# Floating-Body Hydrodynamic Neural Networks

arXiv: https://arxiv.org/abs/2509.13783 · HTML: https://mlsanity.com/paper/2509.13783/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 19 references that are in the map.
- First posted on arXiv 17 Sep 2025.

## Builds on (most cited first, 10 of 10)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data](https://mlsanity.com/paper/2002.12880/) (2020)
- [Symplectic Recurrent Neural Networks](https://mlsanity.com/paper/1909.13334/) (2019)
- [Social-Implicit: Rethinking Trajectory Prediction Evaluation and The Effectiveness of Implicit Maximum Likelihood Estimation](https://mlsanity.com/paper/2203.03057/) (2022)
- [What Truly Matters in Trajectory Prediction for Autonomous Driving?](https://mlsanity.com/paper/2306.15136/) (2023)
- [Denoising Hamiltonian Network for Physical Reasoning](https://mlsanity.com/paper/2503.07596/) (2025)
- [Lagrangian Neural Networks for Reversible Dissipative Evolution](https://mlsanity.com/paper/2405.14645/) (2024)

## Built on by (most cited first, 2 of 2)

- [Fluids You Can Trust: Property-Preserving Operator Learning for Incompressible Flows](https://mlsanity.com/paper/2602.15472/) (2026)
- [History-informed Lagrangian Neural Networks](https://mlsanity.com/paper/2608.13215/) (2026)

## Abstract (arXiv)

Fluid-structure interaction is common in engineering and natural systems, where floating-body motion is governed by added mass, drag, and background flows. Modeling these dissipative dynamics is difficult: black-box neural models regress state derivatives with limited interpretability and unstable long-horizon predictions. We propose Floating-Body Hydrodynamic Neural Networks (FHNN), a physics-structured framework that predicts interpretable hydrodynamic parameters such as directional added masses, drag coefficients, and a streamfunction-based flow, and couples them with analytic equations of motion. This design constrains the hypothesis space, enhances interpretability, and stabilizes integration. On synthetic vortex datasets, FHNN achieves up to an order-of-magnitude lower error than Neural ODEs, recovers physically consistent flow fields. Compared with Hamiltonian and Lagrangian neural networks, FHNN more effectively handles dissipative dynamics while preserving interpretability, which bridges the gap between black-box learning and transparent system identification.