Supplemental Materials for "Planning for Leakage-Aware Collaborative Carbon Mitigation: Optimizer-Informed Multi-Agent Reinforcement Learning in Shandong's Dual Metropolitan Areas"
Abstract
This Supplemental Materials file accompanies the manuscript submitted to the Journal of Urban Planning and Development (ASCE). It contains eleven supplementary figures (Figs. S1–S11) and three supplementary tables (Tables S1–S3), whose numbering matches the in-text citations and supports every robustness, calibration, optimizer-comparison, PPO-training, MRIO-cross-check, and accounting-identity claim that does not fit in the main text. CoverageTen cities within Shandong Province forming the inland Jinan metropolitan area and the coastal Jiaodong metropolitan area; temporal scope 2006–2024 (190 city–year panel observations); explicitly differentiated provincial allocation of mitigation burdens across the two metropolitan areas. ContentsSupplementary Figures (Figs. S1–S11) Fig. S1. Comparison of CO₂ emissions and weighted CO₂ intensity between the Jinan and Jiaodong metropolitan areas, 2006–2024.Fig. S2. Standardized heatmap of representative urban heterogeneity indicators.Fig. S3. Relationship between GDP growth and CO₂ growth across cities, 2015–2024.Fig. S4. City-level mean net structural leakage exposure, 2015–2024.Fig. S5. CO₂-reduction and carbon-intensity decline rates in 2035 under scenarios S1–S5.Fig. S6. Gross mitigation-triggered leakage pressure and leakage-pressure-to-reduction ratio across S1–S5.Fig. S7. Temporal holdout performance of city log-linear, damped-trend, and last-observation benchmark models.Fig. S8. Performance of the neutral 70-variable, leakage-aware 70-variable, and leakage-aware 210-variable open-loop optimizers.Fig. S9. Paired effects of leakage penalty, domain randomization, and their joint use relative to matched S3.Fig. S10. Recorded PPO training outcomes and update diagnostics across six trained policies.Fig. S11. Active-versus-frozen S4 outcome differences and action-response magnitudes under identical shocks.Supplementary Tables (Tables S1–S3) Table S1. Disclosed transition and implementation-burden coefficients — per-policy-action GDP response, carbon-intensity-improvement response, net CO₂ response, PIB coefficient cₖ, and calibration basis (e.g., fixed-asset investment / industrial structure for industrial adjustment; municipal / public-utility and water-saving investment for energy efficiency).Table S2. CO₂ consistency diagnostics and temporal holdout benchmark — GDP × CI accounting identity over 190 city–year observations (maximum relative error = 4.38 × 10⁻¹⁶, exact numerical consistency) and 2021–2022 continuity test (regional z = −0.52; maximum city |z| ≈ 0.64, no detected reconstruction breakpoint).Table S3. Independent ten-city MRIO consistency summary — Spearman rank correlation ρ = 0.636 (asymptotic p = 0.048; permutation p = 0.055; positive rank correspondence with small-sample uncertainty) and Pearson correlation r = 0.757 (p = 0.011; positive linear association).Companion DatasetAll numerical inputs, calibrated artefacts, model outputs, and re-executable NumPy/SciPy source listing are deposited as a separate Zenodo record of resource type Dataset (see "Related works" on this record page). Together, the two records provide a complete reproduction chain: this Publication record supplies the figures and tables that summarise the robustness, optimization, and validation analyses, while the Dataset record supplies the underlying panel, leakage network, optimizer parameters, PPO training artefacts, sensitivity records, and source code that produced them. ReusePermitted under the Creative Commons Attribution 4.0 International License (CC BY 4.0). Please cite both this Supplemental Materials record and the associated manuscript (see "Related works"). Third-party MRIO data (Wang et al. 2025; Xia et al. 2024, 2025) are cited to their original publications and must be obtained under applicable terms; they are not redistributed here. Provenance and IntegrityEach figure and table is the direct rendering of values that are deterministically generated from the seeds and provenance hashes stored in the companion Dataset record. SHA-256 checksums in the Dataset record allow independent verification that the inputs to every figure and table have not been modified since deposit. Files have MD5 checksums archived by Zenodo at deposit time and are re-verified nightly by the repository. ContactCorresponding author: Zhen Peng — School of Architecture and Urban Planning, Qingdao University of Technology, Qingdao, Shandong, China. Email: see the manuscript Acknowledgments.
