Nonintrusive reduced-order modeling of parametrized time-dependent partial differential equations

Christophe Audouze (1) , Florian de Vuyst (2) , Prasanth Nair (1)

1 Computational Engineering and Design Group, School of Engineering Sciences
2 CMLA - Centre de Mathématiques et de Leurs Applications

We propose a non-intrusive reduced-order modeling method based on the notion of space-time-parameter proper orthogonal decomposition for approximating the solution of non-linear parametrized time-dependent partial differential equations. A two-level proper orthogonal decomposition method is introduced for constructing spatial and temporal basis functions with special properties such that the reduced-order model satisfies the boundary and initial conditions by construction. A radial basis function approximation method is used to estimate the undetermined coefficients in the reduced-order model without resorting to Galerkin projection. This nonintrusive approach enables the application of our approach to general problems with complicated nonlinearity terms. Numerical studies are presented for the parametrized Burgers' equation and a parametrized convection-reaction-diffusion problem. We demonstrate that our approach leads to reduced-order models that accurately capture the behavior of the field variables as a function of the spatial coordinates, the parameter vector and time.

Keywords: Reduced-order model; physics-based surrogate model; time-dependent parametrized partial differential equation; proper orthogonal decomposition; radial basis functions

Domains: Modeling and Simulation; Computational Complexity [cs.CC]; Numerical Analysis [math.NA]; Analysis of PDEs [math.AP]

Christophe Audouze, Florian de Vuyst, Prasanth Nair. Nonintrusive reduced-order modeling of parametrized time-dependent partial differential equations. 2010. ⟨hal-00530847v2⟩