Information decomposition for disentangled and interpretable manifold learning of fluid flows via variational autoencoders

TL;DR

This paper presents an information-theoretic framework using variational autoencoders to extract interpretable, disentangled manifolds from high-dimensional fluid flow data, improving interpretability without losing information.

Contribution

It introduces a novel VAE-based approach decomposing the KL divergence into interpretable terms for targeted latent-space design in fluid flow analysis.

Findings

The method outperforms PCA, Isomap, and $eta$-VAE in disentanglement and interpretability.

Latent coordinates effectively separate physical effects in flow data.

The approach is robust to variations in loss-weighting parameters.

Abstract

We introduce an information-theoretic framework that uses variational autoencoders (VAEs) to extract compact, physically interpretable manifolds from high-dimensional flow-field data. To this end, the Kullback--Leibler (KL) divergence in the variational objective is decomposed into three complementary information-theoretic terms: the index-code mutual information, the total correlation, and the dimension-wise KL divergence. These terms explicitly regulate data compression, latent disentanglement, and geometric regularization. This establishes a principled basis for targeted latent-space design, allowing enhanced interpretability without sacrificing information capacity, a common drawback of heavily regularized VAE variants. The approach is evaluated on two synthetic unsteady flow datasets. First, we consider a flow around a cylinder in a channel with variable cylinder position, diameter, and Reynolds number. Later, we also consider the flow around a NACA 0012 airfoil at varying angles of attack and subjected to strong vortex gusts with variable intensity, position, and length scale. Comparisons with Principal Component Analysis, Isometric Feature Mapping, and $\beta$-VAE demonstrate clear advantages in disentanglement and physical interpretability. The learned latent coordinates successfully separate distinct physical effects. Moreover, the proposed method demonstrates strong robustness to variations in the loss-weighting parameters, despite involving a larger number of such parameters.