Polytopic Autoencoders with Smooth Clustering for Reduced-order Modelling of Flows

• URL: http://arxiv.org/abs/2401.10620v1
• Date: Fri, 19 Jan 2024 10:52:57 GMT
• Title: Polytopic Autoencoders with Smooth Clustering for Reduced-order Modelling of Flows
• Authors: Jan Heiland, Yongho Kim
• Abstract summary: We propose a polytopic autoencoder architecture that includes a lightweight nonlinear encoder, a convex combination decoder, and a smooth clustering network. We conduct simulations involving two flow scenarios with the incompressible Navier-Stokes equation. Numerical results demonstrate the guaranteed properties of the model, low reconstruction errors compared to POD, and the improvement in error using a clustering network.
• Score: 1.1279808969568252
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: With the advancement of neural networks, there has been a notable increase, both in terms of quantity and variety, in research publications concerning the application of autoencoders to reduced-order models. We propose a polytopic autoencoder architecture that includes a lightweight nonlinear encoder, a convex combination decoder, and a smooth clustering network. Supported by several proofs, the model architecture ensures that all reconstructed states lie within a polytope, accompanied by a metric indicating the quality of the constructed polytopes, referred to as polytope error. Additionally, it offers a minimal number of convex coordinates for polytopic linear-parameter varying systems while achieving acceptable reconstruction errors compared to proper orthogonal decomposition (POD). To validate our proposed model, we conduct simulations involving two flow scenarios with the incompressible Navier-Stokes equation. Numerical results demonstrate the guaranteed properties of the model, low reconstruction errors compared to POD, and the improvement in error using a clustering network.

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