Efficient nonlinear manifold reduced order model

• URL: http://arxiv.org/abs/2011.07727v1
• Date: Fri, 13 Nov 2020 18:46:21 GMT
• Title: Efficient nonlinear manifold reduced order model
• Authors: Youngkyu Kim and Youngsoo Choi and David Widemann and Tarek Zohdi
• Abstract summary: nonlinear manifold ROM (NM-ROM) can better approximate high-fidelity model solutions with a smaller latent space dimension than the LS-ROMs. 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.
• Score: 0.19116784879310023
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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