## 1 Introduction  
Artificial neural network (ANN) models have been widely used for prediction and forecast in various areas including finance, medicine, power generation, water resources and environmental sciences. Although the basic concept of artificial neurons was first proposed in 1943 [1], applications of ANNs have blossomed after the introduction of the back-propagation (BP) training algorithm for feedforward ANNs in 1986 [2], and the explosion in the capabilities of computers accelerated the employment of ANNs. The ANN models have also been used in various coastal and nearshore research [3; 4; 5; 6; 7; 8; 9; 10]. An ANN model is a data-driven model aiming to mimic the systematic relationship between input and output data by training the network based on a large amount of data [11]. It is composed of the information-processing units called neurons, which are fully connected with different weights indicating the strength of the relationships between input and output data. Biases are also necessary to increase or decrease the net input of the neurons [12]. With the randomly selected initial weights and biases, the neural network cannot accurately estimate the required output. Therefore, the weights and biases are continuously modified by the so-called training so that the difference between the model output and target (observed) value becomes small. To train the network, the error function is defined as the sum of the squares of the differences. To minimize the error function, the BP training approach generally uses a gradient descent algorithm [11]. However, it can give a local minimum value of the error function as shown in Figure 1, and it is sensitive to the initial weights and biases. In other words, the gradient descent method is prone to giving a local minimum or maximum value [13; 14]. If the initial weights and biases are fortunately selected to be close to the values that give the global minimum of the error function, the global minimum would be found by the gradient method. On the other hand, as expected in most cases, if they are selected to be far from the optimal values as shown by 'Start' in Figure 1, the final destination would be the local minimum that is marked by 'End' in the figure. As a consequence of local minimization, most ANNs provide erroneous results. To find the optimal initial weights and biases that lead into the global minimum of the error function, a Monte-Carlo simulation is often used, which, however, takes a long computation time. Moreover, even if we find the global optimal weights and biases by the simulation, they cannot be reproduced by the general users of the ANN model. Research has been performed to reveal and overcome the problem of local minimization in the ANN model. [PERSON] and [PERSON] [15] demonstrated that the BP training algorithm has large dependency on the initial weights by performing a Monte Carlo simulation. [PERSON] and [PERSON] [16] proposed an algorithm based on least-squares methods to determine the optimal initial weights, showing that the algorithm can reduce the model's dependency on the initial weights. Recently, genetic algorithms have been applied to find the optimal initial weights of ANNs and to improve the model accuracy [17; 18; 19]. Ensemble methods have also been implemented to enhance the accuracy of the model. They are also shown to overcome the dependency of the ANN model not only on the initial weights but also on training algorithms and data structure [20; 21; 22; 23]. In this study, we employ the harmony search (HS) algorithm to find the near-global optimal initial weights of ANNs. It is a music-based metaheuristic optimization algorithm developed by [PERSON] _et al._[24] and has been applied to many different optimization problems such as function optimization, design of water distribution networks, engineering optimization, groundwater modeling, model parameter calibration, _etc._ The structure of the HS algorithm is much simpler than other metaheuristic algorithms.