Development of thermodynamically consistent machine-learning equations of state: Application to the Mie fluid

Gustavo Chaparro; Erich A Müller

doi:10.1063/5.0146634

Development of thermodynamically consistent machine-learning equations of state: Application to the Mie fluid

J Chem Phys. 2023 May 14;158(18):184505. doi: 10.1063/5.0146634.

Authors

Gustavo Chaparro¹, Erich A Müller¹

Affiliation

¹ Department of Chemical Engineering, Sargent Centre for Process Systems Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom.

PMID: 37161943
DOI: 10.1063/5.0146634

Abstract

A procedure for deriving thermodynamically consistent data-driven equations of state (EoS) for fluids is presented. The method is based on fitting the Helmholtz free energy using artificial neural networks to obtain a closed-form relationship between the thermophysical properties of fluids (FE-ANN EoS). As a proof-of-concept, an FE-ANN EoS is developed for the Mie fluids, starting from a database obtained by classical molecular dynamics simulations. The FE-ANN EoS is trained using first- (pressure and internal energy) and second-order (e.g., heat capacities, Joule-Thomson coefficients) derivative data. Additional constraints ensure that the data-driven model fulfills thermodynamically consistent limits and behavior. The results for the FE-ANN EoS are shown to be as accurate as the best available analytical model while being developed in a fraction of the time. The robustness of the "digital" equation of state is exemplified by computing physical behavior it has not been trained on, for example, fluid phase equilibria. Furthermore, the model's internal consistency is successfully assessed using Brown's characteristic curves.