X-CAL: Explaining latent causality in physical space for fluid mechanics

TL;DR

X-CAL combines variational autoencoders, causality analysis, and explainability techniques to interpret and connect latent representations with physical phenomena in turbulent fluid flows, providing insights into flow structures and interactions.

Contribution

The paper introduces a novel pipeline integrating $eta$-VAE, SURD, and SHAP for causal analysis and interpretability of high-dimensional fluid flow data, linking latent variables to physical structures.

Findings

Learned a near-orthogonal latent space from DNS data.

Quantified directed information flows among latent variables.

Mapped latent-space causality to physical flow structures.

Abstract

We present X-CAL, a pipeline that combines a $\beta$-variational autoencoder ($\beta$-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 $\beta$-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.