Interpolation-based reduced-order modelling for steady transonic flows via manifold learning

Thomas Franz, Ralf Zimmermann, Stefan Goertz, Niklas Karcher

Research output: Contribution to journalJournal articleResearchpeer-review


This paper presents a parametric reduced-order model (ROM) based on manifold learning (ML) for use in steady transonic aerodynamic applications. The main objective of this work is to derive an efficient ROM that exploits the low-dimensional nonlinear solution manifold to ensure an improved treatment of the nonlinearities involved in varying the inflow conditions to obtain an accurate prediction of shocks. The reduced-order representation of the data is derived using the Isomap ML method, which is applied to a set of sampled computational fluid dynamics (CFD) data. In order to develop a ROM that has the ability to predict approximate CFD solutions at untried parameter combinations, Isomap is coupled with an interpolation method to capture the variations in parameters like the angle of attack or the Mach number. Furthermore, an approximate local inverse mapping from the reduced-order representation to the full CFD solution space is introduced. The proposed ROM, called Isomap+I, is applied to the two-dimensional NACA 64A010 airfoil and to the 3D LANN wing. The results are compared to those obtained by proper orthogonal decomposition plus interpolation (POD+I) and to the full-order CFD model.

Original languageEnglish
JournalInternational Journal of Computational Fluid Dynamics
Issue number3-4
Pages (from-to)106-121
Number of pages16
Publication statusPublished - 1. Mar 2014
Externally publishedYes


  • aerodynamics
  • dimensionality reduction
  • Isomap
  • manifold learning
  • proper orthogonal decomposition
  • reduced-order model


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