## 1 Introduction  
In recent years, a global slowdown in water and hydropower construction has led countries to pay attention to the management of existing water and hydropower facilities [1], so the effective development of water \"four pres\" technology has become a key engineering problem in the field of dam safety monitoring [2; 3; 4]. Dams are subjected to a variety of factors such as the nature of the dam foundation engineering, temperature conditions, structural design, and their own loading during their complex and variable service, and their properties will gradually deteriorate with increasing service life [5; 6; 7]. This deterioration may lead to an increase in the probability of accidents in dams, which in turn may cause serious property damage and casualties in the surrounding towns [8; 9; 10]. Therefore, the focus of research has shifted to how to reasonably and effectively construct dam deformation early warning and forecasting models. Among them, it is of great practical importance to rely on actual dam measurement data to study the nonlinear relationship between dam deformation and each deformation characteristic factor, to establish a reliable dam deformation monitoring model, to accurately predict the deformation of dams, and to comprehensively understand their operational status to ensure the long-term safety of dam projects [11]. As the analysis of deformation monitoring information has developed toward a more in-depth field, many scholars have proposed some new methods and techniques to monitor the deformation of dams. Among them, optimization combination models, digital filtering, and principal component regression are widely used in the field of dam safety monitoring [12; 13; 14]. At present, in practical engineering, deformation monitoring models can be divided into three main categories, including statistical models, deterministic models, and machine learning models [15; 16]. Statistical models are based on statistical analysis and the modeling of large amounts of deformation monitoring data to derive probability distributions and trend predictions of the deformation behavior of dams [17]. Typical statistical models are the hydrostatic-thermal-time (HTT) model [18] and the hydrostatic-season-time (HST) model [19]. Among them, the HTT model is applicable when the temperature measurement points of the dam body and foundation can fully describe the variation in its temperature field, and the measured values of each temperature measurement point are used as the temperature components [18]. The HST model, on the other hand, uses harmonic factors to describe the temperature components when the temperature monitoring data inside the dam are lacking or insufficient, and they usually coincide with the deformation of the dam in most cases [19]. Deterministic models are physical models based on the structural properties, material properties, and loads of a dam. By modeling and analyzing the mechanical behavior of a dam, its deformation response and safety conditions can be predicted [20]. Deterministic models usually use numerical computational methods, such as finite element analysis [21]. However, traditional deterministic modeling methods have several limitations and challenges. First, the implementation of the method may require significant time and effort because of the need to build complex models and perform detailed numerical calculations. Second, some assumptions and simplifications are often required for the geometry and boundary conditions of the dam, which may negatively affect the accuracy of the predictions [22; 23]. In addition, the lack of long-term monitoring data makes it difficult for these models to accurately consider the long-term deformation behavior of dams [24]. With the continuous progress of machine learning technology, its application in dam deformation prediction and analysis has become a hot spot for research.