Data-Driven Estimation of Ship Manoeuvring Hydrodynamic Derivatives using a Hybrid MARUS–PINN Framework with LLM-Guided Symbolic Discovery

Identification of hydrodynamic derivatives that govern ship manoeuvring behaviour for autonomous vessels such as unmanned surface vehicles (USVs) is essential for diverse maritime purposes including oceanographic research, environmental monitoring, and autonomous navigation. However, conventional hydrodynamic modelling approaches, such as classical manoeuvring models, experimental methods, and high-fidelity computational fluid dynamics (CFD), are often labour-intensive, costly, and time-consuming, and their estimated parameters may not fully capture real-world operating conditions due to nonlinearities, scale effects, and complex sea states. With the advent of machine learning, recent advances in Physics-Informed Neural Networks (PINNs) offer a promising alternative by embedding governing fluid-dynamic equations directly into the neural learning network, providing the advantages of data-driven learning while maintaining physical consistency. Hence, this thesis investigates a novel approach that combines Marine Robotics Unity Simulator (MARUS)–simulated manoeuvring data, PINN-based parameter learning, and symbolic discovery via Large Language Models (LLMs) to estimate hydrodynamic derivatives with improved robustness, reduced data requirements, and enhanced interpretability compared to conventional system identification methods, while promoting interoperability and standardization through its modular design. To evaluate this hybrid approach, the thesis addresses the following research question: Can a hybrid MARUS–PINN–LLM framework provide more accurate, interpretable, and data-efficient estimates of manoeuvring hydrodynamic derivatives than conventional system identification methods? To this end, an extensive set of experiments and ablation studies is conducted to compare the proposed hybrid model with its purely data-driven and purely physics-based counterparts across parameter accuracy, trajectory reconstruction quality, and generalization to diverse maneuvering conditions of various industry-standard USVs. The results demonstrate that integrating symbolic discovery with PINNs reduces sway-acceleration error by 86%, yaw-rate acceleration error by 66%, and heading-rollout error by 89% relative to purely data-driven baselines, producing compact, physically consistent residual terms that align with established nonlinear hydrodynamic effects while its physics-only counterparts catastrophically diverge from the ground-truths. Taken together, these findings highlight the potential of hybrid physics–machine-learning frameworks to advance the estimation of manoeuvring coefficients for the next generation of autonomous marine systems.