Inferring velocity and pressure fields from particle images via physics-informed neural networks

Particle image velocimetry (PIV) technology is widely used in scientific research and engineering applications, serving as a crucial experimental tool in fluid mechanics. Recently, physics-informed neural networks (PINNs) have been introduced to reconstruct PIV flow fields by integrating measurement data with governing equations during network training. However, existing PINN approaches primarily focus on post-processing PIV data and face challenges in balancing accuracy and computational efficiency. In this work, we simultaneously encode the optical flow equation and the Navier–Stokes equations into the loss function of a neural network. By applying differential operators to discretize grayscale gradients at the pixel level, we constrain the optical flow equation and develop a hybrid physics-informed neural network (OF-PINN) jointly governed by both equations. OF-PINN directly infers velocity and pressure fields from particle images, enabling an unsupervised PIV approach that effectively reconstructs high-quality pressure fields. For diffusion-dominated flows, we incorporate diffusion and smoothness constraint terms into the residuals of the governing equations to enhance OF-PINN performance. Comparative experiments on cylinder flow, turbulence, and hydrofoil PIV cases demonstrate that OF-PINN outperforms conventional cross correlation and Horn–Schunck methods in terms of accuracy and robustness. OF-PINN offers a novel and efficient solution for visualizing complex flow phenomena.