Inversion of a semi-physical ode model

Abstract: This study proposes to examine the design methodology and the performances of an inverse dynamic model by fusion of statistical training and deterministic modeling. We carry out an inverse semi-physical model using a recurrent neural network and illustrate it on a didactic example. This technique leads to the realization of a neural network inverse problem solver (NNIPS). In the first step, the network is designed by a discrete reverse-time state form of the direct model. The performances in terms of generalization, regularization and training effort are highlighted in comparison with the number of weights needed to estimate the neural network. Finally, some tests are carried out on a simple second order model, but we suggest the form of a dynamic system characterized by an ordinary differential equation (ODE) of an unspecified r order.