# Modelling of Underwater Vehicles using Physics-Informed Neural Networks with Control

arXiv: https://arxiv.org/abs/2504.20019 · HTML: https://mlsanity.com/paper/2504.20019/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 32 references that are in the map.
- First posted on arXiv 28 Apr 2025.

## Builds on (most cited first, 13 of 13)

- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [ConFIG: Towards Conflict-free Training of Physics Informed Neural Networks](https://mlsanity.com/paper/2408.11104/) (2024)
- [Physics-Informed Neural Nets for Control of Dynamical Systems](https://mlsanity.com/paper/2104.02556/) (2021)
- [Physics-informed Neural Networks-based Model Predictive Control for Multi-link Manipulators](https://mlsanity.com/paper/2109.10793/) (2021)
- [Combining Physics and Deep Learning to learn Continuous-Time Dynamics Models](https://mlsanity.com/paper/2110.01894/) (2021)
- [UNav-Sim: A Visually Realistic Underwater Robotics Simulator and Synthetic Data-generation Framework](https://mlsanity.com/paper/2310.11927/) (2023)
- [Sim-to-Real of Soft Robots with Learned Residual Physics](https://mlsanity.com/paper/2402.01086/) (2024)
- [RAMP-Net: A Robust Adaptive MPC for Quadrotors via Physics-informed Neural Network](https://mlsanity.com/paper/2209.09025/) (2022)
- [Safe Physics-Informed Machine Learning for Dynamics and Control](https://mlsanity.com/paper/2504.12952/) (2025)
- [Physics-Informed Neural Networks with Skip Connections for Modeling and Control of Gas-Lifted Oil Wells](https://mlsanity.com/paper/2403.02289/) (2024)
- [Domain-decoupled Physics-informed Neural Networks with Closed-form Gradients for Fast Model Learning of Dynamical Systems](https://mlsanity.com/paper/2408.14951/) (2024)
- [Visual Tracking Nonlinear Model Predictive Control Method for Autonomous Wind Turbine Inspection](https://mlsanity.com/paper/2310.14030/) (2023)

## Abstract (arXiv)

Physics-informed neural networks (PINNs) integrate physical laws with data-driven models to improve generalization and sample efficiency. This work introduces an open-source implementation of the Physics-Informed Neural Network with Control (PINC) framework, designed to model the dynamics of an underwater vehicle. Using initial states, control actions, and time inputs, PINC extends PINNs to enable physically consistent transitions beyond the training domain. Various PINC configurations are tested, including differing loss functions, gradient-weighting schemes, and hyperparameters. Validation on a simulated underwater vehicle demonstrates more accurate long-horizon predictions compared to a non-physics-informed baseline