Adaptation and validation of physics-informed neural networks for rotating 3D velocimetry

Abstract Physics-informed neural networks (PINNs) are adapted and experimentally validated for rotating three-dimensional velocimetry (R3DV). Through the application of plenoptic imaging, R3DV enables the capture of time-resolved three-dimensional/three-component (3D/3C) velocity fields in the rotating frame of reference but suffers from anisotropic uncertainty due to the plenoptic camera’s limited baseline parallax. PINNs offer a means to regularize noisy measurements by enforcing physics-based constraints. Through validation against high resolution stereoscopic particle image velocimetry (stereo-PIV), we demonstrate that integrating PINNs with plenoptic particle tracking velocimetry (PTV) significantly improves estimations of depthwise motion. Across a range of Rossby numbers (2−4.5, $$\infty $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>∞</mml:mi> </mml:math> ), the out-of-plane velocity error is reduced by an average of 72.6 $$\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>%</mml:mo> </mml:math> relative to plenoptic-PTV. In addition, the influence of several design considerations and hyperparameters are explored and we identify critical adjustments to conventional PINN configurations that aid in mitigating errors inherent to plenoptic-PTV, namely: (1) balance of the objective function in proportion to theoretical plenoptic uncertainty ratios, and (2) track preconditioning. This work suggests that PINNs can extend the capabilities of plenoptic-based flow diagnostics, enabling single-camera 3D measurements with accuracies on par with high resolution multi-camera techniques under challenging imaging conditions.