{"ID":2836600,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.21883","arxiv_id":"2511.21883","title":"Physically Interpretable Representation Learning with Gaussian Mixture Variational AutoEncoder (GM-VAE)","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.","short_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 Expectat...","url_abs":"https://arxiv.org/abs/2511.21883","url_pdf":"https://arxiv.org/pdf/2511.21883v1","authors":"[\"Tiffany Fan\",\"Murray Cutforth\",\"Marta D'Elia\",\"Alexandre Cortiella\",\"Alireza Doostan\",\"Eric Darve\"]","published":"2025-11-26T20:04:38Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[\"Variational Autoencoder\"]","has_code":false}