Polytopic Autoencoders with Smooth Clustering for Reduced-order Modelling of Flows
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Abstract (arXiv)
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.
Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 13 of its 51 references that are in the map. First posted on arXiv 19 Jan 2024.
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13 of 51 references.
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Citing papers per year: 2024: 1; 2025: 1.
2 papers.