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Article Dans Une Revue Fluids Année : 2022

A Bayesian Nonlinear Reduced Order Modeling Using Variational AutoEncoders

Nissrine Akkari
  • Fonction : Auteur
Fabien Casenave
Elie Hachem
David Ryckelynck

Résumé

This paper presents a new nonlinear projection based model reduction using convolutional Variational AutoEncoders (VAEs). This framework is applied on transient incompressible flows. The accuracy is obtained thanks to the expression of the velocity and pressure fields in a nonlinear manifold maximising the likelihood on pre-computed data in the offline stage. A confidence interval is obtained for each time instant thanks to the definition of the reduced dynamic coefficients as independent random variables for which the posterior probability given the offline data is known. The parameters of the nonlinear manifold are optimized as the ones of the decoder layers of an autoencoder. The parameters of the conditional posterior probability of the reduced coefficients are the ones of the encoder layers of the same autoencoder. The optimization of both sets of the encoder and the decoder parameters is obtained thanks to the application of a variational Bayesian method, leading to variational autoencoders. This Reduced Order Model (ROM) is not a regression model over the offline pre-computed data. The numerical resolution of the ROM is based on the Chorin projection method. We apply this new nonlinear projection-based Reduced Order Modeling (ROM) for a 2D Karman Vortex street flow and a 3D incompressible and unsteady flow in an aeronautical injection system.

Dates et versions

hal-03853606 , version 1 (15-11-2022)

Identifiants

Citer

Nissrine Akkari, Fabien Casenave, Elie Hachem, David Ryckelynck. A Bayesian Nonlinear Reduced Order Modeling Using Variational AutoEncoders. Fluids, 2022, 7 (10), pp.334. ⟨10.3390/fluids7100334⟩. ⟨hal-03853606⟩
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