Explainability, Robustness and Sensitivity of Clustering Algorithms in Scientific Machine Learning: Applications in Turbulence Modeling

Scientific machine learning (SciML) has become increasingly significant across diverse scientific domains, including those vital for National Security missions. Using a comprehensive framework, this study assesses SciML credibility in turbulence modeling, including data provenance, domain knowledge, explainability, code correctness, validation and UQ. Clustering algorithms are used to classify data from Direct Numerical Simulation (DNS) of turbulent flows into distinct physical regimes, which is useful for turbulence model development. The goal is to identify optimal features and clusters. A rigorous sensitivity analysis is conducted, encompassing various noise levels to assess algorithmic performance and understand algorithmic behavior. Notably, the algorithm exhibits remarkable robustness under locally scaled noise. The study also investigates the impact of synthesized data on dataset categorization, revealing consistent clustering behavior with minimal deviations. Also, the study transposes the identified clusters to a subset of impinging jet DNS data, and classifies feature vectors using Gaussian Mixture Models. The results demonstrate the effectiveness of the clustering algorithm across different radial locations and noise levels. This systematic and comprehensive investigation advances the assessment of credibility in computational simulations involving SciML, offering valuable insights for turbulence modeling and impinging jet data applications. This work is supported by the DOE-NNSA ASC program.