Soft robots have shown immense promise in settings where they can leverage dynamic control of their entire bodies. However, effective dynamic shape control requires a controller that accounts for the robot's high-dimensional dynamics, can work in an underactuated setting, and can take into account the robots dynamic environment and unique soft-material characteristics. The digital twin paradigm offers a perfect setting to achieve this. In this talk, we first introduce our physical platform, an anguilloform swimmer with antagonistic fluid elastomer actuators for dynamic shape control. We then discuss the construction of the prototype digital twin via the SOFA modeling environment and high-fidelity nonlinear finite element modeling [1]. While accurate, this model is not practical for real-time control. We therefore compare data-driven model reduction techniques for generating linear models amendable to fast online model-predictive control. We specifically cover three methods: the eigensystem realization algorithm, dynamic mode decomposition with control, and the Lagrangian operator inference (LOpInf) method [2], which takes into account the second-order nature of the mechanics. Using each class of model, we explore their efficacy in model predictive control policies for the dynamic shape control of a simulated eel-inspired soft robot in three experiments: 1) tracking simulated reference trajectories guaranteed to be feasible, 2) tracking reference trajectories generated from a biological model of eel kinematics, and 3) tracking reference trajectories generated by a reduced-scale analog of our physical twin. In all experiments, the LOpInf-based policies generated lower tracking errors than policies based on other models. This work shows a first step towards digital twins for soft robot control, and we point out avenues of improvement and ongoing work.