Accurately modeling the system dynamics of autonomous underwater vehicles (AUVs) is imperative to facilitating the implementation of intelligent control. In this research, we introduce a physics-informed neural network (PINN) method to model the dynamics of AUVs by integrating dynamical equations with deep neural networks. This integration leverages the nonlinear expressive power of deep neural networks, alongside the robust foundation of physical prior knowledge, resulting in an AUV model proficient in long-term motion forecasting. The experimental results indicate that this method is capable of effectively extracting AUV system dynamics from datasets, exhibiting strong generalization capabilities and achieving robust long-term motion prediction. Furthermore, a model predictive control method is proposed, using the learned PINN as the predictive model to accurately track the closed-loop trajectory. This research offers novel perspectives on the dynamics modeling of AUVs and has the potential to be applied in other relevant research endeavors.

Water–air cross-domain vehicles (CDVs) are capable of both flight and underwater navigation, showing broad prospects in marine science, such as underwater observation, disaster response, and rescue operations. It is crucial to investigate the dynamic performance of CDVs hovering above water surfaces to enhance safety and stability. In this study, the performance of a CDV’s ducted propeller hovering at various heights above a water surface was analyzed via computational fluid dynamic (CFD) simulations using the lattice Boltzmann method (LBM) and thrust tests. The results indicate that the air–water mixture formed by the wake of the propeller impacting the water surface is sucked in by the duct, causing the propeller to enter an unstable vortex ring state. At the same rotation speed in the air, the thrust of the propeller system decreases and the required power increases. With an increase in the height of the propeller above the water surface, the thrust and power return to normal. Furthermore, a numerical model was proposed to express the correlation among thrust, propeller rotation speed, and distance from the water surface. This study establishes a foundation for the dynamic modeling of CDVs and can be utilized by other related studies.

Minimizing experimental data while maintaining good AUV path-following performance is essential to reduce controller design costs and ensure AUV safety, particularly in complex and dynamic underwater environments with unknown ocean currents. To address this, we propose a conservative offline model-based Q-learning (CMQL) algorithm. This algorithm is robust to unknown disturbance and efficient in data utilization. The CMQL-based controller is trained offline with dynamics and kinematics models constructed from limited AUV motion data and requires no additional fine-tuning for deployment. These models, constructed by improved conditional neural processes, enable accurate long-term motion state predictions within the data distribution. Additionally, the carefully designed state space, action space, reward function, and domain randomization ensure strong generalization and disturbance rejection without extra compensation. Simulation results demonstrate that CMQL achieves effective path-following under unknown ocean currents with a limited dataset of only 1000 data points. This method also achieves zero-shot transfer, demonstrating its generalization and potential for real-world applications.