Comparison of the response of a time delay neural network with an analytic model

Time-delayed neural networks (TDNNs) can be used to learn the dynamics of an unknown system from input-output data. In many cases a model of the system is also available in the form of a system of ODES, derived either from first principles or using heuristic arguments. In such cases a functional comparison can be made between the dynamic behaviour of the model with that of the trained TDNN for arbitrary inputs. We show that Volterra kernels for both the model system and the TDNN can be obtained, and thus the system responses compared, in a manner that is independent of the input. The techniques of structural bilinearisation of ODES and Volterra series expansion of a TDNN, are demonstrated by application to the Hodgkin-Huxley set of equations.