Developing empirical indices for structural engineering problems via machine learning

The rapid expansion of data availability in engineering disciplines has catalyzed the integration of machine learning (ML) to tackle complex problems. Despite the transformative potential of ML, its opaque nature poses significant challenges for engineers. This paper presents the development of empirical indices to bridge the gap between ML-driven insights and traditional engineering theory/domain knowledge by converting high-dimensional ML insights into interpretable, low-dimensional indices that retain predictive rigor. We explore several methodologies for creating empirical indices, including pure data-driven analysis, non-dimensional analysis, statistical analysis, and large language models (i.e., ChatGPT). Through detailed case studies, we demonstrate the application of these methods to various engineering phenomena. In addition, this study investigates strategies for handling different data types, threshold-based identification, and discusses the criteria for including interactions and higher-order terms in indices. Our findings demonstrate that empirically derived indices can achieve comparable performance to observed experimental results and complex ML models while maintaining interpretability and theoretical consistency. • ML's potential in engineering is transforming complex problem-solving, yet its black-box nature poses challenges. • Empirical indices bridge ML insights with engineering theory by converting complex data to simpler metrics. • Multiple methods like data, nondimensional, statistical analysis and ChatGPT are explored to create empirical indices. • Results show empirical indices match ML models while keeping interpretability and theoretical alignment.