Neural numerical modeling for uncertain distributed parameter systems

In this paper a strategy based on differential neural networks for the identification of the parameters in a mathematical model described by partial differential equations is proposed. The identification problem is reduced to finding an exact expression for the weights dynamics using the differential neural networks properties. The adaptive laws for weights ensure the convergence of the neural network trajectories to the partial differential equation states. To investigate the qualitative behavior of the suggested methodology, here the non-parametric modeling problem for a distributed parameter plant is analyzed: the tubular reactor system.