Physics-Informed Dynamics Modeling: Accurate Long-Term Prediction of Underwater Vehicles with Hamiltonian Neural ODEs

Accurately predicting the long-term behavior of complex dynamical systems is a central challenge for safety-critical applications like autonomous navigation. Mechanistic models are often brittle, relying on difficult-to-measure parameters, while standard deep learning models are black boxes that fail to generalize, producing physically inconsistent predictions. Here, we introduce a physics-informed framework that learns the continuous-time dynamics of an Autonomous Underwater Vehicle (AUV) by discovering its underlying energy landscape. We embed the structure of Port-Hamiltonian mechanics into a neural ordinary differential equation (NODE) architecture, learning not to imitate trajectories but rather to identify the system’s Hamiltonian and its constituent physical matrices from observational data. Geometric consistency is enforced by representing rotational dynamics on the SE(3) manifold, preventing numerical error accumulation. Experimental validation reveals a stark performance divide. While a state-of-the-art black-box model matches our accuracy in simple, interpolative maneuvers, its predictions fail catastrophically under complex controls. Quantitatively, our physics-informed model maintained a mean 10 s position error of a mere 3.3 cm, whereas the black-box model’s error diverged to 5.4 m—an over 160-fold performance gap. This work establishes that the key to robust, generalizable models lies not in bigger data or deeper networks but in the principled integration of physical laws, providing a clear path to overcoming the brittleness of black-box models in critical engineering simulations.