Even though fracture in solids can be rationalized in continuum mechanics, local processes such as the path selection and the formation of facets and kinks along the crack edges cannot be resolved in this framework. The problem is addressed by developing a high-fidelity neural network-based force field NN-F3. An active-learning approach is taken to capture the high strain and non-equilibrium nature of the crack tips in 2D crystals such as graphene and h-BN, which has not been satisfactorily addressed by existing empirical and machine-learning force fields. Atomistic simulations using NN-F3 resolve spatial complexities from lattice-scale kinks to sample-scale crack patterns, which are discussed directly with continuum mechanics predictions and experimental observation. The results show that kinking or deflection of the cracks defines the roughness of cleaved edges and is explained by the alternation of the stress intensity factors. We also find that the selection of crack paths cannot be determined by the anisotropy in the energies of relaxed edges as widely referred to in the literature. The distortion and undercoordination of the cleaved edges play critical roles in the fracture process, which have to be incorporated into the models to predict the crack paths. Measures of fracture toughness are extracted from the fracture patterns, the critical stress intensity factors, or the energies of edges in the intermediate, unrelaxed states.