Neuro - Fuzzy Systems for Intelligent Scienti c Computation

Intelligence has been envisioned as a key component of future problem solving environments for sci-entiic computing. This paper describes a computationally intelligent approach to address a major problem in scientiic computation, i.e., the eecient solution of partial diierential 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 use for the solution of a speciic PDE problem. It achieves this by comparing the characteristics of the given PDE with those of previously observed classes of PDEs. An important step in the reasoning mechanism of PYTHIA is the categorization of PDE 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 pattern classes underlying the domain. In applying the fuzzy min-max network to our domain , we improve the method by relaxing these assumptions. This scheme will form a major component of future problem solving environments for scientiic computing that are being developed by our group.