Partial differential equations and machine learning integration for transit-oriented development

Ahad Amini Pishro

doi:10.1016/j.asoc.2025.113703

Partial differential equations and machine learning integration for transit-oriented development

2025-08-07

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DOI：10.1016/j.asoc.2025.113703

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• Pioneering PDE-ML Integration in TOD: This study presents the first integration of PDEs with supervised ML to classify rail transit stations within a TOD framework. • Heat Equation Applied to NPRT Model: This research applies the heat equation to the NPRT model, providing a novel mathematical approach to capture spatiotemporal passenger dynamics in transit systems. • Balanced Accuracy and Interpretability: Though slightly less accurate than advanced ML models (e.g., DDNN with MSE 0.0034), the PDE-NPRT model performs well (MSE 0.0075–0.0222) and offers greater interpretability. • Multi-Layer Modeling and Validation: A multi-layer framework using regression, clustering, PDEs, and neural networks improves ridership prediction and congestion analysis, with clustering validated by external indices and real-world data.

Keywords:

PDE-ML integration

heat equation

NPRT model

transit-oriented development

ridership prediction

Partial differential equations and machine learning integration for transit-oriented development

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