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Predicting the trajectories of hydraulic fractures in unconventional reservoirs poses a significant challenge due to the heterogeneous nature of the rock matrix. Obtaining an accurate distribution of rock properties from limited measurements of rock samples near wellbores is difficult. In this study, we propose a deep learning framework that utilizes observations of hydraulic fracture patterns to identify nonuniform distributions of rock properties. Our approach utilizes the deep operator network (DeepONet) to map elastic properties to fracture geometries, and establishes an inverse problem to map fracture geometries back to elastic properties. Our results demonstrate a high level of accuracy in predicting nonplanar paths of single and multiple hydraulic fractures in heterogeneous formations. The well-trained model can rapidly evaluate numerous fracture patterns within seconds, surpassing the efficiency of finite element-based methods. Furthermore, fracture trajectories enable the identification of nonuniform distributions of rock properties. The maximum point-wise error of predicted Young's modulus compared to the ground truth is less than 20 %, with accurate identification of distribution patterns. Only a few regions exhibit relatively large errors, approaching 20 %. The presented approach provides valuable insights for the identification of reservoir properties in engineering applications. [Display omitted] • A deep learning surrogate model to predict nonplanar fracture trajectories in heterogenous formation is established. • Nonuniform distributions of Young's modulus can be identified using fractures data. • The approach presented here has the potential to identify other rock mechanical properties. • The well-trained model outperforms conventional numerical methods in terms of computational efficiency. [ABSTRACT FROM AUTHOR]