Neural Modeling With Guaranteed Input-Output Probability Distributions

Neural networks (NNs) are effective models for data-driven system identification. However, these data-based models do not give the probability properties of the system. Is it possible to use NNs to learn both the dynamics and input-output probability distributions to improve the modeling? In this article, we propose a special neural model, which combines the restricted Boltzmann machine (RBM) and the feedforward NNs. The stochastic RBM learns the input-output probability distributions. The feedforward NN learns the dynamics of nonlinear systems. For the input-output probability distributions, we give the calculation methods of their conditional and joint probabilities. The approximation abilities of this neural model are analyzed. We use two nonlinear systems to compare our guaranteed probability distribution method with the other black-box identification methods. The results show that this novel model is much better, when there are big noises and the dynamics of the system are complex.