• A long short term memory for hybrid uplifted reduced order models. 

      Ahmed, Shady E; San, Omer; Rasheed, Adil; Trian, Iliescu (Peer reviewed; Journal article, 2020)
      In this paper, we introduce an uplifted reduced order modeling (UROM) approach through the integration of standard projection based methods with long short-term memory (LSTM) embedding. Our approach has three modeling ...
    • Nonlinear proper orthogonal decomposition for convection-dominated flows 

      Ahmed, Shady E; San, Omer; Rasheed, Adil; Trian, Iliescu (Peer reviewed; Journal article, 2021)
      Autoencoder techniques find increasingly common use in reduced order modeling as a means to create a latent space. This reduced order representation offers a modular data-driven modeling approach for nonlinear dynamical ...
    • On closures for reduced order models— A spectrum of first-principle to machine-learned avenues 

      Ahmed, Shady E; Pawar, Suraj; San, Omer; Rasheed, Adil; Trian, Iliescu; Noack, Bernd R. (Peer reviewed; Journal article, 2021)
      For over a century, reduced order models (ROMs) have been a fundamental discipline of theoretical fluid mechanics. Early examples include Galerkin models inspired by the Orr–Sommerfeld stability equation and numerous vortex ...