Task-driven design of soft robots requires models that are physically accurate and computationally efficient, while remaining transferable across actuator designs and task scenarios. However, existing modeling approaches typically face a fundamental trade-off between physical fidelity and computational efficiency, which limits model reuse across design and task variations and constrains scalable task-driven optimization. This paper presents a unified reduced-order finite element method (FEM)-based surrogate modeling pipeline for generalized task-driven soft robot design. High-fidelity FEM simulations characterize actuator behavior at the modular level, from which compact surrogate joint models are constructed for evaluation within a pseudo-rigid body model (PRBM). A meta-model maps actuator design parameters to surrogate representations, enabling rapid instantiation across a parameterized actuator family. The resulting models are embedded into a PRBM-based simulation environment, supporting task-level simulation and optimization under realistic physical constraints. The proposed pipeline is validated through sim-to-real transfer across multiple actuator types, including bellow-type pneumatic actuators and a tendon-driven soft finger, as well as two task-driven design studies: soft gripper co-design via Reinforcement Learning (RL) and 3D actuator shape matching via evolutionary optimization. The results demonstrate high accuracy, efficiency, and reliable reuse, providing a scalable foundation for autonomous task-driven soft robot design.

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