发表机构
Aix Marseille Univ; CNRS; Centrale Marseille; IRPHE; AMSE（艾克斯-马赛大学; 法国国家科学研究中心; 马赛中央理工学院; 流体与能量物理研究所; 马赛经济与管理科学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出改进型多输入多输出物理信息深度算子网络（M3PI-DeepONet），结合三维纳维-斯托克斯方程，以仅0.3%带标记数据预测腹主动脉瘤非稳态三维流场，速度误差低于4%，推理加速约36倍，推进心血管疾病建模的临床应用。
AI 中文摘要
临床可操作的、患者特异性的血流动力学评估，尤其是壁面切应力、涡结构和压力分布，对于确定腹主动脉瘤（AAA）的危险或不良进展至关重要。尽管物理信息深度算子网络（PI-DeepONet）在补充计算流体动力学（CFD）等成熟工具方面显示出良好前景，但针对复杂三维流动仍存在持续的架构挑战。在此方向上，我们提出了一种改进的多输入多输出PI-DeepONet（M3PI-DeepONet），用于预测理想化AAA几何结构中的非稳态流动。我们模型的核心是聚合注入策略，即融合多个输入分支的潜在表征后再注入主干，使坐标基能够适应多个物理约束。据我们所知，这是首个将分层门控机制与多分支算子网络拓扑相结合的架构，可生成输入自适应的主干基。此外，我们将三维纳维-斯托克斯方程作为控制物理定律，因此模型基于物理信息残差、初始和边界条件，以及仅0.3%的带标记内部数据和选定的分支调节信号进行训练。M3PI-DeepONet可同时预测非稳态三维流速和压力场，其平均相对L2速度误差低于4%，压力误差约为5%；一旦获得用于调节的分支输入，与参考CFD模拟相比，保守保留周期的推理加速约为36倍。本研究推进了深度学习在心血管疾病建模中的应用，向实时、非侵入性临床诊断迈出了一步。
英文摘要
Clinically actionable, patient-specific hemodynamic assessment, specifically wall shear stress, vortex structure and pressure distributions, is critical for determining risky or unfavorable evolution in Abdominal Aortic Aneurysms (AAA). While Physics-Informed Deep Operator Networks (PI-DeepONets) show promising results in complementing established 5 tools such as Computational Fluid Dynamics (CFD), a persistent architectural challenge remains for complex 3D flows. In this direction, we propose a Modified Multi-Input Multi-Output PI-DeepONets (M3PI-DeepONet) designed for predicting unsteady flows in an idealized AAA geometry. Central to our model is the Aggregated Injection strategy, where latent representations from multiple input branches are fused prior to trunk injection, allowing the coordinate basis to adapt to multiple physical constraints. To the best of our knowledge, this is the first architecture to combine the layer-wise gating mechanism with a multi-branch operator-network topology, yielding an input-adaptive trunk basis. Additionally, we integrate the 3D Navier-Stokes equations as governing physical laws, so the model is trained based on physics-informed residuals, initial and boundary conditions, and only 0.3% of the labeled internal data together with the selected branch-conditioning signals. The M3PI-DeepONet simultaneously predicts unsteady 3D flow velocity and pressure fields with an average relative L2 velocity error below 4% and pressure error around 5% while achieving a conservative retained-cycle inference speedup of approximately 36x compared to reference CFD simulations once the branch inputs used for conditioning are available. This work advances the application of deep learning in cardiovascular disease modeling, marking step toward real-time, non-invasive clinical diagnostics.
