NEURAL NETWORKS AS TOOLS TO SOLVE PROBLEMS IN PHYSICS AND CHEMISTRY

Application of the neural network methods to problems in physics and chemistry has rapidly pined popularity in recent years. We show here that for many applications the standard methods of data fitting and approximation techniques are much better than neural networks in the sense of giving more accurate results with a lower number of adjustable parameters. Learning in neural networks is identified with the reconstruction of hypersurfaces based on a knowledge of sample points and generalization with interpolation. Neural networks use sigmoidal functions for these reconstructions, giving for most physics and chemistry problems results far from optimal. An arbitrary data fitting problem may be solved using a single-layer network architecture provided that there is no restriction on the type of functions performed by the processing elements. A simple example illustrating unreliability of interpolation and extrapolation by the typical backpropagation neural network learning of a smooth function is presented. Some results from approximation theory are quoted giving a rigorous foundation to applications requiring correlation of numerical results with a set of parameters.