Addressing the inverse kinematics of multi-section continuum robots is challenging due to structural redundancy, which often results in conflicting training labels for data-driven models. This study proposes a novel discrete analytical framework that resolves this ”self-motion manifold” by establishing a bijective, deterministic mapping between end-effector positions and cable lengths. Using this geometrically consistent dataset (𝑁≈5000 samples), we evaluate and compare three learning-based architectures: Deep Neural Networks (DNN), Implicit Neural Representations (INP), and Gaussian Process Regression (GPR). To ensure a strictly fair comparative evaluation, all models were subjected to rigorous 5-fold cross-validation and equivalent hyperparameter tuning efforts, with the neural baselines evaluated over 30 independent runs to account for initialization stochasticity. The models were validated through both simulation and real-world experiments on a bionic continuum manipulator. Quantitative analysis reveals a distinct performance hierarchy: the GPR model achieves superior precision with the lowest Root Mean Square Error (RMSE: 0.0545–0.0600mm), significantly outperforming the DNN (RMSE: 0.0777–0.0849mm) and INP models (RMSE: 1.0095–1.3135mm). Furthermore, an analysis of practical metrics for real-time control demonstrates that GPR exhibits superior robustness to measurement noise by mathematically embedding continuous elastic mechanics. Crucially, in single-sample evaluations required for closed-loop control, GPR achieves an ultra-low inference latency of 0.2ms, matching the computational efficiency of the highly scalable DNN. These results confirm that GPR surpasses both DNN and INP in tracking fidelity and robustness without compromising real-time responsiveness, identifying it as the optimal strategy for enabling high-fidelity control of continuum robotic systems.