## 1 Introduction  
Gas turbines offer advantages such as lower emissions by using mainly natural gas [1], rapid start-up and acceleration [2], high efficiency with higher combustion temperature [3], and fuel flexibility with varied fuel options while maintaining performance [4]. These benefits have led to widespread industrial applications. For instance, gas turbines have become one of the main power sources in various applications, including thrust for aircraft jet engines, as described by [PERSON] et al. [5], mechanism power for driving compressors or ship propulsion, and electricity generation through generators, as introduced by [PERSON] et al. [6]. With increasing renewable energy integration, the fast start-stop and wide load characteristics of gas turbines make them essential for peak shaving in power systems [7]. To ensure operational efficiency under diverse conditions, accurate predictive modeling of gas turbine power output is crucial [8]. Significant attention has been devoted to the research of gas turbine modeling methods, which can be categorized into two main approaches: mechanism models and data-driven models. Mechanism models describe the material and energy conversion processes of gas turbines, establishing equations based on principles such as energy conservation, material conservation, and thermodynamic properties. An important type of mechanism model is the component-level model, which relies heavily on accurate component characteristic maps that are difficult to obtain [9]. To solve this problem, [PERSON] et al. [10] proposed a design-point performance adaptation approach using the Newton-Raphson method. [PERSON] et al. [11] proposed a new generation method to solve the problem of lacking data, in which the initial map was obtained according to a set of steady operating data, and the coefficients were tuned through sets of transient data. [PERSON] et al. [12] proposed a segmentation-based joint steady-state and transient performance adaptation technique, which takes both the idle point and the design point to scale the performance maps. [PERSON] et al. [13] developed an improved analytical approach for components and employed sensitivity analysis to determine the weight coefficients of the tuning factors, which aimed to enhance the performance adaptation and diagnostics of gas turbines. [PERSON] et al. [14] developed an adaptive model for a PG 9171E gas turbine unit to realize the performance calculation in a shorter time. [PERSON] et al. [15] tested several Kalman Filtering techniques to obtain improved temperature forecasts, which were then used to obtain output power predictions. An open-cycle gas turbine was used to demonstrate the applicability of the proposed method. [PERSON] et al. [16] performed CFD simulations of the aerodynamic and thermal processes of gas turbine blades. To optimize blade designs for enhanced gas turbine performance, they designed and implemented a nested optimization workflow incorporating an Artificial Neural Network (ANN). The mechanism model reveals the internal operating mechanism of the gas turbine and possesses strong interpretability. However, the mechanism model inevitably introduces simplifying assumptions to varying degrees, leading to deviations from actual operating conditions, or else it would suffer a significant computational burden. With the continuous development of industrial digitization, the operational data stored in the Distributed Control System (DCS) of power plants has rapidly increased. Data-driven models can directly learn and identify operational patterns from existing operational data, which helps to understand the underlying laws of the electricity production system and improve the reliability and economy of the equipment. With the successful application of machine learning in various fields, there is an increasing number of studies focusing on data-driven modeling of gas turbines.