Explicit-model exploring framework integrating thermodynamic principles and interpretable machine learning in predicting gaseous speed of sound

The speed of sound is a key thermodynamic property widely used across various energy utilization applications. However, current universal models struggle to accurately predict the gaseous speed of sound in gaseous high-density regions, while data-driven machine-learning methods often lack physical interpretation, causing research limitations and engineering risks. In this work, an explicit-model exploring platform is proposed, which interpretably combines thermodynamic principles and machine learning. Based on a robust physical foundation of the virial equation of state and a small set of representative high-precision experimental data, two universal explicit prediction models are explored. These models exhibit relative root-mean-square deviations of only 0.23 % or 0.30 % when predicting 7688 experimental sound-speed values for 37 fluids within the entire approximate gaseous region, up to 3 times the critical temperature and pressure. Notably, the prediction deviations in dense gas regions, such as near-critical and near-saturation zones, are reduced by approximately 70 % compared to state-of-the-art models. The models' key terms and parameters are analyzed, revealing their interpretability across different thermodynamic regions and fluid properties, as well as offering insights into the contact among mathematical models, thermophysical laws, and molecular interactions. This work indicates a promising new approach to develop thermodynamic models and further provide valuable tools for thermodynamic analyses in energy systems, reducing the need of extensive experimental efforts. Furthermore, this approach serves as an attempt to interpret the 'black-box' of machine learning, offering fresh perspectives for future research in thermodynamic fields.