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

TL;DR

This study compares Proper Orthogonal Decomposition and various Autoencoder architectures for extracting meaningful flow structures from intraventricular flow data, revealing strengths and limitations of each method in terms of interpretability and orthogonality.

Contribution

It systematically evaluates how different Autoencoder variants perform relative to POD in capturing cardiac flow features, highlighting issues with mode orthogonality and interpretability.

Findings

Autoencoders can approximate POD modes with proper latent dimension.

Increasing latent modes in AEs leads to loss of orthogonality and mode redundancy.

Different AE variants show distinct behaviors in mode interpretability.

Abstract

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.