PIGLET: Physics Informed Gaussian Process Regression for the Learning and Estimation of Turbulence

We introduce PIGLET: an open source framework for physics-informed Gaussian process regression (GPR), which can be used to learn statistical descriptions of turbulent flows and interpolate and quantify uncertainty in turbulent flow fields obtained from particle tracking velocimetry (PTV) and Lagrangian particle tracking (LPT) data. Building on our previous work, we describe how Gaussian process models can be formulated to incorporate Navier-Stokes dynamics in addition to incompressibility, boundary conditions and statistical symmetries we have previously documented. We describe a simple, finite-dimensional Gaussian process model, suitable for the generation of probable realisations of a homogeneous turbulent flow field given velocity information sampled by passive tracers. The model can incorporate acceleration information using a Bayesian update. This formulation mitigates the main bottleneck of GPR, allowing reconstruction of flow fields using over 200,000 particle tracks. The result is a technique which can incorporate both non-linear and linear physical constraints as well as statistical symmetries into the estimation and uncertainty quantification of turbulent flow fields from LPT and PTV data. We train and test this model upon synthetic data from homogeneous isotropic turbulence, the turbulent duct flow from the 2nd Data Assimilation Challenge, and experimental data from a square prism wake. PIGLET performs favourably in comparison to the state-of-the-art.