Grain boundaries (GBs) undergo migration during heat treatment and mechanical deformation. Learning GB migration behavior is essential for predicting microstructure evolution in crystalline materials, which is crucial for future industrial applications. In this investigation, the non-Arrhenius behavior of GB migration is systematically studied. By considering the effect of driving force on the activation energy for GB migration, the classical thermal-activation equation is modified. This modification explains the previously reported driving force-induced transition in the thermal behavior of GB migration and the 'anti-driving force' phenomena of GB mobility. Moreover, a three-dimensional interface random walk method was developed to extract the GB mobility tensor from thermal fluctuations in GB position. This advancement allows for the determination of all elements in the GB mobility tensor through a unified expression related to the covariance of GB displacement in different directions, verifying the symmetry of the GB mobility tensor as predicted by the Onsager relation. The driving force dependence of β has led to the misconception that shear coupling is not an intrinsic property of GBs. However, the shear coupling tensor, derived from the mobility tensor, accurately predicts the variation of the apparent shear coupling factor β in response to external driving forces, thereby establishing shear coupling as an intrinsic characteristic of GBs. Additionally, the phenomenon of GB stagnation has been widely observed, often attributed to constraints from solutes and impurities. However, GB stagnation can also occur in pure materials. In the investigation, disruptive jumps in GB area were observed, which disturb the coordinated movement of GB atoms, significantly reduce local GB mobility, and lead to overall GB stagnation. These disruptive atomic jumps can be activated by both high driving forces and high temperatures, with even jumps of a few atoms capable of causing the stagnation of an entire GB. This observation provides a supplementary mechanism to existing theories for explaining GB stagnation and non-Arrhenius behavior of GB migration.