# Inversion Analysis Method for Tunnel and Underground Space Engineering: A Short Review
## 1 Introduction  
In the field of tunnel and underground engineering, the main research objects are the characteristics of excavated rock mass and the surrounding geological environment. During the extremely long process of rock mass formation, a large number of cracks and pores will form in the structure. Coupled with the influence of groundwater, the rock mass will become a discontinuous body composed of various media. This results in extremely complex physical and mechanical properties of the rock mass [1, 2]. Therefore, it is important to invert the initial ground stress and related parameters from on-site monitoring and measurement of displacement, stress, strain, and other multivariate information. By doing so, a tunnel excavation and support plan can be formulated. With the development of construction technology and measurement means, many researchers have begun using measurement data to invert the initial ground stress, structural load, and material characteristic parameters. This replaces previous test methods and facilitates application in follow-up projects. The inverse analysis method involves analyzing physical information data (such as displacement, deformation, stress, strain, or load) measured in the field to establish an effective mapping relationship from the data sample space to the model identification space. It comprises two parts. One is the model identification problem of identifying the model structure style closest to the actual deformation law [3] (such as the constitutive model of geotechnical medium) from the change law of monitoring data. The other is a discussion of the inversion model under linear elastic and nonlinear conditions (stress-strain relationship, time and settlement deformation relationship). Various individual mechanical parameters (such as initial ground stress, structural load, and physical parameters) in the inversion system are identified. Nowadays, many problems are accompanied by inverse problems, such as the most commonly used least square method, which was first proposed by the famous German mathematician [PERSON] in 1795 to calculate the trajectories of planets and comets [4]. In bridge structure monitoring, researchers use the back analysis method to analyze the building structure under the condition of environmental vibration and strong wind. The performance is evaluated, and the results are close to the measured value [5]. In solid geophysical problems, researchers process geophysical data and extract geological data and physical models that are closest to the actual situation [6]. Combined with the data collected by local seismic stations, the prediction of earthquakes in other areas can be realized, and this process is the inversion of geophysical information. From this it can be seen that in practical engineering problems, the study of inverse problems has higher practical value, but compared with forward analysis, inverse analysis still has the characteristics and difficulties of strong nonlinearity, ill-posedness, and the need for a large amount of calculation. With the fourth Industrial Revolution, there is a growing focus on scientific and technological innovation and technological renewal in various engineering fields. Scholars are increasingly using intelligent inversion analysis methods based on optimization algorithms, computer vision, and data mining to solve difficulties existing in the inversion analysis method itself. At the same time, the problems faced by rock mechanics, such as \"limited discretization of data\", \"complexity of failure mechanism\", and \"uncertainty of influencing factors\" have further promoted the discussion of artificial intelligence (Artificial Intelligence, AI) in geotechnical engineering.