Reconstructing nonlinear dynamical systems by neural network residual minimization method

A new neural network residual minimization training method for empirically reconstruction of dynamical systems has been proposed. An unknown dynamical system is expressed as a set of first order ordinary differential equations. An algorithm for training neural network over wider assimilation window is employed. The performance of the method is examined over prediction periods by applying it to the chaotic Lorenz model. A considerable improvement in prediction skill is obtained over the conventional methods. Its application to data from the real climate system is in progress.