A physically interpretable machine-learning method in efficiently and explicitly exploring predictive thermodynamic models for mixture working fluids

Mixture working fluids are key energy carriers in emerging energy and power systems. The speed of sound and its derived properties underpin thermodynamic analysis and flow-related-component design. However, traditional semi-empirical modeling methods struggle to characterize speed of sound that contains thermodynamic differential relationships, while merely data-driven machine-learning approaches also fall short for mixture properties with diverse physical constraints, causing narrow applicability in current sound-speed mixing models. This work attempts to develop a data-to-function machine-learning method with physical guidance, where mixture-related thermodynamic constraints are embedded into the symbolic regression framework in several aspects, forming a comprehensive model-exploration workflow and visually algebraic statistical mechanism. Taking the ideal mixing rule as a baseline and regularized thermodynamic parameters as algebraic elements, the nonpolar and polar characteristics were described stepwise by the symbolic regression algorithm based on limited experimental data, and a universally predictive mixing model is established for commonly used or highly potential mixture working fluids. The model only relies on basic physical parameters and exhibits a relative root mean square deviation of only 0.3 % in predicting 2552 experimental data points of 17 pairs of mixtures across a wide quasi-gaseous region. Notably, the prediction deviations are reduced by 1∼2 orders of magnitude compared to existing universal mixing models in high-density gaseous regions, indicating significant expansion of the available range. The mathematical robustness, physical significance, and error controllability of the model are quantitatively analyzed, supporting the extrapolation to mixtures or thermodynamic regions beyond the training range and verifying some inaccurate data. Taking the speed of sound as the example, the proposed method reveals the usability of interpretable machine learning in explicit modeling of thermodynamic properties for mixtures, forming a new research perspective that can be applied to other similar properties. The results can provide data and modeling techniques for conveniently characterizing thermodynamic properties for new mixture working fluids, thus supporting reliable thermodynamic analysis in pre-studies of novel thermodynamic cycles.