This paper presents and develops an alternative empirical methodology to model and get instantaneous derivative functions for nonlinear dynamic systems by a supervised training using multiple step neural numerical integrator of Adams-Bashforth. This approach, neural network plays the role of instantaneous derivative functions and it is coupled to numerical integrator structure, which effectively is the responsible for execute the propagations in time through a linear combination of feedforward neural networks with delayed responses. It is an important fact that only numerical integrators of highest order effectively learn instantaneous derivative functions with sutable precision, which proves the fact that those of first order can only learn mean derivatives. This approach is an alternative to the methodology that deals with the problems of neural modeling in simple step integration structures of high-order Runge-Kutta type, and this, which is more robust and complex in determining the backpropagation, which requires - in this case - the employment of the chain rule for compounded functions. At the end this paper numerical simulation results of Adam-Bashforth neural integrator are presented in three study cases: 1) nonlinear pendulum without variables control; 2) an abstract model with variables control and 3) Van der Pol system.
Multiple Step Neural Networks; Feedforward Nets; High Order Numerical Integrators; Ordinary Differential Equations; Dynamic Systems Neural Modeling; Back-Propagation Algorithm
