<p>Understanding and modeling the governing equations of complex network dynamics are fundamental for predicting and controlling system behaviors. Library-based sparse regression approaches, such as sparse identification of nonlinear dynamics (SINDy), have demonstrated promising results in data-driven discovery of dynamical models. Nevertheless, their performance often deteriorates under network complexity, measurement noise, and incomplete topological information, leading to instability and inaccurate term selection in high-dimensional settings. To address these challenges, we propose TS-SPIND, a hierarchical tree search-based framework for the sparse identification of nonlinear network dynamics directly from time-series data. TS-SPIND utilizes a probabilistic tree-search strategy to explore and combine candidate functions, effectively balancing exploration and exploitation during the model discovery process. The hierarchical search progresses from root to leaf nodes, generating optimal models across various sparsity levels. These inferred models preserve stable bifurcation thresholds, thereby supporting reliable resilience analysis. Comprehensive experiments on representative systems— including coupled oscillators, epidemic spreading, gene regulation, and brain networks— show that TS-SPIND consistently improves identification accuracy, and robustness under severe conditions of data noise, missing, and spurious links. These results demonstrate that TS-SPIND provides an interpretable and robust computational approach for discovering governing equations of complex network dynamics.</p>