Parametric reduced-order modelling often serves as a surrogate method for hemodynamics simulations to improve the computational efficiency in many-query scenarios or to perform real-time simulations. However, the snapshots of the method require to be collected from the same discretisation, which is a straightforward process for physical parameters, but becomes challenging for geometrical problems, especially for those domains featuring unparameterised and unique shapes, e.g. patient-specific geometries. In this work, a data-driven surrogate model is proposed for the efficient prediction of blood flow simulations on similar but distinct domains. The proposed surrogate model leverages group surface registration to parameterise those shapes and formulates corresponding hemodynamics information into geometry-informed snapshots by the diffeomorphisms constructed between a reference domain and original domains. A non-intrusive reduced-order model for geometrical parameters is subsequently constructed using proper orthogonal decomposition, and a radial basis function interpolator is trained for predicting the reduced coefficients of the reduced-order model based on compressed geometrical parameters of the shape. Two examples of blood flowing through a stenosis and a bifurcation are presented and analysed. The proposed surrogate model demonstrates its accuracy and efficiency in hemodynamics prediction and shows its potential application toward real-time simulation or uncertainty quantification for complex patient-specific scenarios.

翻译：参数化降阶建模常作为血流动力学模拟的替代方法，用于提高多查询场景的计算效率或实现实时模拟。然而，该方法所需的快照必须从同一离散化中采集，这针对物理参数是直接过程，但对于几何问题（尤其是具有非参数化独特形状的域，如患者特定几何结构）则具有挑战性。本研究提出一种数据驱动替代模型，用于在相似但不同的域上高效预测血流模拟。该替代模型利用群表面配准对这些形状进行参数化，并通过在参考域与原始域之间构建的微分同胚，将相应的血流动力学信息整合为几何信息快照。随后使用本征正交分解构建几何参数的非侵入式降阶模型，并训练径向基函数插值器，基于形状的压缩几何参数预测降阶模型的降阶系数。文中分析了两例通过狭窄和分叉的血流示例。该替代模型在血流动力学预测中展现出准确性与高效性，并展示了其在复杂患者特定场景中实现实时模拟或不确定性量化的潜在应用前景。