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A new technique is proposed here to represent the thermodynamic surface of a pure fluid in the fundamental Helmholtz energy form. The peculiarity of the present method is the extension of a generic equation of state for the target fluid, which is assumed as the basic equation, through the distortion of its independent variables by individual shape functions, which are represented by a neural network used as function approximator. The basic equation of state for the target fluid can have the simple functional form of a cubic equation, as, for instance, the Soave-Redlich-Kwong equation assumed in the present study. A set of nine fluids including hydrocarbons, haloalkane refrigerants, and strongly polar substances has been considered. For each of them the model has been regressed and then validated against volumetric and caloric properties generated in the vapor, liquid, and supercritical regions from highly accurate dedicated equations of state. In comparison with the underlying cubic equation of state, the prediction accuracy is improved by a factor between 10 and 100, depending on the property and on the region. It has been verified that about 100 density experimental points, together with from 10 to 20 coexistence data, are sufficient to guarantee high prediction accuracy for different thermodynamic properties. The method is a promising modeling technique for the heuristic development of multiparameter dedicated equations of state from experimental data. KEY WORDS: cubic equation of state; extended equation of state; feed forward neural network; fundamental equation of state; Helmholtz energy equation; pure fluids; thermodynamic properties.