X-CAL: Explaining latent causality in physical space for fluid mechanics
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| author | Sanchis-Agudo, Marcial Cremades, Andrés Martinez-Sanchez, Alvaro Lozano-Duran, Adrian Vinuesa, Ricardo |
| author_facet | Sanchis-Agudo, Marcial Cremades, Andrés Martinez-Sanchez, Alvaro Lozano-Duran, Adrian Vinuesa, Ricardo |
| contents | We present X-CAL, a pipeline that combines a $β$-variational autoencoder ($β$-VAE) with the synergistic-unique-redundant decomposition (SURD)~\cite{surd} approach for causality analysis to interpret low-dimensional latent representations of turbulent fluid flows. Combining $β$-VAE compression with SURD and SHAP (SHapley Additive exPlanations) yields interpretable latent representations and structure-level attributions in physical space, offering a general methodology for causal analysis of high-dimensional flows. Using direct numerical simulation (DNS) data of the flow around a wall-mounted square cylinder at $Re_h=2000$, we (i) learn a compact latent space with near-orthogonal variables, (ii) quantify directed information flows among these variables via the SURD approach, and (iii) map latent-space causality back to physical space through gradient-SHAP fields . By means of percolation analysis of the SHAP fields, we extract the coherent, time-resolved structures that most influence each latent variable. The analysis connects coherent structures with latent variables which are in turn associated with wake-boundary-layer interactions. This method enables translating the insight obtained through causal analysis in the latent space into interpretable phenomena in physical space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_03311 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | X-CAL: Explaining latent causality in physical space for fluid mechanics Sanchis-Agudo, Marcial Cremades, Andrés Martinez-Sanchez, Alvaro Lozano-Duran, Adrian Vinuesa, Ricardo Fluid Dynamics We present X-CAL, a pipeline that combines a $β$-variational autoencoder ($β$-VAE) with the synergistic-unique-redundant decomposition (SURD)~\cite{surd} approach for causality analysis to interpret low-dimensional latent representations of turbulent fluid flows. Combining $β$-VAE compression with SURD and SHAP (SHapley Additive exPlanations) yields interpretable latent representations and structure-level attributions in physical space, offering a general methodology for causal analysis of high-dimensional flows. Using direct numerical simulation (DNS) data of the flow around a wall-mounted square cylinder at $Re_h=2000$, we (i) learn a compact latent space with near-orthogonal variables, (ii) quantify directed information flows among these variables via the SURD approach, and (iii) map latent-space causality back to physical space through gradient-SHAP fields . By means of percolation analysis of the SHAP fields, we extract the coherent, time-resolved structures that most influence each latent variable. The analysis connects coherent structures with latent variables which are in turn associated with wake-boundary-layer interactions. This method enables translating the insight obtained through causal analysis in the latent space into interpretable phenomena in physical space. |
| title | X-CAL: Explaining latent causality in physical space for fluid mechanics |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2601.03311 |