Data-Driven and Physics-Informed Modeling Perspectives for Soft Manipulators: From SINDy to Hybrid Intelligence.

Soft manipulators offer a route to safer, more adaptive and physically intelligent robots, but their compliant bodies remain difficult to model, predict and control. Large deformation, distributed actuation, hysteresis, material variability and contact-rich interaction challenge both classical mechanics-based models and purely data-driven approaches. Here, we examine emerging modeling perspectives for soft manipulators through a conceptual progression from sparse identification of nonlinear dynamics to hybrid intelligence. We discuss how sparse identification of nonlinear dynamics (SINDy), Koopman learning, neural ordinary differential equations, physics-informed neural networks, and hybrid physics machine learning models contribute complementary capabilities, including interpretable reduced-order dynamics, control-ready prediction, continuous-time latent modeling, physics-constrained field reconstruction, and residual correction. We present that no single modeling approach is sufficient for the next generation of soft robotic systems. Instead, progress requires integrated modeling ecosystems that combine mechanical structure, data-driven discovery and task-aware adaptation. Such hybrid-intelligence frameworks can transform models from passive descriptions of deformation into active components of sensing, control, design and decision-making, enabling soft manipulators that are more interpretable, robust and deployable in real-world environments.