## 1 Introduction
When we apply a BEM to a boundary-value problem (BVP) with a zero-thickness plate in a numerical domain, the standard single-domain BEM has difficulty in guaranteeing a unique solution due to rank deficiency. For unique solutions to these BVPs, we must depend on the multi-domain BEM or the dual boundary element method (DBEM), including the hyper-singular integral formulation. In ref. [20], the authors developed the DBEM to address the rank deficiency problem inherent in standard BEM. The core concept of DBEM is to resolve the rank deficiency by employing hyper-singular boundary integral equations, thereby leading to a full DBEM formulation. Several researchers applied the DBEM to investigate the hydrodynamic performance of water waves over zero-thickness barriers [21; 22; 23; 24; 25; 26; 27]. The article [22] used the DBEM to analyze the interaction between zero-thickness immersed barriers and normally incident waves. The authors in [23] developed the DBEM for modified Helmholtz equations to evaluate the hydrodynamic performance of bottom-fixed thin vertical barriers in oblique incident waves. Article [24] extended the DBEM to treat immersed thin vertical and inclined wave barriers. The authors in [25] employed the DBEM to solve the scattering problem involving a locked horizontal zero-thickness wave barrier and compared the results with a finite-thickness wave barrier using a standard BEM. Additionally, the numerical resultsfrom both two BEM approaches were compared with experimental measurements. The authors of [28] investigated the inclined single porous and dual parallel porous plates to develop an efficient wave absorber using a DBEM. The self-conducted experiment validated the numerical solutions. It was found that an inclined single porous plate proved to work well as a competitive wave absorber when compared to the dual parallel plates. Machine learning is becoming increasingly popular for optimizing design parameters in engineering applications. Artificial neural network (ANN) models are especially widely adopted as promising machine learning (ML) models because they can learn complex patterns/relations and make accurate predictions. It is modeled after simplified representations of biological neurons in the brain and consists of interconnected nodes, where each circular node represents an artificial neuron, and the arrows represent the connections between the input and output. With multiple hidden layers, ANN models allow the neural network to identify and interpret complex relationships between input and output features in the data. Thus, it is a powerful tool for applications involving intricate data patterns and relationships. In ref. [29], the authors employed an ANN model to optimize the design of a multilayer porous wave absorber. The porosity and submergence depth of the topmost plate were identified as the key design parameters, with their optimal ranges specified. Article [30] employed a machine learning approach for designing and additively manufacturing porous sound absorbers, utilizing two models: an artificial neural network and a k-nearest neighbor algorithm. The results showed that both models could accurately predict design parameters. A deep learning-based framework is developed in [31] for designing random porous metal structures with a focus on maximizing energy absorption. The authors of [32] proposed a simple approach to controlling plunger wavemakers using an ML approach with a neural network model. Article [33] used an ANN model to actively control the absorption of random waves in a wave flume. The authors of [34] utilized machine learning models to incorporate nonlinear viscous damping for a heavy disk with specified porosities in the time domain. Four different ML models--decision tree, random forest, support vector machine, and neural network--were employed and trained to predict the drag coefficient based on disk porosity and the Keulegan-Carpenter (KC) number as input features.