Data complexity directly affects the dynamics of complex systems, which in turn influences the accuracy and robustness of forecasting models. However, the load data exhibit complex features such as self-similarity, long-term memory, randomness, and chaos. This study aims to quantify and evaluate the complexity features of natural gas loads and to develop a multi-step-ahead forecasting model that integrates data decomposition and ensemble deep learning while considering these complexity features. Firstly, the complexity features of the series are quantified by rolling the fractal dimension, Hurst exponent, sample entropy, and maximum Lyapunov exponent. The analysis contributes to understanding data characteristics and provides information on complex features. Secondly, the ensemble learning eXtreme Gradient Boosting (XGBoost) can effectively screen complexity features and meteorological factors. Concurrently, variational mode decomposition (VMD) provides frequency-domain decomposition capability, while the gated recurrent unit (GRU) captures long-term dependencies. This synergy enables effective learning of local features and long-term temporal patterns, resulting in precise predictions. The results indicate that compared to other models, the proposed method (XGBoost-VMD-GRU considering complex features) demonstrates superior performance in forecasting, with R² of 0.9922, 0.9860, and 0.9679 for one-step, three-step, and six-step prediction, respectively. This study aims to bring innovative ideas to load forecasting by integrating complex features into the decomposition forecasting framework.

Accurate prediction of the air quality index (AQI) is crucial for understanding urban pollution dynamics and protecting public health. This study proposes a dual-branch fusion framework (CL-XGB-Season) to address seasonal heterogeneity in AQI prediction by integrating temporal dynamic features and static patterns. The CNN-LSTM branch captures short-term temporal fluctuations, while a seasonally split XGBoost branch fits long-term static patterns via independent submodels for spring, summer, autumn, and winter. SHAP-based interpretability analysis revealed the dominant drivers across different seasons: the “temperature × O₃” interaction feature plays a key role in summer, characterizing the ozone formation mechanism dominated by photochemical reactions under conditions of high temperature and strong solar radiation; whereas the PM_2.5/PM₁₀ ratio is crucial in winter (where pollution is primarily driven by pollutant accumulation). The dual-branch fusion framework was validated using hourly resolution data from Chongqing for the 2020–2025 period. Results indicate that the framework achieved a prediction accuracy of 0.197 root mean square error (nRMSE) and 0.9611 coefficient of determination (R²) on the test set, outperforming eight ablation variants and five baseline models (ARIMA, Transformer, etc.) in comparative experiments. Ablation studies confirm the necessity of dual branches and seasonal modeling, with the full model reducing nRMSE by 19–63% versus single-model variants. This framework maintains stable seasonal performance and provides actionable insights for targeted air quality management.

Natural gas plays a key role in the low-carbon energy transition due to its clean and efficient characteristics, yet challenges remain in balancing economic efficiency, user behavior, and carbon emission constraints in demand-side scheduling. This study proposes a low-carbon economic operation model for terminal natural gas systems, integrating price elasticity and differentiated user behavior with carbon emission management strategies. To capture diverse demand patterns, dynamic time warping k-medoids clustering is employed, while scheduling optimization is achieved through a multi-objective framework combining NSGA-III, the entropy weight (EW) method, and the VIKOR decision-making approach. Using real-world data from a gas station in Xi’an, simulation results show that the model reduces gas supply costs by 3.45% for residential users and 6.82% for non-residential users, increases user welfare by 4.64% and 88.87%, and decreases carbon emissions by 115.18 kg and 2156.8 kg, respectively. Moreover, non-residential users achieve an additional reduction in carbon trading costs of 183.85 CNY. The findings demonstrate the effectiveness of integrating dynamic price signals, user behavior modeling, and carbon constraints into a unified optimization framework, offering decision support for sustainable and flexible natural gas scheduling.

Wind power integration into mountainous power grids amplifies probabilistic forecasting challenges arising from strong non-stationarity, multi-source meteorological redundancy and frequent curtailment events. To address the limitations of existing approaches, this paper proposes a multi-horizon probabilistic forecasting framework integrating multi-perspective entropy-weighted fusion, permutation-entropy-guided decomposition, and residual-anchored probability modelling. First, an Entropy-Weighted Multi-criteria Permutation Feature Importance (EW-MPFI) module fuses KSG mutual information, Tree-SHAP, and elastic-net permutation importance through entropy-based weighted aggregation, distilling 23-dimensional meteorological inputs into eight informative features while suppressing single-criterion bias. Then, a three-stage decomposition strategy applies ICEEMDAN primary decomposition, permutation-entropy and sample-entropy guided band reconstruction, and SSA secondary refinement on high-frequency components, achieving complexity-aligned multi-scale separation. Finally, a decomposition-aware patch-based Transformer backbone (DPC-Former) generates three-quantile point forecasts, upon which an NGBoost residual layer models the conditional distribution via natural-gradient optimization in the information-geometric parameter space. Case studies on a 130 MW mountainous wind farm in Sichuan, China, covering 8736 15-min samples with 566 curtailment samples (6.48% of the dataset), show that, under the partition-wise offline batch-evaluation protocol, the proposed framework achieves an NMAE of 5.21%, an NCRPS of 3.74%, and a PICP80 of 0.84 across forecasting horizons from 15 min to 4 h. Ablation analysis attributes NMAE improvements of 25.36% and 24.57% to the decomposition and feature-selection modules, respectively, while 50-seed ensembling further reduces NCRPS, NMAE, and NRMSE by 7.40%, 7.00%, and 13.70% relative to single-seed training. A fixed-checkpoint test-block diagnostic further shows limited sensitivity at approximately weekly and three-day decomposition cadences, but a material degradation at a one-day cadence. The reported metrics should therefore be interpreted as offline best-case results rather than as performance under strictly causal real-time deployment.

Land-use change affects carbon emissions and air quality through coupled ecological and urban processes, yet their coordinated mitigation remains insufficiently understood in heavily industrialized inland regions. Using 113 district-county units in the Fenwei Plain, China, this study developed a regional assessment framework for carbon-PM_2.5 co-mitigation under land-use change from 2013 to 2023. The framework integrates dynamic coordination diagnosis, model-estimated improvement-potential assessment, and governance-oriented classification to identify regional differences in coordination status and adjustment capacity. The results showed a phase-wise evolution of the carbon–pollution relationship, with the Synergetic Evolution Index (SEI) shifting toward higher coordination levels in the later period and becoming more stable after 2020. High-synergy areas were concentrated along the Xi’an–Xianyang–Weinan corridor, whereas several peripheral counties remained under combined carbon–pollution pressure. Model-estimated improvement potential showed pronounced spatial heterogeneity and was concentrated mainly in transition zones with moderate coordination levels and relatively strong structural responsiveness. Land-use-related carbon emissions and PM_2.5 pollution were the dominant constraints on responsiveness, whereas ecological conditions and urban expansion played secondary roles. By integrating coordination status, model-estimated improvement potential, and structural responsiveness, four governance-relevant types were identified: consolidation areas, transformation areas, ecological mismatch areas, and urbanization lock-in areas. This study provides a regionally differentiated framework for diagnosing carbon–pollution co-mitigation under land-use change and supports adaptive environmental governance in industrializing inland regions.