Reduced order modelling of intracranial aneurysm flow using proper orthogonal decomposition and neural networks

Reduced order modelling (ROMs) methods, such as proper orthogonal decomposition (POD), systematically reduce the dimensionality of high-fidelity computational models and potentially achieve large gains in execution speed. Machine learning (ML) using neural networks has been used to overcome limitations of traditional ROM techniques when applied to nonlinear problems, which has led to the recent development of reduced order models augmented by machine learning (ML-ROMs). However, the performance of ML-ROMs is yet to be widely evaluated in realistic applications and questions remain regarding the optimal design of ML-ROMs. In this study, we investigate the application of a non-intrusive parametric ML-ROM to a nonlinear, time-dependent fluid dynamics problem in a complex 3D geometry. We construct the ML-ROM using POD for dimensionality reduction and neural networks for interpolation of the ROM coefficients. We compare three different network designs in terms of approximation accuracy and performance. We test our ML-ROM on a flow problem in intracranial aneurysms, where flow variability effects are important when evaluating rupture risk and simulating treatment outcomes. The best-performing network design in our comparison used a two-stage POD reduction, a technique rarely used in previous studies. The best-performing ROM achieved mean test accuracies of 98.6% and 97.6% in the parent vessel and the aneurysm, respectively, while providing speed-up factors of the order ${10}^5$.