Centre for Computational Imaging and Modelling in Medicine (CIMIM), University of Manchester, Manchester, UK.
EPSRC Centre for Doctoral Training in Fluid Dynamics, University of Leeds, Leeds, UK.
Int J Numer Method Biomed Eng. 2024 Oct;40(10):e3848. doi: 10.1002/cnm.3848. Epub 2024 Aug 18.
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 .
降阶模型（ROM）方法，如本征正交分解（POD），可以系统地降低高保真度计算模型的维度，并有可能大大提高执行速度。使用神经网络的机器学习（ML）已被用于克服传统 ROM 技术在应用于非线性问题时的局限性，这导致了最近开发的机器学习增强的降阶模型（ML-ROM）。然而，ML-ROM 的性能在实际应用中尚未得到广泛评估，并且关于 ML-ROM 的最优设计仍然存在问题。在这项研究中，我们研究了将非侵入式参数 ML-ROM 应用于复杂 3D 几何中非线性时变流体动力学问题。我们使用 POD 构建 ML-ROM 进行降维，使用神经网络对 ROM 系数进行插值。我们根据逼近精度和性能比较了三种不同的网络设计。我们在颅内动脉瘤中的血流问题上测试了我们的 ML-ROM，其中在评估破裂风险和模拟治疗结果时，流动可变性效应很重要。我们的比较中表现最好的网络设计使用了两级 POD 降阶，这是以前的研究中很少使用的技术。表现最好的 ROM 在母体血管和动脉瘤中分别实现了 98.6%和 97.6%的平均测试准确率，同时提供了约 的加速因子。
