A data-driven surrogate modeling approach for time-dependent incompressible Navier-Stokes equations with dynamic mode decomposition and manifold interpolation

Abstract

This work introduces a novel approach for data-driven model reduction of time-dependent parametric partial differential equations. Using a multi-step procedure consisting of proper orthogonal decomposition, dynamic mode decomposition, and manifold interpolation, the proposed approach allows to accurately recover field solutions from a few large-scale simulations. Numerical experiments for the Rayleigh-Bénard cavity problem show the effectiveness of such multi-step procedure in two parametric regimes, i.e., medium and high Grashof number. The latter regime is particularly challenging as it nears the onset of turbulent and chaotic behavior. A major advantage of the proposed method in the context of time-periodic solutions is the ability to recover frequencies that are not present in the sampled data.

Surrogate modeling of time-domain electromagnetic wave propagation via dynamic mode decomposition and radial basis function

“…The accuracy and effectiveness of the NIMOR method were illustrated numerically by considering three classical test cases: the scattering of a plane wave by a dielectric disk, by a multi-layer disk, and by a 3-D dielectric sphere. Future research direction include the usage of other interpolation methods, e.g., manifold interpolation [29], to obtain the reduced DMD operator, or the reduction of geometric parameters.…”

“…For instance, Clainchey and et al proposed a higher order DMD (HODMD) method [24] that uses time-lagged snapshots and can be seen as superimposed DMD in a sliding window, which is also applied successfully to identify and extrapolate flow patterns [27]. Despite the DMD method is wildely used for reduced-order modelling of time-dependent problems, it is significantly more challenging for parameterized problems [28,29,30,31]. For solving this limitation, Syadi, Schmid and et al proposed a DMD-based parameter-dependent ROM framework for bifurcation analysis [32], where the time series HF solutions for different parameter values are "stacked" to form an augmented snapshot matrix, and the stacked DMD modes, which are calculated by the augmented snapshot matrix, are interpolated to form a new DMD mode for a new parameter.…”