Efficient nonlinear manifold reduced order model
This work provides a more efficient simulation method for advection-dominated physical phenomena, which are poorly approximated by traditional linear models, benefiting researchers and engineers in computational fluid dynamics.
This paper addresses the limitation of linear subspace reduced order models (LS-ROMs) in simulating physical phenomena with high-dimensional solution spaces, such as advection-dominated flows. The authors developed an efficient nonlinear manifold ROM (NM-ROM) that achieves a speed-up of up to 11.7 for 2D Burgers' equations by learning a more efficient latent space representation and incorporating a hyper-reduction technique.
Traditional linear subspace reduced order models (LS-ROMs) are able to accelerate physical simulations, in which the intrinsic solution space falls into a subspace with a small dimension, i.e., the solution space has a small Kolmogorov n-width. However, for physical phenomena not of this type, such as advection-dominated flow phenomena, a low-dimensional linear subspace poorly approximates the solution. To address cases such as these, we have developed an efficient nonlinear manifold ROM (NM-ROM), which can better approximate high-fidelity model solutions with a smaller latent space dimension than the LS-ROMs. Our method takes advantage of the existing numerical methods that are used to solve the corresponding full order models (FOMs). The efficiency is achieved by developing a hyper-reduction technique in the context of the NM-ROM. Numerical results show that neural networks can learn a more efficient latent space representation on advection-dominated data from 2D Burgers' equations with a high Reynolds number. A speed-up of up to 11.7 for 2D Burgers' equations is achieved with an appropriate treatment of the nonlinear terms through a hyper-reduction technique.