## 1 Introduction  
With the gradual depletion of shallow mineral resources, mining operations are increasingly extending towards deeper areas, resulting in an increase in the stresses on deep-level tunnels and excavations. The existing stress in the surrounding rock is the result of the superposition of spatio-temporal factors such as excavation unloading, excavation disturbance, and stress redistribution on the original rock stress [1]. Therefore, it is difficult to calculate the existing stress on the rock surrounding the tunnel based on the in situ stress. However, the existing stress in the tunnel surrounding rock is a critical parameter used when assessing tunnel stability and optimizing the design thereof. The methods for obtaining the stress field in mines can be divided into direct measurement and indirect inference [2]. Currently, research into mine stress fields mainly focuses on indirect methods of obtaining stress through inversion techniques. Stress field inversion involves using mathematical and mechanical methods to infer and extrapolate the distribution of in situ stress in a target area based on stress measurements at individual discrete points on-site. Common methods for measuring discrete point stresses include the borehole stress relief method [3; 4; 5], hydraulic fracturing [6; 7; 8], and Kaiser effect [9; 10]. However, due to cost constraints, underground space limitations, and repeated damage to tunnel surrounding rock, these methods are difficult to apply directly to measurement of the stress in tunnels or deep-level excavations. In recent years, with the development of computer simulation technology, researchers have used finite measurement points and computer-based methods to invert the stress field, and various techniques have emerged [11]. Common methods include regression analysis [12], artificial neural networks [13], the Surrogate Model Accelerated Random Search [14], and partial least-squares regression [15]. Some researchers have also improved and optimized these methods for engineering applications. For example, [PERSON] et al. [16] proposed a two-stage optimization algorithm to assess the stress field in the underground chambers of the Guangdong Hydropower Station, Yunnan Province, China. [PERSON] et al. [17] trained an evolutionary neural network using stress measurement data and simulated the three-dimensional stress distribution at a project site. [PERSON] et al. [18] overcame the limitations of Linear Elastic Fracture Mechanics analysis using cohesive-zone elements within a finite element framework, providing a fast and reasonably accurate method to estimate the maximum and minimum horizontal stresses using casing fracturing data. [PERSON] et al. [19] proposed a method of optimizing the lateral stress coefficient of the initial stress field using a Generative Adversarial Network in FLAC 3D. [PERSON] et al. [20] utilized evolutionary neural networks to establish a nonlinear mapping relationship between boundary conditions and measured point stresses, inputting measured in situ stresses into the neural network to acquire the corresponding boundary conditions. However, the above inversion methods primarily focus on stress as the reference quantity and study the stress field in a specific geological body under certain conditions, neglecting the influence of excavation of the rock. Additionally, when the stress is high, the rock mass may be in a plastic or damaged state. Therefore, relying on elastic criteria for inversion in deep areas can lead to a lower accuracy. To address the limitations of existing inversion methods, this study proposes a stress-field inversion method for deeply buried drifts based on a finite number of points at which the surface strain is measured. This method uses the elastic strains in the surrounding rock obtained through the borehole stress relief method as target values.