Minimal model dimension/order determination algorithms for recurrent neural networks

This paper focuses on the development of model dimension/order determination algorithms for determining minimal dimensions/orders of recurrent neural networks using only input–output measurements of unknown systems. We present two types of model dimension/order determination approaches. The first type is named all-in-one strategy that includes the minimum description length (MDL) principle and the eigensystem realization algorithm (ERA). This type is capable of identifying the model dimension/order and model parameters simultaneously. The other type is named divide-and-conquer strategy that includes the Lipschitz quotients and false nearest neighbors (FNN). This type usually requires additional parameter optimization algorithms to estimate the model parameters for closely emulating the dynamic behavior of unknown systems. The effectiveness of these four algorithms has been validated through nonlinear dynamic system identification examples. In addition, we provide performance comparisons and discussion on the characteristics of these four algorithms as method-selection guidelines.