In this manuscript, a novelty principle driven fiber transmission model for short-distance transmission with parameterized inputs is put forward. By taking into the account of the previously proposed principle driven fiber model, the reduced basis expansion method and transforming the parameterized inputs into parameterized coefficients of the Nonlinear Schrodinger Equations, universal solutions with respect to inputs corresponding to different bit rates can all be obtained without the need of re-training the whole model. This model, once adopted, can have prominent advantages in both computation efficiency and physical background. Besides, this model can still be effectively trained without the needs of transmitted signals collected in advance. Tasks of on-off keying signals with bit rates ranging from 2Gbps to 50Gbps are adopted to demonstrate the fidelity of the model.