Robust no parametric identifier for a class of complex partial differential equations

In this chapter a strategy based on differential neural networks (DNN) for the identification of a class of models described by partial differential equation with a complex-valued state is proposed. The identification problem is reduced to finding an exact expression for the weights dynamics using the DNNs properties. In this case, the DNN can be viewed as two coupled networks where one of them reproduces the real part of the complex valued equation and the other provides the identification of the imaginary part, where each stimated state is a complex valued state. The adaptive laws for complex weights ensure the convergence of the DNN trajectories to the PDE complex-valued states. To investigate the qualitative behavior of the suggested methodology, here the non parametric modeling problemfor two distributed parameter plants is analyzed: the Scḧodinger and Ginzburg-Landau equations.