Unmanned Underwater Vehicles (UUVs) are critical for a variety of societally-important missions such as ocean monitoring, but mission times are constrained by the compute and power constraints on UUVs. We develop a constrained inverse search model that leverages kinematics-to-thrust and kinematics-to-power neural networks to find a set of optimal fin kinematics with the multi-objective goal of reaching a target thrust under power constraints while creating a smooth kinematics transition between flapping cycles. We demonstrate how a control system integrating this model can make online, cycle-to-cycle adjustments to prioritize different system objectives. Implementing inverse search can allow for a reduction in power consumption of 66% for a 0.1 N tradeoff in thrust propulsion, while rigidity improvements can further reduce thrust loss by 74%, and reduce power consumption by 37%