Physically Interpretable Representation Learning with Gaussian Mixture Variational AutoEncoder (GM-VAE)

• URL: http://arxiv.org/abs/2511.21883v1
• Date: Wed, 26 Nov 2025 20:04:38 GMT
• Title: Physically Interpretable Representation Learning with Gaussian Mixture Variational AutoEncoder (GM-VAE)
• Authors: Tiffany Fan, Murray Cutforth, Marta D'Elia, Alexandre Cortiella, Alireza Doostan, Eric Darve,
• Abstract summary: We propose a Variational Autoencoder (GM-VAE) framework designed to extract, physically interpretable representations from high-dimensional scientific data.<n>Unlike conventional VAEs that jointly optimize reconstruction and clustering, our method utilizes a block-coordinate descent strategy.<n>To objectively evaluate the learned representations, we introduce a metric based on graph-Laplacian smoothness, which measures the coherence of physical instability across the latent manifold.
• Score: 37.18249990338269
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Extracting compact, physically interpretable representations from high-dimensional scientific data is a persistent challenge due to the complex, nonlinear structures inherent in physical systems. We propose a Gaussian Mixture Variational Autoencoder (GM-VAE) framework designed to address this by integrating an Expectation-Maximization (EM)-inspired training scheme with a novel spectral interpretability metric. Unlike conventional VAEs that jointly optimize reconstruction and clustering (often leading to training instability), our method utilizes a block-coordinate descent strategy, alternating between expectation and maximization steps. This approach stabilizes training and naturally aligns latent clusters with distinct physical regimes. To objectively evaluate the learned representations, we introduce a quantitative metric based on graph-Laplacian smoothness, which measures the coherence of physical quantities across the latent manifold. We demonstrate the efficacy of this framework on datasets of increasing complexity: surface reaction ODEs, Navier-Stokes wake flows, and experimental laser-induced combustion Schlieren images. The results show that our GM-VAE yields smooth, physically consistent manifolds and accurate regime clustering, offering a robust data-driven tool for interpreting turbulent and reactive flow systems.

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