Practical engineering prediction models for flow-induced vibration are needed in the design of structures in the ocean. Research has shown that structural vibration response may be influenced by a large number of physical input parameters, such as damping and Reynolds number. Practical response prediction tools used in design are inevitably a compromise between complexity and simplicity of use. Modern machine learning tools may be used to identify which input parameters are most important. Standard machine learning techniques enable the researcher to compile a list of the most important input parameters, ranked or ordered by the effect of each on the prediction error of the model. When all inputs are treated as equals, blind application of machine learning may lead to predictions that are inconsistent with prior physical knowledge. To address this problem, we conducted a parameter selection process using a prior knowledge-based, trend-informed neural network architecture. This approach was used to identify features important to the prediction of the cross-flow vibration response amplitude of long flexible cylinders, given the known prior effect of Reynolds number and damping. The model balances the usual goal of minimizing the model prediction error, but doing so in a manner that closely follows the extensive knowledge we have of the influence of Reynolds number and damping parameter on response. The resulting neural network model was able to reveal additional insights, including the role of mode number shifting, mode dominance and travelling waves in the regulation of VIV response amplitude.