Abstract: Two applications of neural networks on inverse problems are discussed: determination of the initial temperature profile on a slab with adiabatic boundary condition; and an application as a new method for meterological data assimilation. In the thermal science example two different neural networks have been applied: backpropagation and radial basis functions (RBF). For the second application, multilayered perceptrons neural networks are used for data assimilation in strongly non-linear system: Lorenz chaotic system, and one-dimensional shallow-water meteorological equations. Preliminar results are shown and discussed.