Acoustic mode decomposition is used for evaluating the damping of aircraft liners and, in general, to investigate acoustic scattering in flow ducts. Classical methods rely on analytical solutions of the wave properties and accept uncertainties due to simplified descriptions of the duct flow. In contrast, the current study provides a wave decomposition method that does not require explicit analytical knowledge of the wave properties and registers a wide range of flow-related acoustic phenomena. A multilayer perceptron artificial neural network is trained to learn acoustic wave decomposition for plane-wave-like duct modes. Training data are the numerical solutions of the Linearized Navier-Stokes Equations, from which the network not only learns the wave motion properties but also the dispersion of sound into the fluid flow. The network can account for flow-related effects, such as turbulent attenuation, refraction, convection, and thermo-viscous dissipation, which are only included in the classical models based on simplifications. The new method is validated for plane-waves against analytical data and experiments. It is demonstrated that the network can mimic the classical solutions accurately when trained under the same flow simplifications. In addition, it can cope with complex flow effects, such as turbulent attenuation, by including them in the training data. Therefore, the proposed wave decomposition complements the classical plane-wave decomposition when investigating in-duct sound with complex flow conditions. An important continuation of this work is to extend the new wave decomposition method to multi-modal sound fields. As the first step in this direction, it is demonstrated that the proposed training scheme also works for higher-order modes.