## 1 Introduction  
Liquefied natural gas (LNG), as a clean and efficient energy source, has played an increasingly important role in the global energy transition in recent years. With the global emphasis on environmental protection and the optimization of energy structure, natural gas, with its advantages of low carbon emissions and high calorific value, has become one of the key energy sources to replace coal and oil. According to statistics from the Global Carbon Neutral Institute, global gas demand in 2024 increased by about 2.5% year-on-year to reach a record high of 4.200 billion cubic meters [1]. Floating liquefied natural gas storage and regasification units (FLNG SRUs) are considered a vital component of the future LNG supply chain. In this process, one of the key components is the intermediate fluid vaporizer (IFV). The IFV facilitates the conversion of LNG into gaseous natural gas by utilizing seawater or other cooling media. This process necessitates efficient and compact heat exchange equipment such as the printed circuit heat exchanger (PCHE), which is widely recognized as an ideal choice for such applications [2]. Consequently, accurately predicting the local performance of PCHEs, including heat transfer coefficients and other parameters, is essential for optimizing their design and operational efficiency [3]. The accurate prediction of these parameters not only enhances the overall performance of the equipment but also reduces operating costs and improves energy utilization efficiency. For instance, compared with the numerical simulation method, which requires approximately 9 h to achieve convergence, machine learning methods can complete the task in less than an hour [4]. The current research on traditional PCHEs predominantly centers on analyzing their flow and heat transfer characteristics through experimental studies and numerical simulations [5]. The primary aim of these approaches is to establish empirical correlations between flow dynamics and heat transfer performance, thereby enabling precise prediction and optimization of the heat exchanger's behavior during the design phase. Experimental methods involve measuring critical parameters such as fluid flow state, heat transfer efficiency, and pressure drop within the PCHE, offering valuable insights into its actual operational performance [6]. However, experimental methods are limited by high costs, time-consuming procedures, and an inability to comprehensively cover all potential operating conditions [7]. In contrast, numerical simulation methods construct mathematical models to simulate the internal flow and heat transfer processes of the PCHE, facilitating rapid analysis and optimization across a broad spectrum of operating conditions [8]. Numerical simulations not only assist in predicting the performance of PCHE under various scenarios but also provide essential guidance for equipment design [9]. Nevertheless, the accuracy of numerical simulations relies heavily on the fidelity of the flow models and the precision of boundary condition settings, which may lead to discrepancies between model predictions and real-world performance in certain cases. Machine learning, as an emerging field, demonstrates the ability to uncover complex nonlinear relationships that traditional physical models struggle to capture by learning from extensive experimental data. Consequently, it holds substantial promise for the design and optimization of heat exchangers [10]. Particularly in multi-objective optimization, machine learning can simultaneously evaluate multiple design parameters such as thermal efficiency, pressure drop, volume, and cost, thereby providing more precise and efficient solutions for engineering applications [11]. For instance, [PERSON] et al. introduced a novel approach in their energy article by applying machine learning algorithms to PCHEs using supercritical methane as the working fluid, proposing a predictive model based on artificial neural networks (ANNs) with an R\({}^{2}\) value of 0.9996 [12].