are then fed to the PINN to enhance the data and increase precision. As a further benefit, additional derived quantities not available in the raw data, such as the pressure distribution, can be extracted if suitable boundary conditions are provided. We validate the method on synthetic test cases based on the direct numerical simulation of the wake of a fluidic pinball. Furthermore, we test the algorithm in an experimental case of the wake of a stalled wing. The results show that the PINN is able to reduce the error in the estimated fields, provided that the reference data obtained from the estimation with the MLP are sufficiently accurate.