# Learning functionals via LSTM neural networks for predicting vessel dynamics in extreme sea states

arXiv: https://arxiv.org/abs/1912.13382 · HTML: https://mlsanity.com/paper/1912.13382/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Dec 2019.

## Built on by (most cited first, 12 of 12)

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- [State estimation with limited sensors -- A deep learning based approach](https://mlsanity.com/paper/2101.11513/) (2021)
- [Neural Ordinary Differential Equations for Data-Driven Reduced Order Modeling of Environmental Hydrodynamics](https://mlsanity.com/paper/2104.13962/) (2021)
- [Data-Driven System Identification of 6-DoF Ship Motion in Waves with Neural Networks](https://mlsanity.com/paper/2111.01773/) (2021)
- [A Data Driven Method for Multi-step Prediction of Ship Roll Motion in High Sea States](https://mlsanity.com/paper/2207.12673/) (2022)
- [Implementation of the Critical Wave Groups Method with Computational Fluid Dynamics and Neural Networks](https://mlsanity.com/paper/2301.09834/) (2023)
- [Recurrent-type Neural Networks for Real-time Short-term Prediction of Ship Motions in High Sea State](https://mlsanity.com/paper/2105.13102/) (2021)
- [Model-free system identification of surface ships in waves via Hankel dynamic mode decomposition with control](https://mlsanity.com/paper/2502.15782/) (2025)
- [Probabilistic prediction of the heave motions of a semi-submersible by a deep learning problem model](https://mlsanity.com/paper/2111.00873/) (2021)
- [Learning Response-Statistic Shifts and Parametric Roll Episodes from Wave--Vessel Time Series via LSTM Functional Models](https://mlsanity.com/paper/2603.24431/) (2026)

## Abstract (arXiv)

Predicting motions of vessels in extreme sea states represents one of the most challenging problems in naval hydrodynamics. It involves computing complex nonlinear wave-body interactions, hence taxing heavily computational resources. Here, we put forward a new simulation paradigm by training recurrent type neural networks (RNNs) that take as input the stochastic wave elevation at a certain sea state and output the main vessel motions, e.g., pitch, heave and roll. We first compare the performance of standard RNNs versus GRU and LSTM neural networks (NNs) and show that LSTM NNs lead to the best performance. We then examine the testing error of two representative vessels, a catamaran in sea state 1 and a battleship in sea state 8. We demonstrate that good accuracy is achieved for both cases in predicting the vessel motions for unseen wave elevations. We train the NNs with expensive CFD simulations offline, but upon training, the prediction of the vessel dynamics online can be obtained at a fraction of a second. This work is motivated by the universal approximation theorem for functionals [1], and it is the first implementation of such theory to realistic engineering problems.