Layered feedforward neural network is relevant to empirical physical formula construction: A theoretical analysis and some simulation results

Abstract

We theoretically establish that, contrary to superficial observation, constructing an empirical physical formula (or physical law interchangeably) to explain the physical phenomenon is inherently full with several serious obstacles. We theoretically show that an appropriate layered feedforward neural network (LFNN) is relevant to overcome significantly these obstacles. To this purpose, we first form a five element set of obstacles pertaining to the empirical physical formula construction. Second, we show that a suitably chosen LFNN can overcome each of the five obstacles, because the LFNN arbitrarily accurately estimates the unknown empirical physical formula whether the experimental variables are deterministic or probabilistic. To offer a general approach, we treat the LFNN that uses the non-parametric method of sieves estimation. The method allows one to increase properly the number of hidden neurons with growing sample size. Finally, to support our theory, we present some simulation LFNN results with large sample size. Here we use artificial rather than real data simply in order not to prefer any specific physical equation.