Recently, there is a growing interest in adapting data assimilation methods to fluid flow frameworks. Data obtained from particle tracking velocimetry (PTV) enables modelling in a Langragian context, which motivates the development of corresponding techniques and resources [1]. In parallel, Gaussian process regression (GPR) has been adapted to approximate solutions of partial differential equations (PDE) by using kernel representation formulas [2], allowing uncertainty quantification (UQ). A reconstruction approach of flow fields based on a Lagrangian simulation of a viscous flow over a periodic domain was presented by [3]. We propose a reconstruction approach to simulate 2D incompressible flows in a tunnel setting with an obstacle (e.g. cylinder or airfoil profile), by considering estimation from a physics–informed curve–constrained Gaussian process. Considering PTV flow data obtained from high–precision external simulations, with V, the velocity values on trajectories Y, inlet and exit boundary conditions on velocity \widetilde{V} over domain boundary points \widetilde{X}, and physical constraints around an obstacle, we study a hybrid reconstruction approach that combines data and a numerical method on the vorticity system over collocation trajectories Q with vorticity values W. Estimation of velocity will be of the form u*(x,t) =\mathbb{E} ( Z(x) | Z(Y(t)) =V(t), Z(\widetilde{X}) = \widetilde{V}, curl Z(Q(t)) =W(t) ), for (x,t) in \Omega x [0,T], where Z is a vector–valued centered Gaussian process indexed in \Omega with a physics–informed matrix–valued kernel K satisfying a divergence–free condition and continous–type boundary conditions on the obstacle. Further collocation sub–sampling techniques are being studied to enhance the performance of the estimation at each time step, as well as kernel parameters identification by maximum likelihood estimation. Fig. 1 : Velocity field and vorticity reconstruction from GPR References [1] B. Leclaire, P. Cornic, F. Champagnat, E. Fabre, and F. Calmels. A web portal for automatic performance evaluation of lagrangian particle tracking and data assimilation algorithms. In 20th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics, 2022. [2] Y. Chen, B. Hosseini, H. Owhadi, and A.M. Stuart. Solving and learning nonlinear PDEs with Gaussian processes. J. Comput. Phys., 447:110668, 2021. [3] H. Owhadi. Gaussian process hydrodynamics. App. Math. Mech., 44(7):1175–1198, 2023.