Data mining methods applied to numerical approximations analysis of partial differential equations

Classical results analysis of numerical methods is very often limited to the description of tables or graphs of isovalues. This treatment of this "low level" analysis results from the enormous mass of data to be analyzed by inappropriate tools. Our purpose is to suggest a new methodology for numerical data analysis, based on exploratory data mining techniques that have proved in other areas like in biology, medicine, marketing, advertising and communications, all producing "bulimic" data. The principle of the method is based on the constitution of databases of the entire information produced by numerical approximation of mathematical models to assess and to compare the significant differences of performance by the help of techniques like decision trees, Kohonen cards, or neural networks.