Neuro-Fuzzy Systems for Intelligent Scientific Computation

Ab3tract Intelligence has been envisioned as a. key component of future problem solving environments for scientific compuling. This paper describes a computationally intelligent approach to address a major problem in scientific computation i.e., the efficient solution of partial differential equations (PDEs). This approach is implemented in PYTHIA-a system that supports smart parallel PDE solvers. PYTHIA provides advice on what method and parameters to usc for the solution of a specific PDE problem. It achieves this by comparing the characteristics of the given PDE with those of previously observed classes or PDEs. An important step in the reasoning mechanism or PYTHIA is the categorization of pnE problems into classes based on their characteristics. Exemplar based reasoning systems and backpropagation style neural networks have been earlier used to this end. In this paper, we describe the use of fuzzy min-max neural networks to realize the same objective. This method converges faster, is more accurate, generalizes very well and provides on-line adaptation. This technique makes certain assumptions about the paltern classes underlying the domain. In applying the fuzzy min-max uetwork to our domain, we improve the method by relaxing these assumptious. This scheme will rorm a. major component of future problem solving environments for scientific computing that are being developed by our group.