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

2025-12-22

AI Summary

Interpretable dimensionality reduction of left-ventricular hemodynamic data remains challenging due to the need for physically meaningful, orthogonal modal representations. Method: We systematically compare Proper Orthogonal Decomposition (POD) against linear, nonlinear, convolutional, and variational autoencoders (AEs) on CFD-simulated ventricular flow data, quantitatively evaluating their ability to preserve physical interpretability and modal orthogonality. Contribution/Results: We first quantify how AE latent dimensionality governs modal orthogonality, spatial redundancy, and high-frequency noise amplification, establishing the critical dimension threshold for AE-reconstructed modes to approximate POD-like coherent structures. Results show that AEs with appropriately tuned latent dimensions yield near-orthogonal modes whose energy spectra closely match POD; excessive dimensions degrade orthogonality, induce mode duplication, and amplify noise. Performance varies significantly across AE architectures. This work provides principled, interpretable design guidelines and dimension-selection criteria for learning-based modeling of medical hemodynamic flows.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Computer Vision: Multi-modal Vision
• Knowledge Representation and Reasoning: Diagnosis and Abductive Reasoning

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

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.

Problem

• Compares POD and autoencoders for flow pattern extraction
• Assesses interpretability loss in autoencoder-based reduced-order models
• Evaluates mode selection for meaningful cardiac flow representations

Innovation

• Compares POD with autoencoder variants for flow analysis
• Shows autoencoders can mimic POD modes with orthogonality
• Highlights mode selection for interpretable cardiac flow models