# Implementation of the Critical Wave Groups Method with Computational Fluid Dynamics and Neural Networks

arXiv: https://arxiv.org/abs/2301.09834 · HTML: https://mlsanity.com/paper/2301.09834/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 37 references that are in the map.
- First posted on arXiv 24 Jan 2023.

## Builds on (most cited first, 7 of 7)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [A Theoretically Grounded Application of Dropout in Recurrent Neural Networks](https://mlsanity.com/paper/1512.05287/) (2015)
- [Discovering and forecasting extreme events via active learning in neural operators](https://mlsanity.com/paper/2204.02488/) (2022)
- [A sequential sampling strategy for extreme event statistics in nonlinear dynamical systems](https://mlsanity.com/paper/1804.07240/) (2018)
- [Learning functionals via LSTM neural networks for predicting vessel dynamics in extreme sea states](https://mlsanity.com/paper/1912.13382/) (2019)
- [Data-Driven System Identification of 6-DoF Ship Motion in Waves with Neural Networks](https://mlsanity.com/paper/2111.01773/) (2021)

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

- [ShipGen: A Diffusion Model for Parametric Ship Hull Generation with Multiple Objectives and Constraints](https://mlsanity.com/paper/2311.06315/) (2023)
- [C-ShipGen: A Conditional Guided Diffusion Model for Parametric Ship Hull Design](https://mlsanity.com/paper/2407.03333/) (2024)
- [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)

Accurate and efficient prediction of extreme ship responses continues to be a challenging problem in ship hydrodynamics. Probabilistic frameworks in conjunction with computationally efficient numerical hydrodynamic tools have been developed that allow researchers and designers to better understand extremes. However, the ability of these hydrodynamic tools to represent the physics quantitatively during extreme events is limited. Previous research successfully implemented the critical wave groups (CWG) probabilistic method with computational fluid dynamics (CFD). Although the CWG method allows for less simulation time than a Monte Carlo approach, the large quantity of simulations required is cost prohibitive. The objective of the present paper is to reduce the computational cost of implementing CWG with CFD, through the construction of long short-term memory (LSTM) neural networks. After training the models with a limited quantity of simulations, the models can provide a larger quantity of predictions to calculate the probability. The new framework is demonstrated with a 2-D midship section of the Office of Naval Research Tumblehome (ONRT) hull in Sea State 7 and beam seas at zero speed. The new framework is able to produce predictions that are representative of a purely CFD-driven CWG framework, with two orders of magnitude of computational cost savings.