Equations of state (EoS) for fluids have been a staple of engineering design and practice for over a century. Available EoS are based on the fitting of a closed-form analytical expression to suitable experimental data. The mathematical structure and the underlying physical model significantly restrain the applicability and accuracy of the resulting EoS. This contribution explores the issues surrounding the substitution of machine-learned models for analytical EoS. In particular, we describe, as a proof of concept, the effectiveness of a machine-learned model to replicate the statistical associating fluid theory (SAFT-VR Mie) EoS for pure fluids. To quantify the effectiveness of machine-learning techniques, a large set of pseudodata is obtained from the EoS and used to train the machine-learning models. We employ artificial neural networks and Gaussian process regression to correlate and predict thermodynamic properties such as critical pressure and temperature, vapor pressures, and densities of pure model fluids; these are performed on the basis of molecular descriptors. The comparisons between the machine-learned EoS and the surrogate data set suggest that the proposed approach shows promise as a viable technique for the correlation and prediction of thermophysical properties of fluids.