X-CAL：解释物理空间中的潜在因果性以用于流体力学
X-CAL: Explaining latent causality in physical space for fluid mechanics
AI总结：
X-CAL结合β-VAE与SURD方法，通过物理空间映射揭示湍流流体中潜在因果关系的结构与影响
摘要：
我们提出了X-CAL，一种结合β-变分自编码器（β-VAE）与协同-唯一-冗余分解（SURD）方法进行因果分析的管道，用于解释湍流流体流动的低维潜在表示。将β-VAE压缩与SURD和SHAP（SHapley Additive exPlanations）结合，可以得到可解释的潜在表示和结构层面的归因，从而在物理空间中提供一种通用的方法来分析高维流体。使用壁挂正方形圆柱体周围流体的直接数值模拟（DNS）数据，我们在Re_h=2000时（i）学习了一个具有近正交变量的紧凑潜在空间，（ii）通过SURD方法量化这些变量之间的定向信息流，（iii）通过梯度-SHAP场将潜在空间的因果性映射回物理空间。通过SHAP场的渗透分析，我们提取出对每个潜在变量影响最大的相干、时间解析结构。该分析将相干结构与潜在变量联系起来，这些变量又与涡旋-边界层相互作用相关联。该方法使通过潜在空间中的因果分析获得的洞察能够转化为物理空间中的可解释现象。
英文摘要：
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.
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