Sparse Identification of Parametrized Flow Dynamics

  • Oulghelou, Mourad (Arts & Métiers ParisTech)
  • Ammar, Amine (Arts & Métiers ParisTech)

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In general, reduced order models are achieved by projecting the high fidelity equations onto the first vector functions of the Proper Orthogonal Decomposition. With varying parameters, such projected models are likely to experience instabilities even if the original system is asymptotically stable. Moreover, the data may originate from experience making hard the construction of these reduced dynamical systems. To overcome this issue, a data-driven approach to construct stable parametric reduced order models is proposed. Regardless the origin of the data, the approach consists of learning sparse reduced models on sampling parameter points, where the quadratic term is constrained to be skew-symmetric. For unseen points, the Grassmann interpolation is used for model adaptation.