Print Email Facebook Twitter Learning Reduced Order Mappings of Navier-Stokes Title Learning Reduced Order Mappings of Navier-Stokes: An Investigation of Generalization on the Viscosity Parameter Author Kiste, Amund (TU Delft Electrical Engineering, Mathematics and Computer Science) Contributor Tax, D.M.J. (mentor) Naderibeni, M. (mentor) Tömen, N. (graduation committee) Degree granting institution Delft University of Technology Programme Computer Science and Engineering Project CSE3000 Research Project Date 2024-02-02 Abstract Solving Partial Differential Equations (PDEs) in engineering such as Navier-Stokes is incredibly computationally expensive and complex. Without analytical solutions, numerical solutions can take ages to simulate at great expense. In order to reduce this cost, neural networks may be used to compute approximations of the solution for use during engineering processes. PCA-net is a neural network approach that reduces the dimensionality of the input and output data for PDEs in order to allow mapping from a high-dimensional input and output function with a fully connected neural network through the use of Principal Component Analysis (PCA). In this paper, PCA-net is applied to Navier-Stokes with varying viscosities to test the generalization of PCA-net on viscosity parameters. Training is done on four discrete viscosities, while testing is done on continuous viscosities, extrapolating and interpolating around the training set. Results shows good performance on low viscosities, both with interpolation and extrapolation. Mid-to-high viscosity interpolation shows lesser performance, with high viscosity extrapolation diverging to great error. Omitting high viscosities, performance over varying viscosities is close to that shown by previous research. Subject Principal Component Analysis (PCA)Neural NetworksPartial Differential Equations solverNavier-StokesReduced order modellingReduced Basis To reference this document use: http://resolver.tudelft.nl/uuid:172f4461-3474-4357-a118-b0837c0a068e Part of collection Student theses Document type bachelor thesis Rights © 2024 Amund Kiste Files PDF CSE3000_Kiste_Final.pdf 4.48 MB Close viewer /islandora/object/uuid:172f4461-3474-4357-a118-b0837c0a068e/datastream/OBJ/view