## 5 Conclusions  
The BP neural network algorithm, which was based on POI big data, was leveraged to optimize the expansion of commercial space in the central urban area of Weinan City. This study revealed key insights that significantly contribute to urban development and commercial spatial planning research.  
1. This study, which dissected the city into 1097 grid cells, utilized a sophisticated machine learning model to refine the commercial landscape, yielding an R\({}^{2}\) value of 0.7046. The optimization effectively increased the number of commercial facilities from 44,034 to 49,871, showcasing a marked progression in urban commercial optimization. This positive trajectory underscored the viability and reliability of the data-driven approach taken in research, thereby enriching the corpus of urban planning literature with practical, data-backed insights for spatial planning.
2. Conforming to established urban economic theories, such as agglomeration theory and central place theory, this study's results delineated two principal clusters of commercial agglomeration within the city's downtown. The preferential expansion to the north and west delineated a targeted direction for future commercial space development, reflecting a broader pattern of urban spatial growth favoring agglomeration economies. These outcomes not only resonate with previous findings in urban spatial studies but also highlight the relevance of theoretical frameworks in decoding the complexities of commercial space distribution.  
Figure 10: Space guide diagram.  
3. This research suggests a three-tiered optimization strategy for the commercial space in Weinan City's center, encompassing spatial structuring, a development trajectory, and regulatory guidelines. It envisions a multi-centered spatial structure, advocates for a multi-directional development axis, and prescribes adherence to a principle where office space developments precede and inform commercial space expansions. This holistic strategy offers novel insights into urban commercial space dynamics, proposing a synchronized approach to commercial and office space development.  
In summary, the commercial landscape in Weinan City's center is poised for growth, with an emphasis on multi-centric and multi-axis development strategies that are energized with the progression of office spaces. The insights garnered from this study significantly contribute to the formulation of nuanced urban commercial development plans and enhance the scholarly understanding of urban commercial space evolution.  
However, this study was not without its limitations. The reliance on current POI data may not fully account for future changes in urban dynamics, including evolving economic conditions and policy shifts. Further research is needed to incorporate predictive models that account for these variables and to explore the interplay between commercial space development and other urban factors, such as residential patterns and public amenities. Future investigations could also expand upon the integration of real-time data analytics and the exploration of adaptive planning strategies that can dynamically respond to urban growth patterns. These avenues will continue to refine the precision of urban planning and contribute to the sustainable development of urban commercial spaces.  
Conceptualization, D.Y. and J.Z.; methodology, D.Y.; software, J.Z.; validation, D.Y., J.Z. and P.X.; formal analysis, D.Y.; investigation, J.Z.; resources, P.X.; data curation, J.Z.; writing--original draft preparation, J.Z.; writing--review and editing, D.Y.; visualization, P.X.; supervision, D.Y.; project administration, D.Y.; funding acquisition, D.Y. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The data presented in this study are available on request from the corresponding author.  
The authors declare no conflicts of interest.