Formula predicting outcomes

A model is one of the main outcomes of ary scientific enquiry and hence is a major contributor to philosophy of science. A model may be defined as a simplified representation of a phenomenon (an object, system, event, process) or idea produced for the specific purpose of providing an explanation of that entity, the most important outcomes of which are the production of successful predictions of how it will behave under a range of circumstances (Gilbert, Boulter, Elmer, 2000). Entities can be modelled at the three levels at the macroscopic, by representing some of the aspects of the entity that can be seen at the sub-microscopic, by representing the ideas produced to explain the constitution and behaviour of the particles that constitute the entity and at the symbolic, by representing the symbols created to simplify the reference to such particles (as, for instance, chemical formulae and chemical equations). 

Two alternatives would seem to be open in the discussion of this subject. An exhaustive account of known gelling behavior would inevitably result in a technical bias. On the other hand, it should be possible to emphasize the principles, and to illustrate the limits of present understanding by chosen examples. The choice has been made reluctantly, because both types of discussion would be timely, but it would seem more sensible to marshal our ideas about the basis of gel formation before attempting to tabulate and organize the sum of factual knowledge. The present article is written from the viewpoint of the structural chemist who wishes to see how the overall properties of the gel are an outcome of molecular structure, and who would rather have a qualitative understanding in these terms than a physical or mathematical model which, even if capable of predictions with high precision, did not start from the molecular formula. ... 

Loose modelling techniques (discussed in Chapter 2) tend to provide synthesis parameters that bear little relation to the acoustic world. They are usually based entirely upon conceptual mathematical formulae. It is often difficult to predict the outcome and to explore the potential of a loose model. Frequency modulation (FM) is a typical example of loose modelling. FM is a powerful technique and extremely easy to program but difficult to operate computer simulations of Yamaha s acclaimed DX7 synthesiser, for example, are relatively easy to implement on a computer. Nevertheless, it is apparent that the relationship between a timbre and its respective synthesis parameters is far from intuitive. Apart from John Chowning, the inventor of FM synthesis, only a few people have managed to master the operation of this technique. 

Like regression, although the most popular firing criterion for ANNs is minimisation of the squared errors, individual values rather than their sums are estimated. ANNs are applicable in any situation where there is an unknown relationship between a set of input factors and an outcome for which a representative set of historical examples of this unknown mapping is available. The objective of building an ANN model is to find a formula or program that facilitates predicting the outcome from the input factors. 

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