Neural Computation
Nonlinear black-box modeling in system identification: a unified overview
Automatica (Journal of IFAC) - Special issue on trends in system identification
How to be a gray box: dynamic semi-physical modeling
Neural Networks
Neural Networks - 2003 Special issue: Neural network analysis of complex scientific data: Astronomy and geosciences
Neural Networks - 2006 special issue: Earth sciences and environmental applications of computational intelligence
Neural Networks - 2006 special issue: Earth sciences and environmental applications of computational intelligence
Universal approximation bounds for superpositions of a sigmoidal function
IEEE Transactions on Information Theory
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This paper deals with the design methodology of an Inverse Neural Network (INN) model. The basic idea is to carry out a semi-physical model gathering two types of information: the a priori knowledge of the deterministic rules which govern the studied system and the observation of the actual conduct of this system obtained from experimental data. This hybrid model is elaborated by being inspired by the mechanisms of a neuromimetic network whose structure is constrained by the discrete reverse-time state-space equations. In order to validate the approach, some tests are performed on two dynamic models. The first suggested model is a dynamic system characterized by an unspecified r-order Ordinary Differential Equation (ODE). The second one concerns in particular the mass balance equation for a dispersion phenomenon governed by a Partial Differential Equation (PDE) discretized on a basic mesh. The performances are numerically analyzed in terms of generalization, regularization and training effort.