# Machine Learning for Naval Architecture, Ocean and Marine Engineering

J.P. Panda  Department of Mechanical Engineering, DIT University, Dehradun,
Uttarakhand, India

###### Abstract

Machine Learning (ML) based algorithms have found significant impact in many
fields of engineering and sciences, where datasets are available from
experiments and high fidelity numerical simulations. Those datasets are
generally utilized in a machine learning model to extract information about
the underlying physics and derive functional relationships mapping input
variables to target quantities of interest. Commonplace machine learning
algorithms utilized in Scientific Machine Learning (SciML) include neural
networks, regression trees, random forests, support vector machines, etc. The
focus of this article is to review the applications of ML in naval
architecture, ocean and marine engineering problems; and identify priority
directions of research. We discuss the applications of machine learning
algorithms for different problems such as wave height prediction, calculation
of wind loads on ships, damage detection of offshore platforms, calculation of
ship added resistance and various other applications in coastal and marine
environments. The details of the data-sets including the source of data-sets
utilized in the ML model development are included. The features used as the
inputs to the ML models are presented in detail and finally the methods
employed in optimization of the ML models were also discussed. Based on this
comprehensive analysis we point out future directions of research that may be
fruitful for the application of ML to ocean and marine engineering problems.

###### keywords:

Machine learning , data-driven modeling , Experiments , CFD , Naval
Architecture , Ocean Engineering , Marine Engineering

††journal: Ocean Engineeringmyfootnotemyfootnotefootnotetext: corresponding
author<EMAIL_ADDRESS>
##  1 Introduction

In the fields of naval architecture, ocean and marine engineering large
amounts of data are generated from sources such as ocean wave and current
measurements, sea floor mapping by AUVs, ship manoeuvring and recorded wind
speeds interacting with the ships at different locations across the globe,
etc. This data potentially represents latent knowledge that can advance our
understanding of and our solutions for these fields. But the volume and
diversity of this data limits manual analysis by human domain experts. Using
machine learning based techniques researchers can utilize, interpret,
visualize and analyze this data. This enables the generation of data driven
surrogate models for these physical phenomena. These predictive models can be
utilized for estimation of wave height and ship parameters such as container
capacity and added mass coefficient, etc.

Machine learning (ML) is a branch of Artificial Intelligence (AI) that focuses
on enabling computers to infer models from data and constraints. The various
steps involved in developing a ML model are data preparation, feature
engineering, data modelling, and model evaluation. Data preparation involves
collection of raw data, data cleaning (deals with the missing values and
removing outliers) and formatting the raw data that can be incorporated in a
machine learning model. Feature Engineering is the process of converting the
raw data into physics based features, which can be correlated with a quantity
of interest in a particular field of engineering. One example of quantity of
interest in the field of Marine Engineering is the drag coefficient of an
autonomous underwater vehicle (AUV), which has relations with size of the AUV,
velocity of the flow, upcoming turbulence intensity and various other
environmental factors. Feature Engineering provides adequate data for a
machine learning model that can enhance the performance of the model. Next
step of the of the machine learning is data modelling, that is splitting data
into training and testing sets. In the training process both the inputs and
the quantity of interests(outputs) are provided to the model. The machine
learning algorithm maps the input variables with outputs and give a target
function which can be used to predict the unknown parameters for other set of
input variables(testing data).

There are mainly four different types of machine learning techniques. Those
are supervised, unsupervised, semi-supervised and reinforcement learning. In
supervised machine learning the outputs for a given set of inputs are used for
training the model and once the model is trained, it is used for prediction.
In unsupervised learning the outputs for given inputs are unknown. The semi-
supervised learning is in between supervised and unsupervised learning where
some samples may have training labels and others may not. In reinforcement
learning the machine is exposed to the environment, where it learns by
optimizing its reward. Among all the machine learning techniques, the
supervised learning methods are most widely adopted in the engineering
community. In supervised learning labelled data used for for training and
problems of classification and regression are solved. Popular supervised
machine learning algorithms are Linear Regression, Support Vector Machines
(SVM), Neural Networks, Decision Trees, Naive Bayes, etc.

In this article we provide a detailed review of application of ML algorithms
in the naval architecture, ocean and marine Engineering and grouped those into
following categories: wave forecasting, AUV operation and control,
applications in ship research, design and reliability analysis of breakwaters,
detection of damaged mooring lines, applications in propeller research, damage
detection of offshore platforms and few other miscellaneous applications like
beach classification, condition monitoring of marine machinery system,
Performance assessment of shipping operations, autonomous ship hull corrosion
cleaning system, wave energy forecasting, prediction of wind and wave induced
load effects on floating suspension bridges and tidal current prediction.
Based on this comprehensive analysis we point out future directions of
research that may be fruitful for the application of ML to coastal and marine
problems.

##  2 Machine learning basics

Machine learning is the process of finding the associations between inputs and
outputs and parameters of a system using limited data. The learning process
can be summarized as follows [8]:

$\begin{split}R(w)=\int L[y,\phi(x,y,w)]p(x,y)dxdy\end{split}$ (1)

In the above equation, data x and y are the samples form the probability
distribution $p$, the structure of the ML model is defined by $\phi(x,y,w)$,
and $w$ are the parameters. The learning objectives are balanced by the loss
function $L$. There are three broad categories of ML algorithms, those are
supervised, unsupervised, and semi-supervised.

###  2.1 Supervised Learning

In supervised learning, correct information is available to the ML algorithm.
The data utilized for the development of the ML model are labeled data, where
labels are available corresponding to the output. The unknown parameters of
the ML model are determined through minimization of the cost function. The
supervised learning correspond to various regression and interpolation
methods.The loss function of the ML model can be simply defined as:

$\begin{split}L[y,\phi(x,y,w)]=|x||y|b\end{split}$ (2)

Figure 1: Classification of ML algorithms as supervised, semi-supervised and
unsupervised and reinforcement learning. Figure 2: The learning problem

###  2.2 Unsupervised Learning

In unsupervised learning, the features are extracted from the data by
specification of certain criteria and supervision and ground truth levels are
not required. The problems involved in unsupervised learning are clustering,
quantization and dimensionality reduction. The dimensionality reduction
involve proper orthogonal decomposition, autoencoders and principal component
analysis. In clustering, similar groups in data can be identified. The most
common ML algorithm used in clustering of data is the k-means clustering [28].

###  2.3 Semisupervised Learning

In semisupervised learning, the ML algorithm is partially supervised, either
with corrective information from the environment or with limited labeled
training data. In semi-supervised learning two alorithms are mainly used,
those are generative adversarial networks [12] and Reinforcement learning
[108].

##  3 Popular Machine learning algorithms

###  3.1 Artificial Neural Network

Artificial Neural Networks(ANN) (fig.3a) are the machine learning systems
inspired from the biological neural networks. The biological neural
networks(BNN) are the circuits that carry out a specific task when activated.
These are population of neurons interconnected by synapses. Similar to BNNs,
ANNs have artificial neurons(fig.3b). The most widely used ANN is a multilayer
perception(MLP), which has more than one hidden layers and has applications in
both regression and classification problems. The MLP has input layer, hidden
layers and output layer. The MLP correlates inputs to the outputs. While
passing through the hidden layers the inputs are multiplied by weights. Each
neuron in the MLP has a function y that correlates the input. The ultimate aim
is to reduce the error at the output by optimizing the weights. In every layer
of the neural network, the neuron response is given by an activation function,
and a cost is given by a biased weighted sum. For two consecutive layers
$[k-1,k]$, the neural network operation can be expressed mathematically as
follows:

$\begin{split}y_{j}=f_{j}(\sum_{i=1}^{n}w_{ij}x_{i}+b_{j}),i\in[0,n]\wedge
i\in[0,m]\end{split}$ (3)

where $n$ and $m$ are number of layers in $k-1$ and $k$th layers respectively.
For neuron $j$, $y_{j}$ is the output and $x_{i}$ is the input signal from
neuron $i$, $b_{j}$ is the bias of the neuron and $w_{ij}$ is the weight
associated with connections $i$ and $j$.

The MLP can learn from data and optimize the weights. The learning task in
DNNs is obtained by updating the weights and minimizing the output error. The
DNNs employ back-propagation algorithm in the training process and it is good
for both speed and performance. There are several optimization techniques by
which the weights can be calculated. Those are gradient descent, Quasi-
Newton, Stochastic Gradient Descent or the Adaptive moment Estimation etc.

Figure 3: Structure of a neural network

###  3.2 Convolutional Neural Network

Convolutional neural network (CNN) is type of neural network mainly used in
image processing. The CNN has mainly three layers, those are convolutional
layer, pooling layer and a fully connected layer. The schematic of CNN is
shown in fig.5. The job of convolutional layer is to extract latent features
form an image by applying convolutional filters to the input. A set of
learnable filters are the parameters of CNN connected only to a local region
in the input volume spatially, but to the full depth. The detailed methodology
involved in CNN can be presented as follows:

$\begin{split}x^{l}_{i,j}=g(x^{l-1}*W^{l})_{i,j}=g(\sum_{m}\sum_{n}x_{{i+m},{j+n}}^{l-1}w^{l}_{m,n})\end{split}$
(4)

in above equation, $x^{l}_{i,j}$ is (i,j)th value of $l$th layer and
$w^{l}_{m,n}$ is ($m,n)$th weight of convolution filter in the $l$th layer. g
is the non-linear activation function. Suppose, the $(l-1)$th layer has
dimensions of W(width), H(height) and C(Channel) and the $l$th layer
convolutional filter dimensions F(width), F(height) and C(Channel), then the
$l$th layer can be derived by applying the nonlinear activation function g to
the convolution operation. The function of nonlinear activation function is to
model the nonlinear relationship the subsequent layers.

###  3.3 Recurrent neural network

Recurrent neural networks (RNN) are used for processing sequential data. RNNs
can also process data with much longer sequences and sequences with variable
length. RNNs can be designed in different methods as discussed in [27]: a) a
RNN that generate an output at every time step and recurrent connections
between the hidden units, b) a RNN that generate an output at every time step
and recurrent connectivity only from the output at one time step to the hidden
units at the next time step and c) RNNs with recurrent connectivity among the
hidden units that reads entire sequence and produce a single output.

####  3.3.1 Long short-term memory network

Long short-term memory network(LSTM) are the gated RNNs. These networks are
based on the concept of generating paths through time that neither vanish nor
explode. In the LSTM, the gradients can flow for long duration through the
self loops. By making weight of the self loop gated the time scale of
integration can be changed dynamically. The LSTM has successful applications
in handwriting recognition, speech recognition, handwriting generation and
machine translation.

Figure 4: Block diagram of the LSTM network cell, The cells are connected
recurrently to each other [27].

###  3.4 Random Forest

The basic building block of a random forest is a decision tree. The structure
of the decision tree is shown in fig. 6a. The boxes in the decision tree
represent group of features and data. The decision tree seeks if/then/else
rules for obtaining the desired output. Random forest(RF) regression combines
performance of multiple decision trees for predicting a output variable. It is
a assemble learning technique, works on the concept of bagging method. In RF
regression trees are constructed using a subset of random sample drawn with
replacement from training data. The RF algorithm has following steps: a)
Drawing boot strap samples for number of trees from original data b) Growing
unpruned regression trees for each boot strap sample and at each node randomly
sample the number of predictors and choose the best split among those
variables. c) Prediction of output for test data by the averages of the
predictions from all the trees.

###  3.5 Support Vector Machine

Support vector machines are based on the principles of structural risk
minimization and are used for recognizing the subtle patterns in complex
datasets. This machine learning methodology was initially developed for
solving the classification problems, later these were extended towards solving
regression problems. The support vector regression employs kernel functions to
map the initial data into high dimensional space such that the nonlinear
patterns can be converted into a linear problem. The performance of SVM
regressor is largely dependent on the choice of kernel function. There are 4
main types of kernel functions are available, those are Linear, Polynomial,
Sigmoid and Radial Basis Function. The hyper-parameters of the SVM regressor
must be chosen carefully for efficient performance of the model. Inappropriate
choice of hyper parameters would lead to under/ over fitting. The two main
hyper parameters of the SVM regression model are $\epsilon$-insensitive zone
and regularization parameter C. Any deviation from $\epsilon$ can be
calculated from the penalization of the regularization parameter C. The
penalty becomes more important when the values of C is higher and SVR fits the
data. The penalty becomes negligible, when the value of C is small and SVR
gets flat. For higher value of $\epsilon$ SVR becomes flat and for smaller
value of $\epsilon$, SVR fits data.

Figure 5: Architecture of CNN
Figure 6: Architecture of of a random forest, a)a single decision tree b)a
random forest

##  4 Application of Machine learning in the marine environment

###  4.1 Wave forecasting

Waves are generated by complex interaction of wind with the ocean and the
process by which ocean waves are generated is not fully understood and is
extremely uncertain and complex. The information of wave heights at different
locations is essential for operation related activities in the ocean. Most of
the works related to operation activities in the ocean are carried out with
wave heights estimated over a period of some hours or days. Traditionally
deterministic models are used for prediction of height of waves and wave
periods [95]. The ocean waves can both be forecasted and hindcasted using
different physics based approaches. Waves can be forecasted using
meterological conditions and can be hindcasted with different meterological
charts. In wave forecasting, differential equations for wind-wave relationship
and wave energy are solved numerically. The methods using differential
equations generally predict wave heights for a period of 6-72 hours. The cost
of numerical simulations using differential equations is very high and the
simulations are time consuming and the numerical predictions are always
associated with uncertainties. The uncertainties appears in the prediction
results because of the approximations utilized in the model development.

Because of the limitations in the traditional methods of wave height
predictions and the rapid development of ML methods, now researchers have
started utilizing various ML algorithms [55, 19, 13, 119, 48, 76, 16] such as
neural networks [15, 14, 94], recurrent neural networks [58] and random
forests for prediction of wave heights.

Figure 7: Neural network prediction of wave heights and periods [15].

[15] have used a simple 3 layered feed forward neural network to predict the
significant wave height and wave period. They considered the wind speed as
input to the neural network for March 1988 to July 1988 and further from
December 1988 to May 1989. The location of the data collection point was off
Karwar in India. The ANN prediction of wave height is shown in fig. 7. [111]
have used ANN to predict the significant wave height, significant wave period,
maximum wave height and spectral peakedness parameter. The input parameters of
the neural network are : average of the highest one third pressure wave
heights, corresponding pressure wave period, average pressure zero-crossing
period, maximum pressure wave height , average pressure wave height, root mean
square pressure wave height, average of one-tenth highest pressure wave
height, successive pressure wave height correlation and pressure spectral
peakedness parameter. The detailed definitions of the above parameters are
available in [111]. The ANN model was trained using data obtained from
stations ranged from 11 to 41 m. The predicted results are compared with the
results obtained from linear theory. The ANN model predicted better results
for water depths in between 20 to 41 meter in comparison to the linear theory.
[89] used neural networks to estimate wave parameters from cyclone generated
wind fields. They considered 11 cyclones, which crossed the southern east
coast of India in their studies. The inputs to the neural network are
difference between central and peripheral pressure, radius of maximum wind and
the speed of forward motion of cyclone. The outputs of the neural network are
wave heights and periods. They considered the feed forward neural network with
back propagation algorithm in their modelling. The NN model predictions are
contrasted against other established wave hindcasting models and the observed
very good correlation between NN and physics based model results.

[75] used wavelet and neural network hybrid models for real-time forecasting
of wave heights. They developed the hybrid model by combining empirical
orthogonal function analysis and wavelet analysis with the neural network and
used wave height data at different locations and meteorological data in the
surrounding are for training the ANN model. Their developed model was useful
for prediction of wave heights where past wave height and meteorological data
are available. Doong et al. used ANN based models to predict the the
occurrence of coastal freak waves. An actual picture of a coastal freak wave
is shown in fig. 9. These waves are generated by interaction of waves with
various coastal structures such as rocks. They used seven
parameters(significant wave height, peak period, wind speed, wave groupiness
factor, Benjamin Feir Index (BFI), kurtosis, and wind-wave direction
misalignment) for training their model. They used a single hidden layer neural
network with back propagation algorithm. The field data used in their study
were collected from the Longdong Data Buoy(Central weather bureau of Taiwan).
The buoy was at a location of 1 km off the Longdong coast, where the water
depth was 23m. [9] used deep neural networks to estimate significant wave
height using raw ocean images8. A CNN based classification model was
constructed with four CNN structures. Their method of wave height prediction
had two steps: a) the best CNN model for ocean image processing was found
among VGGNet, Inception.v3, ResNet and DenseNet. b) The model performance was
improved using transfer learning and structure modification. It was observed
that the VGGNet and ResNet based model with transfer learning and various
feature extractors yielded good performance in significant wave height
modeling.

Traditionally strom surges are predicted using fluid dynamics methods(finite
difference method) that utilizes large number of equations and the simulations
are time consuming. [88] applied support vector regression methodology to
forecast typhoon surge. The typhoon surge must be accurately predicted to
avoid property loss. For the development of ML model they used the input data
are pressure, wind velocity, wind direction and estimated astronomical tide
and the out put is the storm surge level. The ML model developed with support
vector regression was verified using original data collected at the Longdong
station at Taiwan for the Aere typhoon. The location of the Longdong harbour
is shown in fig. 10. [57] evaluated the efficacy of support vector machine,
bayesian networks and artificial neural networks in predicting the wave
height. The data required for training the models were collected at a buoy
station at Lake Superior. They noticed ANN prediction of the wave height
matched well with the observational data and are better than prediction of the
other ML models.

Figure 8: Raw ocean images [9].
Figure 9: An actual picture of a coastal freak wave [17]. Figure 10: Locations
of Longdong harbour, Taiwan [88].

###  4.2 AUV operation and control

An AUV(autonomous underwater vehicle) is a self propelled unmanned vehicle,
that can conduct various activities in the deepest corners of Ocean or near
the free surface [112]. These don’t involve any human supervision. Typical
applications of AUV includes, sea floor mapping for construction of offshore
structures, characterization physical chemical and biological properties of
ocean, Oceanographic applications and many more. Since there is minimal human
supervision for AUV operation, design of accurate control system of AUV plays
major role in the design of AUV. These vehicles have are robotic devices with
own propulsion system for navigation and have onboard computer for decision
making [93].

Machine learning techniques has various application in the design of control
system of the AUV. [130] used neural networks for modelling an adaptive
trajectory tracking control scheme for under actuated autonomous underwater.
The AUV was subjected to unknown asymmetrical actuator saturation and unknown
dynamics. The AUV kinematic controller was designed by using neural network
compensation and adaptive estimation techniques. The neural network was used
to approximate the complex AUV hydrodynamics and differential of desired
tracking velocities. The stability of the NN model was tested against Lyapunov
theory and backstepping technique. [129] proposed a novel bilateral adaptive
control scheme for achieving position and force coordination performance of
underwater manipulator teleoperation system under model uncertainty and
external disturbance. A new nonlinear model reference adaptive impedance
controller with bound-gain-forgetting (BGF) composite adaptive law is designed
for the master manipulator force tracking of the slave manipulator. They have
used a radial basis function neural network for local approximation of slave
manipulator’s position tracking. The RBFNN based on Ge-Lee (GL) matrix is
adopted to directly approximate each element of the slave manipulator dynamic,
and the robust term with a proper update law is designed to suppress the error
between the estimate model and the real model, and the external disturbance.
[23] proposed a hybrid visual servo(HVS) controller for underwater vehicles
using a dynamic inversion based sliding mode adaptive neural network control.
The method was developed for tracking the HVS reference trajectory generated
from a constant target pose. The dynamic uncertainties were compensated using
a single layer feed forward neural network, with an adaptive sliding mode
controller. The control system proposed was composed of a sliding model
controller combined with a neural network compensator is employed to construct
a pseudo control signal required to track a smooth reference trajectory, that
is generated by a target pose through a reference model. A dynamic inversion
module was also incorporated in the control system to convert the pseudo
control into actual thruster control signals by using approximate dynamic
model of underwater vehicles. The schematic of the proposed control system
architecture is shown in fig.11.

Figure 11: Schematic of the DI-SMANNC for hybrid visual servoing of an
underwater vehicle [23].

[10] proposed an observer based adaptive neural network control approach for a
class of remotely operated vehicles whose velocity and angular velocity state
in the body fixed frame are unmeasured. The thruster control signal was
considered as the input to the tracking control system. An adaptive state
observer based on local recurrent neural network was proposed to estimate the
velocity and angular velocity state online. The adaptive learning method was
also used to estimate the scale factor of the thrust model.

###  4.3 Machine learning applied in ship research

####  4.3.1 Estimation of ship parameters

[90] utilized neural networks to predict container capacity of a container
ship. They used database of previously built ships to predict the number of
containers which can be accommodated on a vessel and to design a container
stowage plan. The input to the neural network are the length, breadth, depth,
deadweight and speed of the vessel and the output is the container
capacity(number of containers). [59] used artificial neural networks to
predict the resistance hullforms. The hull forms are sixteen in number and
those were mainly designed to be used as bulk carriers and tankers by the U.S.
Maritime Admisistration. The experimental data for the residual resistance
coefficient were used to train and test a series of neural networks. They
considered a feed forward multilayered perception in their analysis. The input
vector to the neural network consists of length to breadth ratio, the breadth
to draft ratio, the block coefficient and the Froude number and the output is
the residual resistance coefficient. [7] predicted the added resistance of a
ship in regular head waves. Experimental data collected from model test
measurements was used to train the neural network model. The predicted added
resistance has applications in the preliminary design stage. The function for
the added mass coefficient was approximated as:

$\begin{split}C_{AW}=f(LBP,B,d,CB,Fn,\lambda/LBP)\end{split}$ (5)

where: LBP is the length between perpendiculars, B is the breadth, d is the
draught,CB is the block coefficient, Fn is the Froude number, $\lambda$ is the
wave length and f is the function for the prediction of ship added resistance
coefficient. [131] used support vector machine for estimation of hydrodynamic
coefficients in the mathematical models of ship manoeuvring motion from
captive model test results. The towing test and pure sway test were also
considered in the model testing. The comparison of the test data and SVM
predicted results suggest that, SVM is an effective method in predicting
hydrodynamic coefficients in captive model test. They also noticed that, the
SVM model predictions are comparatively poor, for polluted test data and
uncertainties in the hydrodynamic models. The efficacy of SVM with polluted
test data can be enhanced by treating test data with de-noising approaches.
[123] used a least square support vector machine for estimation of parameters
nonlinear manoeuvring model in shallow water.

####  4.3.2 Automatic Ship docking

[100] proposed an ANN based approach for automatic ship docking in presence of
environmental disturbances (12). The data required for ANN training was
obtained by operating the ship by a skilled captain using a joystick to
control ship’s rudder and thrust. In the ANN based controller model the inputs
are the parameters selected from data analysis(those are state of vessel and
environmental information) and the output are the ship’s propeller speed and
rudder angle. The vessel’s state are its heading and position, speed of the
vessel, the force of vessel in different degrees of freedom, and the
environmental information are force of wind in each degrees of freedom, the
wind speed and wind direction.They used gradient descent method to minimize
the mean square error between the required output value and the actual output
value of the neural network. Based on sensitivity the optimal parameters for
the ANN input are chosen as relative distance between ship and dock and the
heading angle. The output of the ANN is rudder angle and thruster speed.

Figure 12: Schematic of the ANN based control strategy for automated ship
docking [100].

####  4.3.3 Ship manoeuvring simulation

[54] used support vector regression for manoeuvring simulation of catamaran.
The implicit models are derived for the manoeuvring motion, instead of the
traditional method of calculation hydrodynamic coefficients. For development
of the SVM regressor model data obtained from full scale trials were used. The
effects of wind and current induced disturbances were also considered in the
model development. The inputs to the SVM model were rudder angle, surge speed,
yaw rate and sway speed respectively and outputs are derivatives of the surge
speed,sway speed and yaw rate respectively. They utilized Gauss function
kernel in the SVM to improve the performance of the approximation.

Figure 13: Kinematic parameters in ship manoeuvring simulation, detailed
definition of these parameters are available in [54]

####  4.3.4 ship trajectory prediction

[110] used Long Short-Term Memory(LSTM) network to model and predict the
trajectories of the vessels. The ground truth automatic identification data in
the Tianjin port of China was used to train and test the ML model. The inputs
to the LSTM model are geographical location, speed, heading and other status
information and the output is the status of ship at any future moment. It was
observed that, the predicted trajectories are better than the traditional
kalman filter model. The predicted trajectory of the ship is shown in fig. 14.
In the figure, the first 10 minute trajectory data was used to train the LSTM
model and the trajectory after 10th to 20th minute was predicted by the LSTM
model.

Figure 14: Trajectory prediction of the ship [110].

[117] applied artificial neural networks(ANN) to predict trajectory of the
ship. THE AIS data were used for the ANN model development.This method of
trajectory planning is mainly useful for river vessels and river-sea vessels,
when the vessel is near a hydraulic structure and there is problem in
obtaining satellite signals because of interference. The likelihood of
collision can be decreased with application of ML based trajectory prediction
models.

####  4.3.5 Calculation of wind load on ship

Wind loads on ships, is an important parameter that need to calculated
accurately, because that is directly correlated with analysis of ship
stability, maneuvering, station keeping and ship speed estimation. [113]
developed a radial basis function neural network model by using elliptic
Fourier features of closed contours and wind load data collected from wind
load data of three types of ships, those are car carriers, container ships and
offshore supply vessels. The trained neural network was employed for the
prediction of non-dimensional wind load coefficients.

####  4.3.6 Shaft power prediction of large merchant ships

[84] used neural networks to predict shaft power of large merchant ships. The
data required for training the neural network model was obtained from a data-
set of 27 months of continuously monitored data sampled in every 5 minutes
from three vessels of same design(Sample data is shown in fig.15 reproduced
from [84]. The data consists of vessel movements recorded with varied
geographic locations and weather conditions. The variables used in training of
the neural network model are GPS ship speed, ship speed through water, true
wind speed, apparent wind direction, draught, headings, trim and wave height.
The above mentioned parameters/features were used as input to the neural
network model and the output of the neural network is the shaft power. The
shaft power is the product of shaft torque and angular velocity. From accurate
measurement of shaft power the engine efficiency can be calculated.

Figure 15: Box-plot of shaft power vs GPS speed [84].

####  4.3.7 Prediction of fuel consumption of ship main engine

[26] predicted the fuel consumption of main ship engine using different
machine learning algorithms, those are support vector machines, random forest
regressors, tree regressors, ensemble methods and artificial neural networks.
[26] mainly compared the predictive capability of above mentioned models in
the prediction of the fuel consumption. Two different ship board data-sets
were collected using two different strategies of data collection, noon reports
and automated data logging and monitoring, were used for the model
development. The ML models developed using different algorithms were found to
be accurately predict the fuel consumption under different weather condition,
load condition, sailing distance, drafts and speed. [20] used ANN and multi-
regression techniques to estimate the ship power and fuel consumption. The
data used for the ML model development was obtained from [21]. The data-set
consists of data from two sea voyages collected at different loading
conditions. [25] also used deep neural networks to develop a fuel consummation
model and used that model in the route optimisation process. [38] feed forward
neural networks to predict the ship fuel consumption. The effect of data
prepossessing on the model predictive accuracy was mainly analyzed. [126] used
LSTM to model the real time fuel consumption of vessels and utilized the ML
model to optimize the fuel consumption of the inland vessel using Reduced
Space Searching Algorithm.

Figure 16: ANN based model framework for fuel consumption prediction [20].

####  4.3.8 Ship collision avoidance

[24] used generative adversarial network(GAN) to generate appropriate
anthropomorphic collision avoidance decisions and bypass the process of ship
collision risk assessment based on the quantification of a series of
functions. The LSTM cell was combined with GAN to improve capacity of memory
and the current availability of the overall system. The data required for the
development of the ML model was obtained from ship encounter azimuth map. The
data-set has 12 types of ship encounter modes from automatic identification
system(AIS) big data [125]. The proposed ML model can be applied in
intelligent collision avoidance, route planning and operational efficiency
estimation.

###  4.4 Design and reliability analysis of breakwaters

Breakwaters are constructed in ports and harbors to prevent an anchorage from
the erosion from the harsh wave climate and long shore drift. The breakwaters
the intensity of wave action in the ocean[83, 37, 116].

[41] used artificial neural networks to design and reliability analysis rubble
mound breakwater. The inputs to the neural networks are chosen by taking
different combinations of the variables, $P$, $N$, $S_{d}$, $\zeta_{m}$,
$cos\theta$, $h/H_{s}$, $SS$, $h/L_{s}$ and $T_{s}$. $h/H_{s}$ is the water
depth parameter, $L_{s}$ is the period of significant wave, $h/H_{s}$ is the
significant wave height, $P$ is the permeability of the breakwater, $N$ is the
number of wave attack and the other parameters have their usual meaning as
used in breakwater reliability analysis[41]. Based on different input
combinations they used five neural networks to model the stability of the
breakwater and the predictions of the neural networks are compared against
conventional empirical model of [114]. The stability model of [114] has the
from:

$\begin{split}N_{s}=6.2P^{0.18}(\frac{S_{d}}{\sqrt{N_{w}}})^{0.2}\frac{1}{\sqrt{\zeta_{m}}}\end{split}$
(6)

for $\zeta_{m}<\zeta_{c}$.

[40] have used ANN to estimate the damage of breakwaters considering tidal
level variations. They employed the wave height prediction neural network into
a Montecarlo simulation. The ANN was used to predict the wave height in front
of the breakwater. The inputs to the ANN are deep sea wave height and the
other was the tidal level in front of the breakwater and the significant wave
height is the output of the ANN.

###  4.5 Detection of damaged mooring lines

[11] used ANN to detect the damaged mooring line in tension leg platform
through pattern analysis of floater responses. They used numerical simulation
data(time series data of environment and floater responses) of charm3D for
training and testing of the neural network. The environmental data are related
to wave and wind, while the floater response data are related to the six
degrees of freedom: surge,sway, heave, roll, pitch and yaw. They considered a
ANN with five hidden layers in their modeling. The number of nodes in each
layer as follows (16,100,300,500,300,100,9). 16 and 9 correspond to the first
and last layer and other numbers indicate the number of neuron in respective
hidden layers. Their ANN model was a classification network, whose job was to
detect which mooring line is damaged by assigning an explicit label to it. [2]
used radial basis function neural network to detect the fault in the mooring
line. The effects of uncertainties in the modeling (material, boundary,
measurement uncertainties, hydrodynamic effects) were considered in developing
the ML models.

###  4.6 Machine learning applied in propeller research

Propellers are used in ships and submarines to create thrust to propel the
vehicle [87, 45, 74] . The blades are designed in such a manner so that their
rotational movement through the fluid generates a pressure difference between
the two surfaces of blades. The propellers used in marine Engineering
applications are mostly screw propellers with helical blades rotating on a
propeller shaft. [56] used gene expression programming(GEP) to evaluate
hydrodynamic performance and cavitation volume of the marine propeller with
various geometrical and physical conditions. CFD data of propeller thrust,
torque and cavitation volume at different rake angle, pitch ratio, skew angle,
advance velocity ratio and cavitation number are utilized in the development
of the GEP model. The mathematical expressions are developed for torque,
thrust and cavitation volume in terms of the physical and geometrical
parameters. [99] used ANNs to predict the hydrodynamic performance and
cavitation volume of propellers at different operating conditions. The data
utilized in training and testing of the ANN model was obtained from CFD
simulations of the flow past the propeller with varied geometrical and
physical parameters. The input variables to the neural network are taken as
rake angle, skew angle, pitch ratio, advanced ratio and cavitation number and
the output variables are propeller thrust, propeller torque and cavitation
volume. They generated 180 different data-sets by varying the input
parameters. For different output, they considered different configuration of
ANN for minimum mean squared error. They considered feed-forward and back-
propagation ANNs in their simulations. Their ANN models very good prediction
accuracy(greater than 0.99). [42] used convolutional neural networks to study
the risk of propeller cavitation erosion. The CNN model was trained using
various ship model test results of cavitation characteristics. Three types of
CNN were used for the ML model development, those are VGG, GoogleNet and
ResNet. [92] used ANN to model propeller induced erosion alongside quay walls
in shallow water harbours and compared the predictive capability of the ANN by
contrasting the results with other regression based models. The structure of
the ANN used in modeling of the propeller induced erosion is shown in fig. 17.
The ANN has five inputs, one output and six hidden layers. The input
parameters to the neural network are Clarence distance from propeller tip to
bed, propeller diameter, distance to quay wall, rudder angle and densimetric
Froude number and the output of the neural network is the depth of maximum
scour at a particular time instant. The data required for the ANN model was
obtained from deep rectangular GRP-lined plywood tank, using two open
propellers.

Figure 17: Neural network used in modeling of the propeller induced erosion
[54].

###  4.7 Damage detection of offshore platforms

Offshore platforms are large structures installed in deep seas with facilities
drilling of well to explore natural gas and petroleum that lies in the seabed.
These are damaged during their service life, because of complex marine
environments and human factors. In order to ensure the safety of marine
operations, the structural health monitoring such as, vibration based damage
detection technique must be employed. The vibration based damage detection
method can identify the presence, location severity of the damages of
structures. [4] used one-dimensional convolutional networks to detect the
damage sensitive features automatically from a offshore platform using raw
strain response data. The CNN model was validated using numerical simulations
of jacket-type offshore platform for random and regular wave excitation in
different directions. Different damage locations and the noise effect were
considered for finding the damage localization and damage severity. The
feature extraction capability of the CNN was enhanced using the data pre-
processing procedure based on convolution and deconvolution for noisy data.
The CNN model developed was tested for three different cases: e.g. offshore
platform subject to a sinusoidal excitation, a white noise extraction and a
impulse excitation. Basically the model of [4] is an extension of the work of
[1], in which they had used CNN to detect the damage of a grandstand simulator
at Qatar University.

###  4.8 Miscellaneous applications in the marine environment

####  4.8.1 Beach classification

[53] applied SVM and ANN to classify nine different types of beaches, those
are mainly micro-tidal sand and gravel beaches. The beach types are a) sand
and gravel beaches, b) sand and gravel separated beaches, c) gravel and sand
separated beaches, d) Gravel and sand beaches, e) pure gravel beaches, f)
supported sand beaches, g) open sand beaches, h) bi-supported sand beaches, i)
enclosed beaches. The ML model results are compared with results of
discriminant analysis. The 14 variables used in the classification model
development are: modality, $D_{50}$, $D_{10}$, $D_{90}$, source, breaking wave
height perpendicular to the beach, frequency, direction associated with the
wave height perpendicular to the beach, length profile, type profile, slope of
the berm, distance to the source and Posidonia depth. The above mentioned
terms has their usual definitions and is available in [53]. The ML models
developed with the above 14 variables, were optimized with variation of
neurons in the hidden layers and the SVM was modelled with different kernels,
those are linear, polynomial, radial basis function and sigmoid.

Figure 18: Types of sandy beaches.(A) open sand beach.(B) supported sand
beach.(C) bi-supported sand beach.(D) enclosed sand beach [53].

####  4.8.2 Condition monitoring of marine machinery system

Condition based maintenance is an advanced data-driven method of machine
maintenance, in which historical data collected by shipboard monitoring system
is utilized by intelligence analysis tool to guide the planned maintenance.
This makes the machine maintenance work, more scientific, systematic, and
planned. [109] used one class classification technology, that needs one class
samples to train the model. Six different classifiers were used in the
modeling of the condition monitoring system, those are one class support
vector machine, support vector data description, Global k-nearest neighbors,
Local outlier factor, Isolation forest, Angle-based outlier detection. In the
development of ML models, the data-set of marine gas turbine propulsion system
was used.

Figure 19: Schematic of the support vector machine classification. A non-
linear mapping was used to map the observations into a higher dimensional
space [77].

####  4.8.3 Performance assessment of shipping operations

Energy efficient operations can lead to reduced fuel consumption and reduction
in environment pollution. The improvements in the energy use efficiency can be
achieved both by technical upgrades and through behavioural changes of the on
board crew members. [77] used multi-class support vector machines to identify
the presence of energy efficient operations. The support vector machine
utilized a radial basis function kernel, that facilitates the adaptive
modeling of the interface between the classes and thus significantly improves
classification performance as shown in fig.19. The data required for
developing the ML model was obtained through discussions with senior officers
and technical superintends(mainly the positive and negative patterns of energy
efficient operations were identified). The main source of data utilized in the
model development was collected from noon reports [86] and based on the noon
reports the energy consumption data were divided per consumer and covered the
auxiliary machine parts used for generation of electricity, boilers, main
engine, pumps and incinerators.

####  4.8.4 Autonomous ship hull corrosion cleaning system

The ships can be smoothly operated with cleaning of the hulls in shipyards.
[49] used autonomous system based on reinforcement learning [108] to remove
the corrosion of a ship by water blasting. The cleaning of ships by autonomous
robotic systems ensure reduced consumption of water, time and energy in
contrast to the manual cleaning. [49] developed a water blasting framework for
a novel robot platform, which can navigate smoothly on a vertical plane and is
designed with the adhesion mechanism of a permanent magnet. In order to ensure
shortest travel distance and time to save resources used in the cleaning
process, the complete way-point path planning is modeled as a classic travel
salesman problem. The level of corroded areas after water-blasting was
assessed by using deep convolutional neural networks. A detailed discussion of
the operation strategy of the robot is available in [49]. The block diagram of
the close loop optimal automated water blasting is shown in fig.20.

Figure 20: The block diagram of close loop optimal automated water blasting
[49].

####  4.8.5 Wave energy forecasting

Wave energy is a promising source of renewable energy. [5] employed artificial
neural networks to predict wave energy flux and other wave parameters. The The
neural network model optimized using moth-flame optimization and the proposed
model was assessed using 13 different data-sets collected from locations
across the Atlantic, Pacific coast and Gulf of Mexico. [72] used LSTM to
forecast power generation of a wave energy converter using artificial neural
networks. The effective forecast of wave energy will lead to reduced cost of
investment in construction of the device and it is also essential for
operation and management of electric power. They have used both experimental
and numerical data for training and testing of the model. The experimental
data was utilized from [30] and the numerical data was obtained from numerical
simulations using Flow-3D software. In their study, a ML model was developed
for a correlation between wave height and the generated electric power. [115]
developed a novel time efficient approach to calibrate VARANS-VOF models for
simulation of wave interaction with porous structures using Artificial Neural
Networks. These methods are useful for reducing time consumption in predicting
the wave parameters using traditional fluid dynamics methods.

####  4.8.6 Prediction of wind and wave induced load effects on floating
suspension bridges

[124] used ANN and SVM to predict long-term extreme load effects of floating
suspension bridges. They used ML models as surrogate models, in conjunction
with the Monte-carlo based methods, for the faster prediction of the loads.
For their case study a 3-span suspension bridge with 2 floating pylons under
combined wind and wave actions was used as shown in fig.21. In the new Monte-
Carlo framework, the implicit limit-state function was replaced by the
surrogate models based on ANN and SVM. It was noticed that, the ML based
Monte-Carlo method require less computational effort and predicted more
accurate results.

Figure 21: A finite element model of 3-span suspension bridge with 2 floating
pylons [124].

####  4.8.7 Tidal current prediction

The traditional method of tidal current prediction employs computer
applications with classical harmonic analysis. Those are computationally
expensive for real time predictions. [96] used Bayesian machine learning
(Gaussian processes) for the prediction of tidal currents. With use of ML
based techniques the uncertainties and complexity of the problem were enabled
to represent in the modeling basis. The data used in the development of ML
algorithm were collected from National Oceanic and Atmospheric Administration
(NOAA). The location of tidal current observation sites are Southampton Shoal
Channel, Old Port Tampa, Sunshine Sky Bridge and Martinez-AMORCO Pier. The
data obtained from these sites were used for long-term predictions. The
Gaussian process with periodic kernel function was found to be suitable for
the modeling problem concerned, because of its harmonic nature. [34] utilized
deep learning models to develop tools for in situ prediction of ocean
currents, those are, a Long Short-Term Memory (LSTM) Recurrent Neural Network
and a Transformer. The data utilized for model development were also obtained
from NOAA. In addition to speed, they also predicted the direction of ocean
currents. It was noticed that the predictions of Ocean currents are more
accurate in contrast to the predictions of harmonic methods[34]. [106] used
ANN to model the currents of Bay of Bengal. They mainly improved the velocity
predictions using ANN model.

###  4.9 Application of ML in CFD

The field of Naval Architecture, Ocean and Marine Engineering often employs
CFD as a tool for modeling and prediction of flow past ships and underwater
vehicles [82, 66, 67], visualization of flow past propellers [87], analysis of
wave induced load on offshore structures, simulations of waves and currents
and simulations of wave energy converters [69, 70, 68] . The commercial
software used in CFD analysis are ANSYS FLUENT [22], STAR-CCM+ [6] and
SHIPFLOW [46]. CFD is cheaper in comparison to experimental methods and can be
applied for flow prediction in larger and complex domains, like modeling flow
past larger ships and predicting complex flow past propellers. The basic
building block of such CFD tools are turbulence models. In literature, ML
techniques are either applied for faster flow prediction using surrogate
models or developing turbulence closure models using large data-sets of direct
numerical simulations(DNS) or experiments.

In this section, we will provide a detailed overview of application of ML
algorithms in CFD and turbulence modeling. The Naval Architects and CFD
engineers working with different research problems may employ such advanced
techniques for modeling and prediction of the complex oceanic flow fields.

####  4.9.1 Fluid flow field prediction using reduced order models

[98] used deep neural networks for flow prediction over airfoils. They used a
deep convolutional neural network for extraction of features from the
different shapes of the airfoil and utilized those shape related features
along with Reynolds number and angle of attack as inputs to the DNN model. The
outputs to the DNN are pressure and velocity components across the airfoil.
The data required for training the DNN model is obtained from CFD simulations.
They predicted the flow field at much faster speed (150 times) in comparison
to the traditional CFD methods and the results are as accurate as the
traditional CFD predictions. [33] utilized CNN to predict pressure
distribution around airfoils. The data-set library was formed using numerical
simulation data from deformed airfoils. The airfoil was parametrized using the
signed distance function(SDF).

Figure 22: The SDF representation of base airfoil [33].

[91] utilized DNN fro non-intrusive model order reduction of the parametric
inviscid transonic flow past an airfoil. They preserved the accuracy of flow
prediction at a significant lower computational cost. [43] used CNN to predict
the velocity field for flow in in a scramjet isolator. The data required for
training model was obtained from numerical simulations of flow at different
Mach numbers and back pressures. The CNN has multiple reconstruction and
feature extraction modules. A mapping relationship was established between the
wall pressure on isolator and the velocity field on the isolator. [44] used DL
approach for super-resolution flow field reconstruction of a scramjet
isolator. In contrast to the work of [43], [44] used experimental data-sets
for the development of the DL model. They used both single path and multi-path
network models based on CNNs for flow field reconstruction. It was noticed
that the multi-path CNNs has better predictive accuracy in comparison to the
single path CNNs. [50] used CNN for predicting unsteady volume wake three-
dimensional flow fields. The ML model was trained with past information of
flow velocity and pressure. They also performed different analysis to find
structural similarities among feature maps to reduce the number of feature
maps containing redundant flow structures. Such reduction process can decrease
the size of neural network without affecting the prediction performance. [29]
developed a reduced order model(ROM) for unsteady flow prediction by combining
CNN and LSTM, which are trained in a sequential manner. The CNN model was
trained using DNS data obtained from numerical simulations with 80 bluff
bodies and tested on 20 bluff bodies. They also tested the ML-ROM model for
unseen bluff bodies, and the predicted results were quite satisfactory, this
shows the universality of ML-ROM based models. [73] modeled three dimensional
complex flow using ROM. The ROM consists of a CNN and a LSTM. The function CNN
was to map high dimensional flow fields into a low-dimensional latent space
and the LSTM was used to predict temporal evolution of latent vectors.The data
required for training the ROM was obtained from DNS. [51] utilized MLP in
conjuction with radial-logarithmic filter mask (RLF) for developing a
universally applicable ML concept fast flow field estimation for various
geometry types. The function of RLF is to provide information about the
geometry in a compressed form for the MLP. They applied new concept for both
internal and external flows such as airfoils and car shapes. The ML model was
developed with data generated from CFD simulations for different geometries
and the was tested for different unknown geometries.

[107] proposed a physics constrained deep learning (DL) approach for surrogate
modeling of fluid flows. The surrogate model was developed without relying on
CFD simulation data. They proposed a structured DNN to enforce the initial and
boundary conditions and the Navier-Stokes (NS) equation were incorporated into
the loss of the DNN in the training. [39] proposed a novel deep learning (DL)
approach (Point net architecture) for flow prediction in irregular geometries
when the flow field is either a function of the size and shape of the bluff
body or the shape of the domain. The grid vertices (spatial positions) of the
mesh in the CFD domain were taken as the input to the DL model and
corresponding flow parameters at those points were considered as output. The
point net architecture learns the non-linear relationship between the inputs
and outputs. The Point net model was trained for in-compressible laminar
steady flow past a cylinder and for testing its generalizability, it was used
for prediction of flow around multiple objects and airfoils. The ML model
predictions are found to be satisfactory and also accurate.

Figure 23: Sample input and output data for the point-net [39].

####  4.9.2 Turbulence modeling with ML

Turbulent flows are a classification of fluid flows that are characterised by
the manifestation of spatio-temporal chaos, hyper-sensitivity to
perturbations, increased rates of diffusion, heat and mass transfer, etc. As
has been observed turbulence is the norm and not the exception in nature [71].
In engineering context the ability to predict the evolution of turbulence is
of critical importance [85]. Because of the chaotic nature exact numerical
prediction of turbulent flows is impracticable. Most engineering CFD studies
rely on turbulence models to account for turbulence. The accuracy of CFD
simulations are largely dependent on choice of turbulence models.

The simplest class of turbulence models are the mixing length based models,
also referred to as one equation models [103]. While these are simple and
computationally inexpensive they require extensive input parameters for each
case. Many of these parameters cannot be determined without reliable CFD
simulations leading to a paradoxical situation. Because of this one equation
models are not regularly used in engineering applications. The second category
of turbulence models is the eddy viscosity based models that includes popular
models like the $k-\epsilon$, $k-\omega$ models. These use the concept of an
eddy viscosity to form a constitutive equation between the Reynolds stresses
and the instantaneous mean gradients. Eddy viscosity based models are
universal, robust and computationally inexpensive. But they have significant
limitations in flows separation and re-attachment [104, 60], flows around
inhomogeneities like walls [85], flows with moderate to high degrees of
anisotropy [85, 61], etc. The final category of turbulence models are Reynolds
Stress Models, that utilize the Reynolds Stress Transport Equations to
formulate individual transport equations for the components of the Reynolds
stress tensor. These include the Launder-Reece-Rodi (LRR) model [47], the
Speziale-Sarkar-Gatski (SSG) model [105, 97], the Mishra-Girimaji model [63,
65], etc. Reynolds stress models offer higher accuracy and robustness at a
higher computational cost. However Reynolds stress models have limitations as
well especially in flows with high influence of rotational effects [62],
significant streamline curvature [64], etc. We observe that while there are
many different turbulence models, they all have significant limitations that
affect their accuracy, their applicability and their robustness. All the above
mentioned models are developed by calibrating the model coefficients with
respect to experimental or direct numerical simulation(DNS) data. With
increase in computational facilities and data storage capacity and
advancements in the ML techniques, current emphasis of turbulence researchers
have been shifted towards development of turbulence models by using different
ML algorithms [35] such as random forest, gradient boosting trees and deep
neural networks. In this section, a detailed discussion turbulence models
developed with ML approaches will be provided.

[18] proposed new methods in turbulence and transition modeling using neural
networks and Gaussian processes. They developed improved functional forms
using ML and applied those functional forms to predict the flow field. [101]
used neural networks for developing model augmentations for the Spalart-
Allmaras model. The model forms are constructed and incorporated into the CFD
solver. [52] used deep neural networks to develop a model for Reynolds stress
anisotropy tensor by using high fidelity DNS data. They have proposed a new
neural network (Tensor Basis Neural Network) that can accommodate the
invariant properties (Galilean Invariance) into the modeling basis. The neural
network structure was optimized using Bayesian optimization[102]. A
significant improvement in flow predictions were noticed when the ML model
predictions are compared against the baseline RANS models. A data-driven
Physics Informed Machine Learning(PIML) approach was proposed by [118], in
which the discrepancies in the RANS modeled Reynolds stresses were
reconstructed. They used Random forests for modeling of the discrepancies with
DNS data and the model developed was used to predict flow field for other flow
cases, which were not used for model development. [121] proposed a systematic
approach for choosing the input feature variables used in turbulence modeling.
They considered strain rate tensor, rotation rate tensor, pressure gradient,
TKE gradient, Wall distance based Reynolds number, turbulence intensity and
ratio of turbulent time-scale to mean strain time-scale as the input features
to model the discrepancy between RANS modeled and true Reynolds stresses. They
used gradient of the flow features in place of the actual value to ensure
Galilean invariance [85]. Finally the predictive capability of the ML model
was tested against square duct and periodic hill flows. [36] proposed Tensor
Basis Random Forest(TBRF), a novel machine learning algorithm to predict the
Reynolds stress anisotropy tensor(RSAT). The use of tensor basis ensures the
Galilean invariance in the prediction of the RSAT. The TBRF was trained with
various flow cases of DNS/LES data and was tested for unseen flows. The
predicted values of the RSAT was finally employed in a RANS solver for flow
prediction in unseen flows. [132] developed surrogate turbulence model for
prediction of flow past airfoils at high Reynolds numbers. Rather than using
DNS or LES data, they utilized results from numerical simulations of Spallart-
Allmaras (SA) model for training the DNN. The model was trained with six
different six different free stream conditions for NACA0012 airfoil.

[80] have proposed a data-driven model for the pressure strain correlation of
turbulence[78, 81] using Reynolds stress anisotropy, dissipation, turbulence
kinetic energy and the strain rate as the input to the DNN . They used DNS
data of flow in channels at different friction Reynolds numbers for the
development of the DNN based model and the model was tested for flows in
different Reynolds numbers and also for a fully unknown test case of Couette
flow in channels. The model predictions was also contrasted against other
established pressure strain correlation models. [79] compared the predictive
capability of random forest, gradient boosted tree and DNN in Reynolds stress
transport modeling. They mainly considered the modeling of the pressure strain
correlation of turbulence. Using Bayesian optimization they recommended the
optimal hyper-parameters of the DNN.

[120] proposed ML based subgrid-scale models(SGS) using DNN and RF for LES.
They considered 30 flow variables as inputs to the ML model and analysed the
feature importance of input variables and found that the filtered velocity and
second derivative of the input velocity has larger influence on the output
variable. The newly proposed ANN based SGS model has a correlation coefficient
of 0.7. The proposed ANN based SGS model was found to be accurate than the
Smagorinsky model and the dynamic Smagorinsky model for flow predictions in
isotropic turbulence. [127] used a deconvolutional artificial neural
network(DANN) for modeling SGS. The input features for the DANN are the
filtered velocities at different spatial points. It was observed that the DANN
model predicted the SGS stress more accurately than the approximate
deconvolution method and the velocity gradient model with a corrrelation
coefficient of $0.99$. [122] developed ANN based algebraic models for the SGS
in LES of turbulence at the Taylor Reynolds number ranging from 180 to 250.
They had constructed the coefficients of the non-linear algebraic model using
the ANN. It was shown that the ANN based non-linear algebraic model predicted
the SGS stress more accurately in a priori tests.

##  5 Challenges and Priority Research Directions

Machine learning applications are having significant successes and impact
across different problems in marine engineering, ocean engineering and naval
architecture. Nonetheless we need to ensure a higher degree of trust in ML
models, enable adequate verification and validation (V&V) of data driven
models, and utilize the strengths of data driven algorithms together with the
decades of purely physics based understanding that has been developed in these
fields [32].

An important step is to include physics and domain knowledge in machine
learning models [3]. This can be done at various levels for example the choice
of the model algorithm and its hyperparameters, the features that are inputted
to the algorithm, or directly appending physics constraints in the loss
functions and optimization. As an illustration we can enforce mass and
momentum conservation as constraints by appending additional losses that
penalize the violation of these constraints in the loss functions of the
turbulence models generated by deep neural networks. This would ensure more
physical data driven models. This would also reduce the space of functions
that the optimizer has to query over and lead to better models that require
less training data.

Another important step is generating measures of interpretability and
explainability from ML models [128]. As an illustration in physics based
models that are commonplace in marine and ocean engineering every term and
each expression has physical meaning and represents different physics based
interactions and processes. Machine learning models do not allow such
understanding and rationalization. This lack of transparency leads to an
understandable lack of trust in ML models from scientists and engineers
working in marine and ocean applications. This also obviates any model
validation. Verification and validation are essential steps to be executed
before the deployment of any physics based models in marine and ocean
engineering and should be so for data driven models as well. Model
verification for ML models can be and is carried out using test datasets to
estimate generalization error. For model validation we need to be able to
unearth the model’s reasoning for its predictions. Due to the black box nature
of algorithms like deep neural networks, this is not possible yet. Hence there
is a critical need to interpret and explain the reasoning of trained ML models
before they can start to replace traditional physics and empiricism based
models.

A final need is to ensure robustness in the performance of ML models [31].
Traditional models in marine and ocean applications have been based on
physics. Physical laws such as symmetries, conservation of mass, momentum and
species, etc are universal and extend to all ranges of parameter space. But
machine learning models are restricted to the range where training data was
utilized for their optimization. In regions of feature space far from the
training data ML models make extremely poor predictions. For their general
application there is a need to guarantee robustness in model performance.

##  6 Concluding remarks

In this article, we have provided a detailed review of application of machine
learning algorithms in ocean engineering, naval architecture and marine
engineering applications. The different machine learning algorithms are
discussed in detail. The ML applications in the marine environment were
classified into several categories such as wave forecasting, AUV operation and
control, ship research, design and reliability analysis of breakwaters,
applications in propeller research etc. The features used in modeling
different marine processes and parameters were discussed in detail. The source
of data utilized in model development are presented. The features used as
inputs to the ML models are discussed in detail. Different algorithms used in
optimization of the ML models were also discussed. A detailed overview of
application of ML in CFD and turbulence modeling were also presented. Based on
this comprehensive review and analysis we point out future directions of
research that may be fruitful for the application of ML to ocean and marine
engineering as well as problems in naval architecture. This review article
will provide an avenue for marine engineers and naval architects to learn the
basics of ML models and its applications in the ocean engineering, naval
architecture and marine engineering applications.

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