Recovering Quasi-2D Navier-Stokes Model Parameters via Weak Formulation

Quantitative prediction of thin-layer fluid flow based on a modified two-dimensional Navier-Stokes model demands that the model and its parameters accurately describe the system. Algorithms exist that can infer model parameters from trajectory observations alone, but differential model reconstruction is greatly hindered by noisy data; noise makes numerical derivatives rather inaccurate. Unobservable quantities (e.g. pressure) complicate things further, and although higher order PDEs in which they aren't present (e.g. the vorticity transport equation) can be used instead, this only exacerbates the first problem. Thus, we developed a method that considers a weak formulation instead of the model PDE directly, which allows us to estimate parameters despite some quantities being noisy and others being unobservable altogether. We confirm the quality of the method by accurately finding the parameters for simulation data obtained from a quasi-2D Navier-Stokes model, with added Gaussian noise. We also apply the method to spatiotemporally-chaotic experimental data and predict new parameter values.