## 5 Conclusions and Limitations
### Limitations and Future Research Directions  
Despite the contributions of this research to the understanding of railway network resilience, several methodological and analytical limitations warrant acknowledgment and provide avenues for subsequent scholarly inquiry. The network abstraction employed in this study necessarily simplifies certain operational complexities of railway systems. Further refinement of the modeling framework should address temporal heterogeneity in train scheduling and passenger flow distributions, capacity constraints and congestion effects at critical network nodes and edges, and intermodal transfer dynamics at significant interchange junctions within the broader transportation ecosystem. The present investigation provides predominantly static characterizations of network resilience. Subsequent research endeavors should extend the analytical framework to incorporate spatio-temporal modeling methodologies that account for circadian, seasonal, and annual operational variations. Additionally, correlation analyses between socio-economic development trajectories and corresponding resilience metric evolution would enhance our understanding of how railway networks evolve in response to changing social and economic conditions. Adaptive response mechanisms that emulate the progressive refinement of institutional interventions following perturbation events represent another promising direction for investigation. The optimization framework implemented in this study employs relatively simplified constraint conditions. Future scholarly work should develop more sophisticated optimization paradigms that integrate fiscal constraints and implementation periodicity considerations. Formulation of multi-objective optimization models that equilibrate resilience enhancement with economic efficiency metrics would provide more practical guidance for railway planning and management. These frameworks could support scenario-based sensitivity analysis in emergency preparedness contexts, allowing for more robust contingency planning. Future investigations should endeavor to bridge the theoretical-practical divide through empirical case studies of documented railway disruption incidents and their corresponding recovery trajectories. Development of predictive algorithmic frameworks for cascade failure anticipation and formulation of standardized resilience assessment methodologies would significantly enhance the practical application of the research findings. Such advancements would contribute substantially to the enhancement of critical infrastructural reliability and operational sustainability in the face of diverse perturbation scenarios, ultimately improving the resilience of railway transportation systems against various disturbances. Data curation, Y.L. ; formal analysis, K.S. ; funding acquisition, T.D. ; methodology, T.D., Y.L. and K.S. ; project administration, J.C.; supervision, J.C.; validation, T.D. and Y.L. ; writing--original draft, T.D., Y.L. and K.S. ; writing--review and editing, J.C. All authors have read and agreed to the published version of the manuscript. This research was supported by the Science and Technology Research and Development Program of China State Railway Group Co., Ltd. (Grant Nos. N2024S009 and N2024X016) and the Innovation Project of China Railway International Co., Ltd. (Grant No. CRIC-CX2024 BM02). Not applicable. The original contributions of this study are included in the article, and further inquiries can be directed to the corresponding author. **Conflicts of Interest:** Author [PERSON] was employed by the company China Railway International Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. The authors declare that this study received funding from China State Railway Group Co., Ltd. and China Railway International Co., Ltd.