## 2 Literature Review  
[PERSON] placed particles in an infinitely large fluid medium to observe their settling velocity, obtained the relationship between the Reynolds number and the drag coefficient, and established [PERSON] law for Newtonian fluids under different flow states to describe the free settling law of single particles in liquids [3]. Early research on single-particle settling has gradually evolved to consider the comprehensive effects of various factors such as fluid properties, particle shape, particle size, and crack wall [4]. For example, researchers have experimentally studied the settling behavior of proppant particles in viscoelastic fluids and established corresponding settling velocity models [5]. At the same time, through numerical simulation methods, researchers simulated the convection, settlement, and other forms of movement of proppants in cracks to better predict their distribution and transport patterns [6]. These research results not only provide a theoretical basis for understanding the settling process of proppants, but also provide guidance for practical engineering applications. In the study of particle transport laws, foreign research started earlier and achieved a series of important results [7]. Researchers studied the movement mode of proppants in cracks, including settlement, convection, and lateral transport, and established corresponding mathematical models and numerical calculation methods. These studies have revealed the migration mechanisms and the distribution patterns of proppants in fractures, thus providing a basis for optimizing fracturing design and improving fracturing effectiveness [8; 9]. In contrast, domestic research started relatively late, but significant progress has been made in recent years. Drawing on foreign research achievements in combination with the actual situation in China, domestic scholars have carried out large amounts of experimental research and theoretical analysis work. Researchers conducted in-depth research on the settlement and transport laws of proppants through a combination of experiments and numerical simulations [10]. For example, by analyzing the force and motion mechanisms of particles in solid-liquid two-phase flows, the settlement formula of proppant in fracturing fluid was derived, and a corresponding mathematical model was established [11]. In addition, the influence of different parameters on the settling and migration patterns of proppants was simulated through experiments, providing an important theoretical basis for optimizing fracturing processes and improving oil and gas extraction efficiency [12]. At present, some achievements have been made in the study of the transport and settlement laws of proppants both domestically and internationally, but there are still some challenges and problems, including how to more accurately describe the movement process of proppant in cracks and how to consider the influence of factors such as crack morphology and rock properties on proppant transport [13]. [PERSON], M et al. compared simulations to experiments to find the values of the interfacial adhesion surface energy and the rolling friction coefficient between particles used for simulation [14]. This article proposes a method based on a multi-task learning network to fit the migration and settling patterns of backflow proppants in tight sandstone fracturing, providing a better model for subsequent fracturing backflow. In the future, with the deepening of research and technological progress, we believe that these problems will be better solved.