Problem solving has been defined as higher-order cognitive process. Researchers have investigated problem solving separately in different knowledge domains.
With the focus on problem solving by computers, I characterize in analytic, knowledge-based and data-driven methods, of crucial importance in, say, engineering, applied to products and processes to take corrective actions to prevent failures or more general control risk.
They usually have trade offs in adequateness, accuracy, robustness, performance and economic aspects, like development efforts and resource requirements.
The most elegant models and solvers are often only valid in small domains and simple data-driven methods are resistant to generalizing.
Usually, one needs to find an intelligent combination of the three. The importance of knowledge-based and data-driven methods increases with the amount and complexity of data. R&D concentrates on uniquely combining statistical methods-machine learning-kernel-based techniques with cognitive approaches like fuzzy rule-based methods and we have successfully applied such combinations when controlling processes and their risk.
We have now analyzed and prototyped the new probability and statistical solvers in Mathematica 8, built in statistical distributions, distribution builders and parameter testers and I say, they are amazing.
They will open us new ways of solving even more complex problems in business and finance, process- and manufacturing engineering, energy supply, climate and weather, .. to public management, combining them with our machine learning framework for better analysis, prediction and control. Mlf is Mathematica 8 compatible already.