A neural-fuzzy technique for interpolating spatial data via the use of learning curve
In this paper, we present a new and simple method for function interpolation based on the use of neural networks and fuzzy logic. We particularly discuss the application of the technique in spatial data analysis. In this application domain, conventional early-stopping criteria to avoid over-training in neural networks based on the use of minimum error on validation set, may not be suitable. In the proposed method, we use “interpolated error” to stop training. The trained networks are used as fuzzy rules, and these rules are interpolated to the location of interest. We demonstrate the methodology in petroleum reservoir modelling in which properties are estimated between two oil wells. Data from a third well, which are withheld from the training process, is used to evaluate different prediction models. We also compare our method with the recent data-splitting approach using self-organising map (SOM) with the use of early-stopping in neural training. The results of this study show that the SOM approach is only applicable to wells in which their locations are half-way between the two given wells. The proposed methodology, however, provides the best results in the test well and is also suitable for any location of interest. The end result is a simple and computationally-cheap method in engineering studies.
KeywordsNeural Fuzzy Interpolation Spatial Data Well Logs
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