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In this paper, a novel robust, compact, and flexible neural-network model for a fiber Raman amplifier (FRA) is presented. The model can be used in various applications with promising accuracy and low requirement for memory. Analytical expressions are derived in order to make the optimal pump-power configuration much easier, and the computational time is reduced dramatically in comparison with other gain-design methods in real-time pump-power adjustment. The calculated on-off gain spectrum and the noise figure using the proposed model agree well with the experimental results. The model has a potential value in simulation and pump-power dynamic control.