08 September 2021

Soutenance de thèse – KUMAR Nishant

"Data-Driven flow modelling using machine learning and data assimialtion approaches"


High-fidelity models used for solving Turbulent flows are intractable in applications where repeated realizations are required, such as for optimization or flow control. Model order reduction aims to construct low-dimensional reduced-order models (ROMs) to accurately approximate the underlying high-fidelity dynamics. The traditional Galerkin projection model reduction is intrusive since it requires the knowledge of the governing equations and/or to have access to the source code describing the physical model. Intrusive model reduction is therefore not suited for problems with no or limited knowledge of the physical system. In these cases, an alternative is offered by nonintrusive ROMs or pure data-driven modelling where reduced models are learnt from time-series data obtained from simulations or experiments. In this thesis, intrusive and nonintrusive data-driven approaches of reduced- order modelling are presented for the dynamical prediction of fluid flows.


For the intrusive approach, Proper Orthogonal Decomposition (POD) based ROM (POD-ROM) is considered. The POD method offers the advantage of preserving the nonlinear dynamics by projecting the governing equations onto low-dimensional optimal modes. First, sparse regression methods issued from statistical learning are used to identify the linear unknowns of the ROM. A bootstrap method is then proposed to quantify in a probabilistic framework the uncertainties associated with the regres- sion methods. Subsequently, the POD-ROM is augmented with a nonlinear eddy viscosity model that provides an interpretable physics-based closed-form representation of the flow dynamics. Finally, the closure term parameters are estimated with a Dual Ensemble Kalman filter approach (Dual EnKF) which integrates the model outputs and measurements while taking into account the respective uncer- tainties.

For the nonintrusive approach, regression models based on Neural Networks (NN-ROM) are con- sidered as an alternative to the POD-ROM. This method addresses the limitations of POD-ROM – the lack of an a priori guarantee of stability, and requirement of closure to account for the unresolved modes – at the cost of interpretability of the resulting surrogate model. The derived NN-ROM serves as a time-stepping method for the POD projection coefficients. A novel multistep, residual-based, parametrized neural network is proposed. This framework is augmented with Data Assimilation (DA) to provide accurate long-term dynamical predictions.

The proposed intrusive and nonintrusive approaches have been applied on a canonical dynamical system (Lorenz), on numerical data from low Reynolds number simulations of a cylinder wake flow and a low Mach number jet, and finally on experimental data of a wake flow.

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