# Attention-Based Hydrogen Refueling Imputation Model for Efficient Hydrogen Refueling Stations
## 1 Introduction  
The 1970s energy crises surfaced the vulnerability of dependence on fossil fuels, sparking various studies of alternative energy sources [1]. Additionally, environmental concerns such as air pollution and global warming have revealed a demand for cleaner and more sustainable energy. These have led to the development of renewable energy sources, including hydrogen, wind, and solar [2]. Hydrogen is a potentially emissions-free alternative fuel that produces only water as a by-product. It could be a key solution for reducing air pollution and mitigating climate change [3]. Hydrogen can contribute to a clean energy cycle if it is obtained by electrolysis of water from renewable energy sources while generating electricity in fuel cells. Recently, as various studies have been conducted, interest in hydrogen vehicles has also increased. With significant policy support, the market has been growing.  
Despite these advantages and interests, its optimization methodology is still in the early stages of development [4] because hydrogen energy is a relatively new energy source compared to wind and solar energy sources. Note that the optimization methodology can enhance the sustainability and effectiveness of hydrogen systems [5]. It should be a significant consideration. In particular, hydrogen refueling stations (HRSs) typically comprise equipment for hydrogen supply, compression, gas storage, and dispensing to refuel vehicles. These components significantly impact refueling efficiency and costs [6]. Thus, the optimization of diverse components, numerically, is required for efficient HSRs.  
Recently, many optimization methodologies have been proposed to cope with the increasing demand for hydrogen vehicles. For instance, [PERSON] and [PERSON] [7] proposed anoptimization model for mobile HRSs to address infrastructure gaps. [PERSON] et al. [8] proposed an energy management system with an optimization model to minimize operating costs and improve efficiency. In this paper, we propose an optimization model estimating missing values, which occur randomly under various factors, for efficient HRSs.  
During hydrogen refueling, numerical data values may be missing due to internal and external factors, such as pressure and temperature. This affects the refueling performance of HRSs. For example, in an actual HRS, a certain amount of hydrogen energy must be supplied to a hydrogen vehicle within a specific time. However, the state of charge (SoC) of the vehicle depends on various independent variables observed by diverse equipment, so missing values in these independent variables can lead to inaccurate SoC estimation. This causes oversupply and undersupply.  
To overcome this issue, we propose an attention-based hydrogen refueling imputation (AHRI) model, which restores the missing values of the dependent variable using intact elements of various independent variables. The AHRI model consists of the attention mechanism [9] and long short-term memory (LSTM) [10] modules to effectively capture dependencies of variable and time, respectively. In particular, considering data variables can vary depending on environmental conditions and equipment in an HRS, we use the attention mechanism. It determines the primary features, which improves the predictive performance and helps adapt to new conditions. With the proposed model, we provide an optimal hydrogen optimization process, which can be performed on real-time data [11] by an HRS and utilized in automated system operation to optimize internal and external factors of hydrogen refueling.  
This work has the following major contributions:  
* We propose a novel imputation model (AHRI) to restore the missing values that occur during hydrogen refueling due to internal and external factors.
* We constitute an AHRI model with an attention mechanism and LSTM models to capture the dependencies of variables and time effectively.
* The proposed AHRI significantly outperforms conventional imputation algorithms on the real data collected when hydrogen vehicles are charged [11].