A Differentiable Composite Approximation Framework for Autonomous Underwater Vehicle Maneuvering Modeling from Sea-Trial Data

Autonomous Underwater Vehicles (AUVs) require precise dynamic models for navigation and control. While traditional polynomial models offer interpretability, they often struggle with complex, coupled nonlinearities. Conversely, purely data-driven models (like neural networks) are flexible but prone to overfitting and poor generalization when trained on limited, noisy sea-trial data. This paper addresses the challenge of building reliable AUV maneuvering models from field data by integrating these two approaches into a unified, differentiable framework.

The authors introduce a composite-approximation formulation that treats both the polynomial hydrodynamic basis and the neural adaptive-basis as differentiable components of a single predictor. Instead of the common 'grey-box' approach—where a polynomial model is fixed first and then a neural network is trained to compensate for the residual—this method uses a gradient-based co-calibration process. The polynomial coefficients are kept adjustable within bounded ranges, allowing the model to refine its physical baseline while the neural component captures remaining nonlinear discrepancies. To handle environmental noise, the authors incorporate a turning-motion-based current estimation procedure to transform measured field data into water-relative velocity targets, ensuring the model learns the vehicle's intrinsic dynamics rather than kinematic drift.

The proposed framework was evaluated using sea-trial data from a 7-meter AUV. The results demonstrate that the joint calibration of the polynomial and neural components outperforms several baselines, including polynomial-only, neural-only, and frozen-prior hybrid models. By allowing the polynomial coefficients to adapt during training, the model achieves better recursive trajectory and velocity prediction, suggesting that the co-calibration process effectively balances physical structure with data-driven flexibility.