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The last few decades have led to the rise of research focused on propulsion and control systems for bio-inspired unmanned underwater vehicles (UUVs), which provide more maneuverable alternatives to traditional UUVs in underwater missions. Recent work has explored the use of time-series neural network surrogate models to predict thrust and power from vehicle design and fin kinematics. We expand upon this work, creating new forward neural network models that encapsulate the effects of the material stiffness of the fin on its kinematic performance, thrust, and power, and are able to interpolate to the full spectrum of kinematic gaits for each material. Notably, we demonstrate through testing of holdout data that our developed forward models capture the thrust and power associated with each set of parameters with high resolution, enabling highly accurate predictions of previously unseen gaits and thrust and FOM gains through proper materials and kinematics selection. As propulsive efficiency is of utmost importance for flapping-fin UUVs in order to extend their range and endurance for essential operations, a non-dimensional figure of merit (FOM), derived from measures of propulsive efficiency, is used to evaluate different fin designs and kinematics and allow for comparison with other bio-inspired platforms. We use the developed FOM to analyze optimal gaits and compare the performance between different fin materials. The forward model demonstrates the ability to capture the highest thrust and FOM with good precision, which enables us to improve thrust generation by 83.89% and efficiency by 137.58% with proper fin stiffness and kinematics selection, allowing us to improve material selection for bio-inspired fin design.