## 1 Introduction
Although a large number of modeling studies have been performed on individual compressors [17], complex pipeline networks [18], throttle valves [19], etc., there are few studies on the dynamic characteristics of equipment coupling, real-time simulation, and prediction methods of large systems. The Greitzer lumped parameter model was proposed by [PERSON] [20] in 1976 to capture the dynamic characteristics and instability characteristic mechanism of compressor systems. Subsequently, [PERSON] and [PERSON] [21; 22] developed a renowned unified model of a rotary stall and compressor surge (MG model) in their work. Building upon this foundation, scholars have conducted extensive modeling research on nonlinear systems [5]. With advancements in computer technology, system modeling methods tailored to application requirements have become widely adopted. Series and parallel compressor models based on the Greitzer model and bond graph model were developed by [PERSON] and [PERSON] [23] to analyze the parallel and series characteristics of compressors. [PERSON] et al. [24] [PERSON] deep learning technology to predict the starting characteristics of compressor blades, achieving improved accuracy. [PERSON] et al. [25] proposed a mathematical correction model for the rotation characteristics of aero-engine compressors, which effectively reduced the average error of the performance of aero-engine compressors. For different applications, scholars develop models targeting distinct performance metrics of compressor systems, albeit with inherent limitations. The MG model is inapplicable under unsteady and compressible conditions[PERSON] Data-driven and performance curve optimization models rely heavily on data; they lack insight into the physical mechanisms of the actual compressor and cannot predict performance characteristics beyond the range of the training data. Therefore, the existing compressor modeling method is not suitable for a compressor digital twin. In previous studies, [PERSON] et al. [13] proposed an MDSG (Modular Dynamic System Greitzer) compressor model that takes into account physical mechanism modeling, data-driven modeling, and modular rapid solution[PERSON] However, the model still has limitations in the application of data and the interaction between simulation space and physical devices. In short, to obtain a compressor modeling method that meets the requirements of digital twin, it is necessary to integrate a variety of modeling methods and finally realize the simulation, prediction, monitoring, optimization, and other functions. The goal of this paper is to develop a hybrid modeling method for the BPNN-MDSG ATF compressor digital twin. Building on the MDSG modeling approach, we improve the integration and utilization of twin data. By using BPNN and MDSG, we train the neural network to determine key parameters of the compressor's performance curve. In creating the digital twin model for an actual ATF system, we use sensor signals as control conditions in virtual space, performing offline real-time simulations under typical operating conditions to validate the reliability of the BPNN-MDSG modeling method. We conduct feature prediction and optimization of operational strategies within virtual space while also discussing the dynamic impact of the anti-surge valve on the ATF system. Based on digital twin predictions, characteristic graphs depicting stable operation and valve performance are generated to guide practical equipment.