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We report on the use of backpropagation based neural networks to implement a phase of the computational intelligence process of the PYTHIA expert system for supporting the numerical simulation of applications modelled by partial differential equations (PDEs). PYTHIA is an exemplar based reasoning system that provides advice on what method and parameters to use for the simulation of a specified PDE based application. When advice is requested, the characteristics of the given model are matched with the characteristics of previously seen classes of models. The performance of various solution methods on previously seen similar classes of models is then used as a basis for predicting what method to use. Thus, a major step of the reasoning process in PYTHIA involves the analysis and categorization of models into classes of models based on their characteristics. In this study we demonstrate the use of neural networks to identify the class of predefined models whose characteristics match the ones of the specified PDE based application.