arXiv:2512.19376physics.flu-dyncs.LG2025-12

比较了POD与自编码器在心室流场中的模式表现,发现自编码器在特定条件下可复现物理可解释结构。

A Critical Assessment of Pattern Comparisons Between POD and Autoencoders in Intraventricular Flows

  • 用不同自编码器与POD对比,分析其在心室流场中提取特征的能力
  • 当潜空间维度适当时,自编码器模式接近正交且能捕捉动能占比
  • 随模式增多,自编码器出现冗余和高频噪声,影响物理可解释性

理解心室内血流动力学需要对流动结构进行紧凑且物理可解释的表征,因为典型流动模式与心血管疾病密切相关,有助于早期发现心脏功能恶化。传统速度或压力场可视化难以揭示驱动这些动态的相干机制。降阶建模方法如本征正交分解(POD)和自编码器(AE)架构,可从复杂数据中提取主导流动特征。本研究系统比较了多种自编码器变体(线性、非线性、卷积、变分)与POD,在计算流体动力学模拟得到的左心室流场上的表现。结果表明,当潜空间维度合适时,自编码器生成的模态趋于近似正交,定性上与捕捉特定动能比例的POD模态相似。随着潜变量模式数量增加,自编码器模态逐渐失去正交性,导致线性相关、空间冗余及重复出现的高频率成分。这种退化降低了可解释性,并在基于自编码器的降阶模型中引入类似噪声的成分,可能阻碍其与物理模型或神经网络代理的集成。不同自编码器在正交性保持和特征定位方面表现出差异,总体表明自编码器可在特定潜空间配置下重现类似POD的相干结构,但需谨慎选择模态以确保对心脏流场动态的物理意义表征。

原文摘要 · Abstract (English)

Understanding intraventricular hemodynamics requires compact and physically interpretable representations of the underlying flow structures, as characteristic flow patterns are closely associated with cardiovascular conditions and can support early detection of cardiac deterioration. Conventional visualization of velocity or pressure fields, however, provides limited insight into the coherent mechanisms driving these dynamics. Reduced-order modeling techniques, like Proper Orthogonal Decomposition (POD) and Autoencoder (AE) architectures, offer powerful alternatives to extract dominant flow features from complex datasets. This study systematically compares POD with several AE variants (Linear, Nonlinear, Convolutional, and Variational) using left ventricular flow fields obtained from computational fluid dynamics simulations. We show that, for a suitably chosen latent dimension, AEs produce modes that become nearly orthogonal and qualitatively resemble POD modes that capture a given percentage of kinetic energy. As the number of latent modes increases, AE modes progressively lose orthogonality, leading to linear dependence, spatial redundancy, and the appearance of repeated modes with substantial high-frequency content. This degradation reduces interpretability and introduces noise-like components into AE-based reduced-order models, potentially complicating their integration with physics-based formulations or neural-network surrogates. The extent of interpretability loss varies across the AEs, with nonlinear, convolutional, and variational models exhibiting distinct behaviors in orthogonality preservation and feature localization. Overall, the results indicate that AEs can reproduce POD-like coherent structures under specific latent-space configurations, while highlighting the need for careful mode selection to ensure physically meaningful representations of cardiac flow dynamics.

流场分析自编码器降阶建模心脏动力学

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