Data-driven Nonlinear Parametric Model Order Reduction Framework using Deep Hierarchical Variational Autoencoder
This work addresses efficient simulation of complex nonlinear and multiphysics systems (e.g., fluid-structure interaction) for engineering applications, representing a domain-specific incremental improvement.
The authors tackled the problem of parametric model order reduction for nonlinear dynamic systems with many degrees of freedom by proposing a deep hierarchical variational autoencoder (LSH-VAE) with a hybrid loss function, achieving significantly improved accuracy and stability compared to conventional methods while maintaining large speed-up factors.
A data-driven parametric model order reduction (MOR) method using a deep artificial neural network is proposed. The present network, which is the least-squares hierarchical variational autoencoder (LSH-VAE), is capable of performing nonlinear MOR for the parametric interpolation of a nonlinear dynamic system with a significant number of degrees of freedom. LSH-VAE exploits two major changes to the existing networks: a hierarchical deep structure and a hybrid weighted, probabilistic loss function. The enhancements result in a significantly improved accuracy and stability compared against the conventional nonlinear MOR methods, autoencoder, and variational autoencoder. Upon LSH-VAE, a parametric MOR framework is presented based on the spherically linear interpolation of the latent manifold. The present framework is validated and evaluated on three nonlinear and multiphysics dynamic systems. First, the present framework is evaluated on the fluid-structure interaction benchmark problem to assess its efficiency and accuracy. Then, a highly nonlinear aeroelastic phenomenon, limit cycle oscillation, is analyzed. Finally, the present framework is applied to a three-dimensional fluid flow to demonstrate its capability of efficiently analyzing a significantly large number of degrees of freedom. The performance of LSH-VAE is emphasized by comparing its results against that of the widely used nonlinear MOR methods, convolutional autoencoder, and $β$-VAE. The present framework exhibits a significantly enhanced accuracy to the conventional methods while still exhibiting a large speed-up factor.