## 1 Introduction  
Surface subsidence caused by underground coal mining is a global problem [1; 2; 3; 4; 5]. After coal mining, the original rock stress of the overlying rock strata is redistributed and eventually reaches a new balance through bending, collapse, and spalling, which eventually leads to a series of geological disasters (surface subsidence, damage to buildings, landslides, etc.). Therefore, predicting the surface deformation caused by underground mining in advance can not only help evaluate damage to surface buildings but also provide data support for improving the upper limits of underground coal mining [6; 7; 8; 9]. In the traditional mining subsidence research process, two monitoring lines are usually established on the surface of the first mining face in the mining area. Traditional surveying and mapping technologies (such as geometric leveling and GPS-RTK technology) are used to obtain the three-dimensional deformation of the surface. The parameters of the prediction model are inverted and combined with underground mining information and prediction models. Then, the surface deformation likely to be caused by subsequent mining is predicted based on the obtained parameters [10; 11; 12]. The disadvantages of this approach are high monitoring costs, labor intensity, and the difficulty of meeting the requirements of high temporal and spatial monitoring resolution in mining areas. InSAR technology has the advantages of low cost, short monitoring cycles, and large coverage. It provides an opportunity to overcome the shortcomings of traditional monitoring technology. However, due to drastic surface deformation in mining areas, it is prone to decoherence and struggles to monitor large deformation areas [13; 14; 15; 16]. Underground mining usually involves inadequate, sufficient, and super-sufficient dynamic mining processes, so the surface deformation it causes is a complex, gradual, and nonlinear spatiotemporal evolution process. Most existing prediction models were established under the assumption of stable surface settlement conditions. Since surface stability requires a certain amount of time to establish, if the prediction parameters under stable settlement conditions are directly used to predict the deformation during mining, the surface deformation value will be overestimated to a certain extent. In order to overcome these defects, the most common solution at present is to multiply a time function on the basis of the prediction model to correct it. Experts and scholars have proposed different time functions to express the surface deformation variable. One is the Knothe time function and its improved model [17; 18; 19; 20; 21] and the other is a multi-parameter function such as the Sroka-Schoper, B-normal, Weibull, EnKF methods, Hook, Gompertz, arc tangent, and logistic [22; 23; 24; 25; 26; 27] functions. However, some of the above improved functions still have shortcomings, such as too many parameters and parameter selection difficulties, which reduce the model's estimated accuracy to a certain extent. Based on this, relevant scholars have integrated the probability integral method prediction model (PIM) with the dynamic prediction function and combined it with InSAR-measured data [28; 29; 30; 31; 32] to achieve the prediction of dynamic deformation over a large area of a mining area, which has greatly expanded the application field of InSAR. However, the above methods have the following two main problems. First, the accuracy of a dynamic prediction model based on InSAR technology depends on the accuracy of InSAR monitoring and the coverage of monitoring points. However, the large gradient deformation in the center of the mining basin often causes the InSAR monitoring technology to lose coherence, resulting in an inability to obtain effective monitoring points or an underestimation of the deformation. Second, the traditional dynamic prediction model achieves the purpose of dynamic prediction by multiplying the prediction model by a time function.