Efficient data assimilation of unsteady 3D turbulent flows using intrusive generative models
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With their numerous applications ranging from monitoring to control, digital twins attract growing interest. A digital twin generally relies on a surrogate model coupled to the real system by a stream of measurements. Often formulated in a Bayesian way, this data assimilation requires either highly-informative measurements or highly-informative generative surrogate (prior). For lower-fidelity measurements, unsteady 3D turbulent flows systems remain out of scope. Indeed, the slow Kolmogorov N-width decay, the chaotic and intermittent dynamics restrict the capacity of deterministic surrogate models. Generative (stochastic) models open a new path. However, most existing approaches remain fully-data-driven and lake the reliability of mechanistic models. As surrogate, we propose an intrusive stochastic reduced order model (ROM) [1]. It results from a Proper-Orthogonal Decomposition (POD) Galerkin of a randomized Navier-Stokes model. A physics-based multiplicative noise ensures both samples variability and physical structure of each sample – e.g. energy conservation. Robust and efficient noise calibration is also facilitated by this physical ground. For larger Reynolds number, we perform the POD-Galerkin on a randomized Large Eddy Simulation (LES). Additional randomness accounts for hyperreduction errors. Eventually, we couple the ROM with measurements through a particle filter [2]. Numerically, we perform this data assimilation procedure on 3D unsteady wake flows at Reynolds numbers 300 and 3900. Beside the huge dimensionality of such systems, we accurately predict the first POD modes using few pointwise measurements.