Development of a Helmholtz free energy equation of state for fluid and solid phases via artificial neural networks

A longstanding challenge in thermodynamics has been the development of a unified analytical expression for the free energy of matter capable of describing all thermodynamic properties. Although significant strides have been made in modeling fluid phases using continuous equations of state (EoSs), the crystalline state has remained largely unexplored because of its complexity. This work introduces an approach that employs artificial neural networks to construct an EoS directly from comprehensive molecular simulation data. The efficacy of this method is demonstrated through application to the Mie potential, resulting in a thermodynamically consistent model seamlessly bridging fluid and crystalline phases. The proposed EoS accurately predicts metastable regions, enabling a comprehensive characterization of the phase diagram, which includes the critical and triple points.