Mathematical modeling ANNs-based

Narang A, Subramanian KK, Lauffenburger DA. A mathematical model for chemoattractant gradient sensing based on receptor-regulated membrane phospholipid signaling dynamics. Ann. Bio-med. Eng. 2001 29 677-691. 

The study for predicting the velocity profiles in pultrusion by Gorthala et aL (1994) used a variable viscosity model. A comprehensive two-dimensional mathematical model in cylindrical coordinates was developed for resin flow, cure and heat transfer. A control-volume-based finite difference method (FDM) (Patankar method) was used for solving the governing equations. The use of artificial neural networks (ANNs) for pultrusion modelling in terms of the real process data and their potential for intelligent machine control was proposed by Wilcox and Wright (1998). Liu et al. (2000 Liu, 2001 Liu and Hillier, 1999) implemented a finite element/control volume... 

Parameters previously tested do have their own numerical representation, but there are SOFC features that either cannot to be expressed in numerical form or can only be expressed with great difficulty, i.e. electrolyte material, anode material, cathode material, cell type (planar, tubular), etc. In those situations a hybrid model can be applied which consists of the ANN model and additional mathematical expressions (hybrid model means a combination of known relationships and an ANN-based model). For instance, there are two options for accommodating the material type of electrolyte in an ANN-based model ... 

The next step was to produce rank ordered lists of the sites based on their suitability for locating clothing production sites. Although we can refer the classification of the chosen sites to the experts by questionnaire, the multi-attribute utility (MAU) model, a traditional systematic model for scoring, is more suitable for dealing with this classification problem, which will be utilized to benchmark the relative performance of the proposed ANN classification decision model. The MAU model can be mathematically stated as follows ... 

ANNs are mathematical methods based on the transfer of information through a network of functional imits, called neurons. The model is built up from the experimental data presented, which is assumed to contain the information necessary to establish the neural model [2]. 

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