Data assimilation with physics-informed neural network surrogates constructed against prediction uncertainty

A physics-informed neural network (PINN) surrogate is developed to represent the discrepancy between computational fluid dynamics (CFD) simulations and observations, enabling surrogate-based data assimilation. Utilizing the multi-block CFD framework of the Building Cube Method (BCM), the PINN surrogate is constructed and trained in parallel only in the subdomains where it is required for data assimilation. One-dimensional problems illustrate the overlapping strategy between finite-difference solutions and PINN surrogates for estimating uncertain parameters in governing equations. Low- and high-Reynolds-number flows are then investigated using the three-dimensional incompressible Navier-Stokes equations within the BCM framework, where a porous region is introduced and its macroscopic porous drag is estimated from observations. In the Navier-Stokes cases, a time-averaged PINN surrogate is constructed in combination with the mean flow field obtained from a large eddy simulation (LES) to perform data assimilation based on the mean flow field. The drag parameters of the porous region located in the wake of a circular cylinder are successfully estimated by superimposing the LES flow field and the PINN surrogate.