Additive-feature-attribution methods: a review on explainable artificial intelligence for fluid dynamics and heat transfer

TL;DR

This review shows that explainability techniques, and in particular additive-feature-attribution methods, are crucial for implementing interpretable and physics-compliant deep-learning models in the fluid-mechanics field.

Abstract

The use of data-driven methods in fluid mechanics has surged dramatically in recent years due to their capacity to adapt to the complex and multi-scale nature of turbulent flows, as well as to detect patterns in large-scale simulations or experimental tests. In order to interpret the relationships generated in the models during the training process, numerical attributions need to be assigned to the input features. One important example are the additive-feature-attribution methods. These explainability methods link the input features with the model prediction, providing an interpretation based on a linear formulation of the models. The SHapley Additive exPlanations (SHAP values) are formulated as the only possible interpretation that offers a unique solution for understanding the model. In this manuscript, the additive-feature-attribution methods are presented, showing four common implementations in the literature: kernel SHAP, tree SHAP, gradient SHAP, and deep SHAP. Then, the main applications of the additive-feature-attribution methods are introduced, dividing them into three main groups: turbulence modeling, fluid-mechanics fundamentals, and applied problems in fluid dynamics and heat transfer. This review shows thatexplainability techniques, and in particular additive-feature-attribution methods, are crucial for implementing interpretable and physics-compliant deep-learning models in the fluid-mechanics field.

Figures (12)

• Figure 1: Example model to illustrate the deep-SHAP
• Figure 2: Summary of the SHAP analysis of the input features for predicting the eddy viscosity. The figure shows the mean absolute SHAP values (left) and bee swarm plots of SHAP values (right). Each dot represents a single grid point, when multiple points are located in the same horizontal position, they pile up vertically to show the probability density. The present figure shows the value for the viscosity ratio $q_9$, the strain-rotation ratio $q_4$, the wall proximity $q_8$, the pressure gradient-shear ratio $q_3$, the streamwise pressure gradient normalized with the local kinetic energy and the Reynolds number per unit of length $q_2$ as well as the misalignment of the velocity vector with respect to the streamline velocity. Figure extracted from he2022 with permission from the publisher (Elsevier).
• Figure 3: Connection of the SHAP values (importance scores) of each flow magnitude used for the prediction of the turbulence model with the corresponding grid point of the domain. The figure shows the normalized local feature importance scores of the neural-network model based on the deep-SHAP attribution method. Figure extracted from mandler2023 with permission from the publisher (Elsevier).
• Figure 4: Mean absolute SHAP values for the nine modes of the model in a certain time of simulation. The figure shows the results for both, samples that relaminarize (class 1) and do not relaminarize (class 0). Figure extracted from lellep2022 with permission from the publisher (Cambridge University Press).
• Figure 5: Instantaneous visualization of the intense Reynolds stress structures. This Figure shows (views A) the type of turbulent structure, (views B) the SHAP (Shappley additive explanation) values ($|\phi_i|$) and (views C) the SHAP values divided by the volume ($|\phi_i/V^+|$) of the corresponding structures. The dashed line marks $y^+=20$, which separates wall-attached and wall-detached structures. Figure extracted from cremades2024 with permission from the publisher (Springer Nature).