Methodology of Recurrent Laguerre-Volterra Network for Modeling Nonlinear Dynamic Systems

In this paper, we have introduced a general modeling approach for dynamic nonlinear systems that utilizes a variant of the simulated annealing algorithm for training the Laguerre-Volterra network (LVN) to overcome the local minima and convergence problems and employs a pruning technique to achieve sparse LVN representations with l(1) regularization. We tested this new approach with computer simulated systems and extended it to autoregressive sparse LVN (ASLVN) model structures that are suitable for input-output modeling of nonlinear systems that exhibit transitions in dynamic states, such as the Hodgkin-Huxley (H-H) equations of neuronal firing. Application of the proposed ASLVN to the H-H equations yields a more parsimonious input-output model with improved predictive capability that is amenable to more insightful physiological/biological interpretation.