arXiv:2608.13629stat.MLcs.LG2026-08

用物理约束的深度网络,快速预测动脉瘤血流变化。

Learning Unsteady Aneurysm Hemodynamics with Physics-Informed DeepONets

论文配图:Learning Unsteady Aneurysm Hemodynamics with Physics-Informed DeepONets
图 1 · 摘自论文原文
  • 多分支输入融合+分层门控,让模型自适应不同血流条件。
  • 仅用0.3%标注数据,速度比传统模拟快36倍,误差低于4%。
  • 适合需要实时血流分析的临床诊断场景。

临床中,患者特异性血流动力学评估(如壁面剪切应力、涡结构和压力分布)对判断腹主动脉瘤(AAA)风险演化至关重要。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)方面表现良好,但复杂三维流动仍面临架构挑战。本文提出改进的多输入多输出物理信息深度算子网络(M3PI-DeepONet),用于预测理想化AAA几何中的非稳态流动。核心是聚合注入策略:多个输入分支的潜在表示在注入主干前融合,使坐标基函数能适应多重物理约束。据我们所知,这是首个将逐层门控机制与多分支算子网络拓扑结合的架构,生成输入自适应的主干基函数。同时,通过引入三维纳维-斯托克斯方程作为物理规律,模型基于物理残差、初始与边界条件,以及仅0.3%的标注内部数据和选定分支条件信号进行训练。该模型可同步预测非稳态三维速度场与压力场,平均相对速度误差低于4%,压力误差约5%,且在分支输入可用后,推理速度相比参考CFD模拟提升约36倍。本研究推动了深度学习在心血管疾病建模中的应用,迈向实时、无创临床诊断的重要一步。

原文摘要 · Abstract (English)

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.

血流模拟深度学习物理信息动脉瘤

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