Inferring parameters and reconstruction of two-dimensional turbulent flows with physics-informed neural networks

Obtaining system parameters and reconstructing the full flow state from limited velocity observations using conventional fluid dynamics solvers can be prohibitively expensive. Here we employ machine learning algorithms to overcome the challenge. As an example, we consider a moderately turbulent fluid flow, excited by a stationary force and described by a two-dimensional Navier–Stokes equation with linear bottom friction. Using dense in time, spatially sparse and probably noisy velocity data, we reconstruct the spatially dense velocity field, infer the pressure and driving force up to a harmonic function and its gradient, respectively, and determine the unknown fluid viscosity and friction coefficient. Both the root-mean-square errors of the reconstructions and their energy spectra are addressed. We study the dependence of these metrics on the degree of sparsity and noise in the velocity measurements. Our approach involves training a physics-informed neural network by minimizing the loss function, which penalizes deviations from the provided data and violations of the governing equations. The suggested technique extracts additional information from velocity measurements, potentially enhancing the capabilities of particle image/tracking velocimetry.