Bulg. J. Phys. vol.33 no.s3 (2006), pp. 034-51

Experimental Modelling of Physical Laws

I. Grabec
Faculty of Mechanical Engineering, University of Ljubljana, Sl-1000, Ljubljana, Slovenia
Abstract. Experimental modelling of physical laws starts with a statistical estimation of the probability density function (PDF) of measured variables. This function is expressed by an estimator whose kernel is the instrument scattering function. Experimental information and redundancy of observation are defined in terms of information entropy. The redundancy increases logarithmically with the number of acquired data, while the experimental information converges to a limit value that determines the complexity of the phenomenon. The model cost function is defined by the difference of the redundancy and the experimental information. The proper number of data utilized in the experimental modelling of the PDF is estimated from the minimum of the cost function. In a two-dimensional case the marginal and conditional PDFs are extracted from the estimated joint PDF and applied in the definition of the mutual information. As an optimal estimator of a physical law that relates measured variables the conditional average is derived. It represents a non-parametric regression that is generally applicable in modelling of natural laws. The analysis of its properties is based on a new definition of prediction quality. The experimental modelling is especially applicable in the description of complex phenomena taking place in physical, technical, and medical environments.

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