Identifying regions of importance in wall-bounded turbulence through explainable deep learning (2302.01250v4)

Abstract: Despite its great scientific and technological importance, wall-bounded turbulence is an unresolved problem in classical physics that requires new perspectives to be tackled. One of the key strategies has been to study interactions among the energy-containing coherent structures in the flow. Such interactions are explored in this study for the first time using an explainable deep-learning method. The instantaneous velocity field obtained from a turbulent channel flow simulation is used to predict the velocity field in time through a U-net architecture. Based on the predicted flow, we assess the importance of each structure for this prediction using the game-theoretic algorithm of SHapley Additive exPlanations (SHAP). This work provides results in agreement with previous observations in the literature and extends them by revealing that the most important structures in the flow are not necessarily the ones with the highest contribution to the Reynolds shear stress. We also apply the method to an experimental database, where we can identify completely new structures based on their importance score. This framework has the potential to shed light on numerous fundamental phenomena of wall-bounded turbulence, including novel strategies for flow control.

• The paper introduces an explainable deep learning framework that uses U-net and SHAP to identify key turbulent structures with a 2% prediction error.
• It finds that wall-attached ejections are the most impactful, while smaller structures show greater relative significance per unit volume.
• The study extends the methodology to experimental datasets, highlighting its potential to enhance turbulence modeling and control strategies.

An Examination of the Role of Explainable Deep Learning in Understanding Wall-Bounded Turbulence

The paper "Identifying regions of importance in wall-bounded turbulence through explainable deep learning" proposes a novel methodological framework that combines deep learning with explainable AI techniques to better understand the dynamics of wall-bounded turbulence—a persistently challenging problem in fluid dynamics. By leveraging a deep learning architecture known as U-net, alongside the game-theoretic SHAP (SHapley Additive exPlanations) values, the research investigates the importance of coherent structures in turbulent flow dynamics.

Methodological Approach

The paper utilizes a U-net deep learning model, trained on high-fidelity direct numerical simulation (DNS) data of turbulent channel flows, to predict future states of the flow fields. This capability allows the researchers to assess the predictive importance of coherent structures within the turbulence. The model’s predictions, validated with a low error margin of 2% against test data, demonstrate the efficacy of U-nets in capturing complex spatial dependencies in turbulence.

By applying SHAP to the trained U-net model, the authors provide a means of explaining the impact of each identified flow structure on the model’s predictions. SHAP values serve to quantify the marginal contribution of individual structures to the prediction error reduction, offering a novel and objective metric for assessing the significance of turbulent structures.

Key Findings

The paper’s application of SHAP analysis reveals several important findings. Despite traditional measures emphasizing the contribution of structures to Reynolds shear stress, the results show that the most predictive (i.e., impactful) structures as measured by SHAP values are not necessarily those contributing most to Reynolds shear stress. Specifically, it was identified that wall-attached ejections have the highest importance score for predictions, though when measured per unit volume, smaller structures often exhibit greater relative significance.

The research extends these methods to experimental datasets, highlighting their potential applicability beyond numerical simulations. The analysis across different Reynolds numbers reveals that the importance of structures such as sweeps tends to increase with higher Reynolds numbers, noting an agreement with prior empirical findings.

Implications and Future Perspectives

The methodologies outlined provide a fresh lens through which to evaluate the dynamics of wall-bounded turbulence, pushing beyond mere statistical association toward a more causal understanding of flow structures. This framework offers possibilities for improving turbulence modeling and advancing control strategies in fluid dynamics applications. Notably, the usage of SHAP within this context could bear significant implications for enhancing data-driven subgrid-scale models and facilitating turbulence control strategies that can be economically beneficial in various engineering scenarios.

Looking ahead, the authors suggest that the insights gathered using this framework can play a vital role in more practical high-Reynolds-number experiments and applications. The extended framework's application to experimental datasets demonstrates its utility in less ideal conditions, suggesting broader domains of applicability, including areas where traditional DNS data is not feasible.

Conclusion

By integrating explainable AI techniques into deep learning models for turbulence simulation, this paper advances both theoretical and applied fluid dynamics. It sets a precedent for interpreting complex machine learning models in physics-based applications, showing how a nuanced understanding of coherence in turbulent structures can lead to optimized flow prediction and control strategies. Future research might further explore the methodologies introduced, deepening our understanding and expanding their practical utility in diverse fluid dynamics applications.