# Learning Adaptive Hydrodynamic Models Using Neural ODEs in Complex Conditions

arXiv: https://arxiv.org/abs/2410.00490 · HTML: https://mlsanity.com/paper/2410.00490/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in RL for robot navigation and UAV control, one of 15 directions in Deep reinforcement learning methods.
- Builds on 26 of its 50 references that are in the map.
- First posted on arXiv 1 Oct 2024.

## Placed in

- Deep reinforcement learning methods / [RL for robot navigation and UAV control](https://mlsanity.com/deeprl/rl-for-robot-navigation-and-uav-control/)

## Builds on (most cited first, 26 of 26)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Image Transformer](https://mlsanity.com/paper/1802.05751/) (2018)
- [Perceiver-Actor: A Multi-Task Transformer for Robotic Manipulation](https://mlsanity.com/paper/2209.05451/) (2022)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [Transformers in Time Series: A Survey](https://mlsanity.com/paper/2202.07125/) (2022)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [Learning robust perceptive locomotion for quadrupedal robots in the wild](https://mlsanity.com/paper/2201.08117/) (2022)
- [Equivariant Flows: sampling configurations for multi-body systems with symmetric energies](https://mlsanity.com/paper/1910.00753/) (2019)
- [Parameterized Neural Ordinary Differential Equations: Applications to Computational Physics Problems](https://mlsanity.com/paper/2010.14685/) (2020)
- [Physics-Guided Deep Learning for Dynamical Systems: A Survey](https://mlsanity.com/paper/2107.01272/) (2021)
- [Flow Navigation by Smart Microswimmers via Reinforcement Learning](https://mlsanity.com/paper/1701.08848/) (2017)
- [ODE Transformer: An Ordinary Differential Equation-Inspired Model for Sequence Generation](https://mlsanity.com/paper/2203.09176/) (2022)
- [The transformative potential of machine learning for experiments in fluid mechanics](https://mlsanity.com/paper/2303.15832/) (2023)
- [Physics-informed deep-learning applications to experimental fluid mechanics](https://mlsanity.com/paper/2203.15402/) (2022)
- [Scientific Exploration of Challenging Planetary Analog Environments with a Team of Legged Robots](https://mlsanity.com/paper/2307.10079/) (2023)
- [Cat-like Jumping and Landing of Legged Robots in Low-gravity Using Deep Reinforcement Learning](https://mlsanity.com/paper/2106.09357/) (2021)
- [Zero-Shot Transfer of Neural ODEs](https://mlsanity.com/paper/2405.08954/) (2024)
- [SIMBa: System Identification Methods leveraging Backpropagation](https://mlsanity.com/paper/2311.13889/) (2023)
- [Learning to Swarm with Knowledge-Based Neural Ordinary Differential Equations](https://mlsanity.com/paper/2109.04927/) (2021)
- [Imitation and Adaptation Based on Consistency: A Quadruped Robot Imitates Animals from Videos Using Deep Reinforcement Learning](https://mlsanity.com/paper/2203.05973/) (2022)
- [Neural Distributed Controllers with Port-Hamiltonian Structures](https://mlsanity.com/paper/2403.17785/) (2024)
- [Physically Consistent Neural ODEs for Learning Multi-Physics Systems](https://mlsanity.com/paper/2211.06130/) (2022)
- [Data-Driven Dynamics Modeling of Miniature Robotic Blimps Using Neural ODEs With Parameter Auto-Tuning](https://mlsanity.com/paper/2404.18580/) (2024)
- [Adaptive Asynchronous Control Using Meta-learned Neural Ordinary Differential Equations](https://mlsanity.com/paper/2207.12062/) (2022)

## Built on by (most cited first, 3 of 3)

- [On the definition and importance of interpretability in scientific machine learning](https://mlsanity.com/paper/2505.13510/) (2025)
- [Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization](https://mlsanity.com/paper/2602.13513/) (2026)
- [From inverse problems to neural operators: prediction, mechanism, and generalization of data-driven models](https://mlsanity.com/paper/2606.08956/) (2026)

## Abstract (arXiv)

Reinforcement learning-based quadruped robots excel across various terrains but still lack the ability to swim in water due to the complex underwater environment. This paper presents the development and evaluation of a data-driven hydrodynamic model for amphibious quadruped robots, aiming to enhance their adaptive capabilities in complex and dynamic underwater environments. The proposed model leverages Neural Ordinary Differential Equations (ODEs) combined with attention mechanisms to accurately process and interpret real-time sensor data. The model enables the quadruped robots to understand and predict complex environmental patterns, facilitating robust decision-making strategies. We harness real-time sensor data, capturing various environmental and internal state parameters to train and evaluate our model. A significant focus of our evaluation involves testing the quadruped robot's performance across different hydrodynamic conditions and assessing its capabilities at varying speeds and fluid dynamic conditions. The outcomes suggest that the model can effectively learn and adapt to varying conditions, enabling the prediction of force states and enhancing autonomous robotic behaviors in various practical scenarios.