Why can't equations of state be replaced by machine learning models?
For n data points there exists an n-1 order polynomial that perfectly fits the data. 

Therefore there is no basis for "a neural network or whatever" being better.

Furthermore, it simply isn't true that the Peng-Robinson equation "has no underlying physical meaning".  

The Peng-Robinson equation (like Van der Waals) recognizes that atoms/molecules occupy space and that attractive forces exist between them.  

As Peng and Robinson say in their article:


  Since two-constant equations have their inherent limitations,
  and the equation obtained in this study is no exception,
  the justification for the new equation is the compromise
  of its simplicity and accuracy.


That being said, neural networks have been used to find equations of states.  See for example Equation of state and artificial neural network to predict the thermodynamic properties of pure and mixture of liquid alkali metals 


  Generally, ANN is powerful and successful method for complex non-linear systems due to unique advantages such as high speed, simplicity and large capacity which reduce engineering attempt. In recent years, ANN modeling has been successfully used for prediction of thermophysical properties of pure and mixture fluids [24], [25], [26] and [27].