In the past decades, representation models of dynamical processes have been developed via both traditional math-analytical and  less traditional computational-intelligence approaches.  This challenge to system sciences goes on because essentially involves the mathematical approximation theory.  A comparison study based on cybernetic input-output view in the time domain on complex dynamical processes has been carried out.  An analytical decomposition representation of complex multi-input-multi-output thermal processes is set relative to the neural-network approximation representations, and shown that theoretical  background of both emanates from Kolmogorov's theorem. The findings provided a new insight as well as highlighted the efficiency and robustness of fairly simple industrial digital controls, designed and implemented in the past, inherited from input- output decomposition model approximation employed.