Predicting Approximate Governing Formula from Experimental Observations

Abstract

Experiments help in understanding systems. Often experiments are conducted by varying some controllable parameters. The governing mathematical expressions involving the basic parameters may not always be known. This often causes a hindrance in the deep understanding of the experimental observations. In this paper, a method is suggested by which it may be possible to approximately predict the governing formula using the experimental data. Predicting the approximate formula is instrumental in developing appropriate theory and making sense out of the experimental data. The governing formula is predicted by suitable mathematical combination of basic parameters. The use of ‘Simulated Annealing’ optimization method is made to approximately predict the governing formula from the data obtained from experiments. The method seems to be robust and can accommodate various experimental errors (like small instrumental errors, human negligence in some readings). Illustrative examples are given. One of the examples is about beam experiments, wherein it is shown how to approximately predict deflection formula. The suggested methodology holds promise in understanding system behavior from experimental observations.