Non-Intrusive Reduced Order Modelling of Aneurysm Haemodynamics Using Proper Orthogonal Decomposition and Neural Networks

  • MacRaild, Michael (University of Leeds)
  • Sarrami-Foroushani, Ali (University of Leeds)
  • Lassila, Toni (University of Leeds)
  • Ravikumar, Nishant (University of Leeds)
  • Frangi, Alejandro (University of Leeds)

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Using high-fidelity mathematical models in many-query and real-time scenarios remains challenging due to the high dimensionality of the discretised governing equations. Reduced order models (ROMs) are low-order representations of high-order models that preserve essential behaviour at the cost of some degree of accuracy, and hence are commonly used to provide fast alternatives to expensive high-fidelity models. In this paper, we design and test a non-intrusive ROM using proper orthogonal decomposition for dimensionality reduction and an encoder-decoder neural network for interpolation and apply it to parameterised intracranial aneurysm blood flow. Modelling flow variability in aneurysms with traditional numerical models requires repeated evaluations of an expensive Navier-Stokes solver. Furthermore, this problem is time-dependent and nonlinear, so it is an ideal exemplar application for our ROM. We investigate various strategies for sampling the ROM parameter space and compare the accuracy of each strategy. Finally, for the best-performing sampling strategy, we present results on the accuracy and acceleration offered by the ROM relative to the full-order model.