Dynamic Multi-Scale Ensemble iTransformer for Day-Ahead Electric Load Forecasting

Tuan Anh Nguyen; Trung Dung Nguyen

doi:10.12928/biste.v8i4.17107

Authors

Tuan Anh Nguyen Industrial University of Ho Chi Minh City (IUH)
Trung Dung Nguyen Industrial University of Ho Chi Minh City (IUH)

DOI:

https://doi.org/10.12928/biste.v8i4.17107

Keywords:

Electric Load Forecasting, iTransformer, Multi-Scale Temporal Learning, Dynamic Ensemble, Day-Ahead Forecasting

Abstract

Accurate day-ahead electric load forecasting is essential for reliable power-system operation, yet high-resolution demand exhibits nonlinear short-term variations alongside strong daily and weekly recurrence. This study addresses the difficulty of representing these complementary temporal patterns within a single forecasting model. The research contribution is a validation-driven Dynamic Multi-Scale Ensemble iTransformer framework that integrates a tuned iTransformer with explicit daily, weekly, multi-week, and load-profile references, removes highly redundant candidates, and adaptively combines the retained forecasts across load states and forecast-horizon blocks. The framework uses only historical load observations and follows a chronological, leakage-free protocol for model tuning, candidate selection, weight optimization, strategy selection, and final testing. It was evaluated on New South Wales electricity demand data sampled at 5-minute intervals, using the previous 288 observations to forecast the next 288 observations. The proposed model achieved the best overall performance among the six evaluated methods. It yielded an MAE of 478.485 MW, an RMSE of 690.116 MW, a MAPE of 7.031%, an sMAPE of 6.718%, and an R² of 0.8484. Its MAPE was lower than those of Seasonal Naive (7.979%) and the standalone iTransformer (8.691%), corresponding to relative reductions of 11.88% and 19.10%, respectively. CNN, Persistence Naive, and LSTM achieved MAPEs of 12.419%, 17.596%, and 19.830%, respectively. These results show that explicit multi-scale temporal references and validation-optimized adaptive fusion complement the learned iTransformer representation, thereby improving deterministic day-ahead load forecasting accuracy.

References

D. Kiruthiga and V. Manikandan, “Levy flight-particle swarm optimization-assisted BiLSTM + dropout deep learning model for short-term load forecasting,” Neural Comput. Appl., vol. 35, no. 3, pp. 2679–2700, 2023, https://doi.org/10.1007/s00521-022-07751-y.

W. Lin, D. Wu, and M. Jenkin, “Electric Load Forecasting for Individual Households via Spatial-temporal Knowledge Distillation,” IEEE Trans. Power Syst., vol. 40, no. 1, pp. 572–584, 2024, https://doi.org/10.1109/TPWRS.2024.3393926.

S. Islam, T. M. R. Bashar, and M. Munem, “Enhanced very short-term load forecasting with multi-lag feature engineering and prophet-XGBoost-CatBoost architecture,” Energy, vol. 335, no. June, p. 137981, 2025, https://doi.org/10.1016/j.energy.2025.137981.

M. Pleños, “Time Series Forecasting Using Holt-Winters Exponential Smoothing: Application to Abaca Fiber Data,” Zesz. Nauk. SGGW w Warszawie - Probl. Rol. Światowego, vol. 22, no. 2, pp. 17–29, 2022, https://doi.org/10.22630/prs.2022.22.2.6.

S. Smyl, G. Dudek, and P. Pełka, “Contextually enhanced ES-dRNN with dynamic attention for short-term load forecasting,” Neural Networks, vol. 169, no. December 2022, pp. 660–672, 2024, https://doi.org/10.1016/j.neunet.2023.11.017.

S. Smyl, G. Dudek, and P. Pełka, “Contextually enhanced ES-dRNN with dynamic attention for short-term load forecasting,” Neural Networks, vol. 169, no. September 2023, pp. 660–672, 2024, https://doi.org/10.1016/j.neunet.2023.11.017.

D. Liu, X. Lin, H. Liu, and J. Zhu, “A coupled framework for power load forecasting with Gaussian implicit spatio temporal block and attention mechanisms network,” Comput. Electr. Eng., vol. 123, no. PD, p. 110263, 2025, https://doi.org/10.1016/j.compeleceng.2025.110263.

G. Tziolis et al., “Direct short-term net load forecasting in renewable integrated microgrids using machine learning: A comparative assessment,” Sustain. Energy, Grids Networks, vol. 37, no. December 2023, p. 101256, 2024, https://doi.org/10.1016/j.segan.2023.101256.

F. Gao, J. Song, and X. Shao, “Short-term interval-valued load forecasting with a combined strategy of iHW and multioutput machine learning,” Ann. Oper. Res., vol. 346, no. 3, pp. 2009–2033, 2025, https://doi.org/10.1007/s10479-024-06446-y.

M. S. Iqbal and M. Adnan, “Energy & Buildings Edge computing and transfer learning-based short-term load forecasting for residential and commercial buildings,” Energy Build., vol. 329, p. 115273, 2025, https://doi.org/10.1016/j.enbuild.2025.115273.

M. Heleno, W. Zhang, K. Sun, L. R. Garcia, and T. Hong, “Energy & Buildings A cross-dimensional analysis of data-driven short-term load forecasting methods with large-scale smart meter data,” Energy Build., vol. 344, p. 115909, 2025, https://doi.org/10.1016/j.enbuild.2025.115909.

L. Xiao, Q. Bai, and B. Wang, “A dynamic multi-model transfer based short-term load forecasting,” Appl. Soft Comput., vol. 159, p. 111627, 2024, https://doi.org/10.1016/j.asoc.2024.111627.

T. H. M. S. Rashid et al., “Energy Conversion and Management : X A data-driven framework for seasonal PV forecasting and coordinated EV charging to improve hosting capacity in unbalanced distribution grids,” Energy Convers. Manag. X, vol. 30, p. 101708, 2026, https://doi.org/10.1016/j.ecmx.2026.101708.

P. Aduama, A. S. Al-sumaiti, V. K. Saini, and R. Kong, “Energy and AI Explainable optimized voting ensemble for photovoltaic power forecasting,” Energy AI, vol. 24, no. January, p. 100690, 2026, https://doi.org/10.1016/j.egyai.2026.100690.

A. Sharma and S. K. Jain, “A Novel Two-Stage Framework for Mid-Term Electric Load Forecasting,” IEEE Trans. Ind. Informatics, vol. 20, no. 1, pp. 247–255, 2024, https://doi.org/10.1109/TII.2023.3259445.

Z. Zhang, C. Zhang, Y. Dong, and W. Hong, “Knowledge-Based Systems Bi-directional gated recurrent unit enhanced twin support vector regression with seasonal mechanism for electric load forecasting,” Knowledge-Based Syst., vol. 310, p. 112943, 2025, https://doi.org/10.1016/j.knosys.2024.112943.

G. Duan, Y. Du, Y. Shang, H. Xue, and R. Zhang, “Research on Support Vector Regression Short-Time Traffic Flow Prediction Model for Secondary Roads Based on Associated Road Analysis,” Appl. Sci., vol. 15, no. 4, 2025, https://doi.org/10.3390/app15041779.

R. Rodríguez-Pérez and J. Bajorath, “Evolution of Support Vector Machine and Regression Modeling in Chemoinformatics and Drug Discovery,” J. Comput. Aided. Mol. Des., vol. 36, no. 5, pp. 355–362, 2022, https://doi.org/10.1007/s10822-022-00442-9.

Y. Lu and G. Wang, “A load forecasting model based on support vector regression with whale optimization algorithm,” Multimed. Tools Appl., vol. 82, no. 7, pp. 9939–9959, 2023, https://doi.org/10.1007/s11042-022-13462-2.

J. Luo, Y. Zheng, T. Hong, A. Luo, and X. Yang, “Fuzzy support vector regressions for short-term load forecasting,” Fuzzy Optim. Decis. Mak., vol. 23, no. 3, pp. 363–385, 2024, https://doi.org/10.1007/s10700-024-09425-x.

N. Tsalikidis, A. Mystakidis, C. Tjortjis, P. Koukaras, and D. Ioannidis, “Energy load forecasting: one-step ahead hybrid model utilizing ensembling: N. Tsalikidis et al.,” Computing, vol. 106, no. 1, pp. 241-273, 2024. https://doi.org/10.1007/s00607-023-01217-2.

M. Dostmohammadi, M. Z. Pedram, S. Hoseinzadeh, and D. A. Garcia, “A GA-stacking ensemble approach for forecasting energy consumption in a smart household: A comparative study of ensemble methods,” J. Environ. Manage., vol. 364, p. 121264, 2024, https://doi.org/10.1016/j.jenvman.2024.121264.

A. Lindholm, N. Wahlström, F. Lindsten, and T. B. Schön, “Machine Learning,” Mach. Learn., 2022, https://doi.org/10.1017/9781108919371.

R. Bareth, M. Kochar, and A. Yadav, “Comparative Analysis of different Machine learning Models for Load Forecasting,” 2023 IEEE IAS Glob. Conf. Renew. Energy Hydrog. Technol. GlobConHT 2023, pp. 1–5, 2023, https://doi.org/10.1109/GlobConHT56829.2023.10087406.

Y. Chen, C. Lin, Y. Zhang, J. Liu, and D. Yu, “Day-ahead load forecast based on Conv2D-GRU_SC aimed to adapt to steep changes in load,” Energy, vol. 302, p. 131814, 2024, https://doi.org/10.1016/j.energy.2024.131814.

M. Goyal and M. Pandey, “A Systematic Analysis for Energy Performance Predictions in Residential Buildings Using Ensemble Learning,” Arab. J. Sci. Eng., vol. 46, no. 4, pp. 3155-3168, 2020, https://doi.org/10.1007/s13369-020-05069-2.

H. Osman, A. Azab, A. Alghazi, S. Duffuaa, and F. Baki, “Results in Engineering Forecasting electric vehicle charging loads using random forest and gene expression programming ensemble models,” Results Eng., vol. 28, p. 108369, 2025, https://doi.org/10.1016/j.rineng.2025.108369.

V. Veeramsetty, K. R. Reddy, M. Santhosh, A. Mohnot, and G. Singal, “Short-term electric power load forecasting using random forest and gated recurrent unit,” Electr. Eng., vol. 104, no. 1, pp. 307–329, 2022, https://doi.org/10.1007/s00202-021-01376-5.

M. Mohamed, F. E. Mahmood, M. A. Abd, M. Rezkallah, and A. Hamadi, “Load Demand Forecasting Using eXtreme Gradient Boosting ( XGboost ),” 2023 IEEE Ind. Appl. Soc. Annu. Meet., pp. 1–7, 2023, https://doi.org/10.1109/IAS54024.2023.10406613.

P. Saini and S. K. Parida, “A novel probabilistic gradient boosting model with multi-approach feature selection and iterative seasonal trend decomposition for short-term load forecasting,” Energy, vol. 294, p. 130975, 2024, https://doi.org/10.1016/j.energy.2024.130975.

Z. Qinghe, X. Wen, H. Boyan, W. Jong, and F. Junlong, “Optimised extreme gradient boosting model for short term electric load demand forecasting of regional grid system,” Sci. Rep., vol. 12, no. 1, pp. 1–12, 2022, https://doi.org/10.1038/s41598-022-22024-3.

P. Saini and S. K. Parida, “A novel probabilistic gradient boosting model with multi-approach feature selection and iterative seasonal trend decomposition for short-term load forecasting,” Energy, vol. 294, p. 130975, 2024, https://doi.org/10.1016/j.energy.2024.130975.

Z. Li et al., “Fuel economy and emission optimization of spark-ignition pure methanol engine based on gradient boosting neural network and many-objective Bayesian optimization,” Fuel, vol. 426, p. 139573, 2026, https://doi.org/10.1016/j.fuel.2026.139573.

Z. Song, F. Xiao, Z. Chen, and H. Madsen, “Energy and AI Probabilistic ultra-short-term solar photovoltaic power forecasting using natural gradient boosting with attention-enhanced neural networks,” Energy AI, vol. 20, no. March, p. 100496, 2025, https://doi.org/10.1016/j.egyai.2025.100496.

S. Lei and F. Wang, “A Two-stage Short-term Load Forecasting Method Based on Comprehensive Similarity Day Selection and CEEMDAN-XGBoost Error Correction,” 2023 Int. Conf. Futur. Energy Solut., pp. 1–6, https://doi.org/10.1109/FES57669.2023.10183307.

L. Zhang and D. Jánošík, “Enhanced short-term load forecasting with hybrid machine learning models: CatBoost and XGBoost approaches,” Expert Syst. Appl., vol. 241, 2024, https://doi.org/10.1016/j.eswa.2023.122686.

Q. Yang, Y. Lin, S. Kuang, and D. Wang, “A novel short-term load forecasting approach for data-poor areas based on K-MIFS-XGBoost and transfer-learning,” Electr. Power Syst. Res., vol. 229, p. 110151, 2024, https://doi.org/10.1016/j.epsr.2024.110151.

R. Banik and A. Biswas, “Enhanced renewable power and load forecasting using RF-XGBoost stacked ensemble,” Electr. Eng., vol. 106, no. 4, pp. 4947–4967, 2024, https://doi.org/10.1007/s00202-024-02273-3.

Z. Wang, L. Chen, and C. Wang, “Weekly periodicity feature-driven CNN-GRU and LightGBM hybrid model for short-term multi-step building load forecasting,” Energy, vol. 355, p. 141163, 2026, https://doi.org/10.1016/j.energy.2026.141163.

H. Auto-tuning, S. Lei, and F. Wang, “A Short-term Net Load Forecasting Method Based on Two-stage Feature Selection and LightGBM with,” 2023 IEEE/IAS 59th Ind. Commer. Power Syst. Tech. Conf., pp. 1–6, https://doi.org/10.1109/ICPS57144.2023.10142095.

L. Yang, Q. Duan, B. Pan, and Z. Wang, “Post-pandemic holiday load forecasting considering social factors influences based on TL-Informer-LightGBM model,” Electr. Power Syst. Res., vol. 247, p. 111861, 2025, https://doi.org/10.1016/j.epsr.2025.111861.

X. Yao, X. Fu, and C. Zong, “Short-Term Load Forecasting Method Based on Feature Preference Strategy and LightGBM-XGboost,” IEEE Access, vol. 10, pp. 75257–75268, 2022, https://doi.org/10.1109/ACCESS.2022.3192011.

B. Predić et al., “Cloud-load forecasting via decomposition-aided attention recurrent neural network tuned by modified particle swarm optimization,” Complex Intell. Syst., vol. 10, no. 2, pp. 2249–2269, 2024, https://doi.org/10.1007/s40747-023-01265-3.

W. Waheed, Q. Xu, M. Aurangzeb, S. Iqbal, S. Hanif, and Z. M. S. Elbarbary, “Heliyon Empowering data-driven load forecasting by leveraging long short-term memory recurrent neural networks,” Heliyon, vol. 10, no. 24, p. e40934, 2024, https://doi.org/10.1016/j.heliyon.2024.e40934.

X. He, W. Zhao, Z. Gao, Q. Zhang, and W. Wang, “A hybrid prediction interval model for short-term electric load forecast using Holt-Winters and Gate Recurrent Unit,” Sustain. Energy, Grids Networks, vol. 38, p. 101343, 2024, https://doi.org/10.1016/j.segan.2024.101343.

Q. Shen, L. Mo, G. Liu, J. Zhou, Y. Zhang, and P. Ren, “Short-Term Load Forecasting Based on Multi-Scale Ensemble Deep Learning Neural Network,” IEEE Access, vol. 11, pp. 111963–111975, 2023, https://doi.org/10.1109/ACCESS.2023.3322167.

V. Gundu and S. P. Simon, “Quality analysis of combined similar day and day ahead short-term load forecasting using recurrent neural networks,” Sadhana - Acad. Proc. Eng. Sci., vol. 47, no. 1, 2022, https://doi.org/10.1007/s12046-022-01825-2.

U. Javed et al., “A novel short receptive field based dilated causal convolutional network integrated with Bidirectional LSTM for short-term load forecasting,” Expert Syst. Appl., vol. 205, no. February, p. 117689, 2022, https://doi.org/10.1016/j.eswa.2022.117689.

P. Zeng, L. Qi, C. Hu, and X. Ye, “A high-efficiency voltage stabilization strategy for energy harvesting systems integrating a CNN – LSTM prediction model and a buck – boost closed-loop circuit,” Electr. Power Syst. Res., vol. 259, p. 113174, 2026, https://doi.org/10.1016/j.epsr.2026.113174.

W. Xiong, “Bus load forecasting based on maximum information coefficient and CNN-LSTM model,” 2023 IEEE Int. Conf. Image Process. Comput. Appl., pp. 659–663, 2023, https://doi.org/10.1109/ICIPCA59209.2023.10257944.

J. Zhu, J. Yang, M. Peng, X. Cui, and X. Liang, “A CNN-LSTM-attention ( CLA ) hybrid model with PID-based search algorithm ( PSA ) for heat load forecasting in district heating system,” J. Build. Eng., vol. 111, no. 135, p. 113325, 2025, https://doi.org/10.1016/j.jobe.2025.113325.

Z. Chen, Y. Wang, L. Wang, and R. Gong, “A CNN-LSTM-SE model for the short-term roll and heave forecasting of a,” Ocean Eng., vol. 350, p. 124264, 2026, https://doi.org/10.1016/j.oceaneng.2026.124264.

J. Dong, Y. Jiang, P. Chen, J. Li, Z. Wang, and S. Han, “International Journal of Electrical Power and Energy Systems Short-term power load forecasting using bidirectional gated recurrent units-based adaptive stacked autoencoder,” Int. J. Electr. Power Energy Syst., vol. 165, p. 110459, 2025, https://doi.org/10.1016/j.ijepes.2025.110459.

A. Sharma and S. K. Jain, "A Novel Two-Stage Framework for Mid-Term Electric Load Forecasting," in IEEE Transactions on Industrial Informatics, vol. 20, no. 1, pp. 247-255, 2024, https://doi.org/10.1109/TII.2023.3259445.

X. Li, S. Wang, and Z. Chen, “Hierarchical reconciliation of convolutional gated recurrent units for unified forecasting of branched and aggregated district heating loads,” Energy, vol. 313, p. 134097, 2024, https://doi.org/10.1016/j.energy.2024.134097.

H. I. El-azab, R. A. Swief, N. H. El-amary, and H. K. Temraz, “Machine and deep learning approaches for forecasting electricity price and energy load assessment on real datasets,” Ain Shams Eng. J., vol. 15, no. 4, p. 102613, 2024, https://doi.org/10.1016/j.asej.2023.102613.

X. Li, H. Guo, L. Xu, and Z. Xing, “Bayesian-Based Hyperparameter Optimization of 1D-CNN for Structural Anomaly Detection,” Sensors, vol. 23, no. 11, 2023, https://doi.org/10.3390/s23115058.

S. Zhang, R. Chen, J. Cao, and J. Tan, “A CNN and LSTM-based multi-task learning architecture for short and medium-term electricity load forecasting,” Electr. Power Syst. Res., vol. 222, no. October 2022, p. 109507, 2023, https://doi.org/10.1016/j.epsr.2023.109507.

W. Zeng et al., “Hybrid CEEMDAN-DBN-ELM for online DGA serials and transformer status forecasting,” Electr. Power Syst. Res., vol. 217, 2023, https://doi.org/10.1016/j.epsr.2023.109176.

S. A. Alsamraee and S. Khanna, “A hybrid transformer – TCN – GRU based model for thermal load forecasting of a large university campus,” Energy, vol. 344, p. 140114, 2026, https://doi.org/10.1016/j.energy.2026.140114.

P. Ran, K. Dong, X. Liu, and J. Wang, “Short-term load forecasting based on CEEMDAN and Transformer,” Electr. Power Syst. Res., vol. 214, p. 108885, 2023, https://doi.org/10.1016/j.epsr.2022.108885.

J. Chen, D. Wu, Q. Ma, Z. Zhao, Y. Wu, and Y. Ren, “ACTNet : Adapting CNN-Transformer-based foundation model for remote sensing change detection,” Pattern Recognition, vol. 180, 2026, https://doi.org/10.1016/j.patcog.2026.114066.

Z. Tian, W. Liu, W. Jiang, and C. Wu, “CNNs-Transformer based day-ahead probabilistic load forecasting for weekends with limited data availability,” Energy, vol. 293, p. 130666, 2024, https://doi.org/10.1016/j.energy.2024.130666.

I. U. Khalil, A. Ul Haq, and N. ul Islam, “A deep learning-based transformer model for photovoltaic fault forecasting and classification,” Electr. Power Syst. Res., vol. 228, p. 110063, 2024, https://doi.org/10.1016/j.epsr.2023.110063.

Y. Zhou, L. Wang, J. Zhao, and W. Li, “A short-term photovoltaic power prediction method based on the BSLO dual-optimized VMD-CNN-iTransformer-LSTM combined model,” Measurement, vol. 277, p. 121600, 2026, https://doi.org/10.1016/j.measurement.2026.121600.

B. Fang, L. Xu, Y. Luo, Z. Luo, and W. Li, “A method for short-term electric load forecasting based on the FMLP-iTransformer model,” Energy Reports, vol. 12, pp. 3405–3411, 2024, https://doi.org/10.1016/j.egyr.2024.09.023.

F. Li, Y. Yu, H. Zhou, and R. Dong, “DFIMformer : Dynamic frequency-enhanced iTransformer for multiscale time series forecasting,” Inf. Syst., vol. 141, p. 102747, 2026, https://doi.org/10.1016/j.is.2026.102747.

B. Fang, L. Xu, Y. Luo, Z. Luo, and W. Li, “A method for short-term electric load forecasting based on the FMLP-iTransformer model,” Energy Reports, vol. 12, pp. 3405–3411, 2024, https://doi.org/10.1016/j.egyr.2024.09.023.

H. Nagpal, A. Soppelsa, H. Madsen, and R. Fedrizzi, “Energy & Buildings An adaptive multi-seasonal ARIMA approach for domestic hot water load forecasting : A pilot study,” Energy Build., vol. 347, p. 116226, 2025, https://doi.org/10.1016/j.enbuild.2025.116226.

L. Ji, Y. Zou, K. He, and B. Zhu, “ScienceDirect Carbon Carbon futures futures price price forecasting forecasting based based with with ARIMA-CNN- LSTM model LSTM model,” Procedia Comput. Sci., vol. 162, pp. 33–38, 2020, https://doi.org/10.1016/j.procs.2019.11.254.

F. Khosravi and M. Shadaram, “Retentive Time Series : A Scalable Machine Learning Model for Traffic Prediction in Elastic Optical Networks,” IEEE Access, vol. 13, pp. 1–17, 2025, https://doi.org/10.1109/ACCESS.2025.3585076.

A. A. Sleem and M. N. Syed, "Novel Predictive Factors to Boost Short-Term Electricity Demand Forecasting Using Machine Learning Models," in IEEE Access, vol. 13, pp. 147265-147290, 2025, https://doi.org/10.1109/ACCESS.2025.3600864.

S. Khaleghian, T. Doan, J. O. E. Knox, A. Harris, M. Sartipi, and S. Member, “Data-Driven Insights Into EV Charging Patterns : Machine Learning Models Reveal Key Predictors of Station Utilization in Tennessee,” IEEE Access, vol. 13, pp. 51458–51483, 2025, https://doi.org/10.1109/ACCESS.2025.3553086.

E. A. Alghamdi, M. H. Alkinani, E. A. L. I. Aldhahri, and N. Ayub, “REST Network : An Ensemble Deep Learning Approach for EV Charging Load Forecasting in Artificial Port Supply Chains,” IEEE Access, vol. 13, pp. 133128–133144, 2025, https://doi.org/10.1109/ACCESS.2025.3589292.

M. Alaraj, C. Martins, M. Radi, M. Darwish, and M. Majdalawieh, “Spatial – Temporal Deep Learning for Electric-Vehicle Charging Demand : An Exploratory Study of Graph Convolutional and LSTM Networks Performance,” IEEE Access, vol. 13, pp. 202203–202213, 2025, https://doi.org/10.1109/ACCESS.2025.3636433.

L. Peng, S. Yun, X. Liu, and G. Fan, “Uncertainty quantification and load forecasting based on CPO-VMD and hybrid deep learning,” Electr. Power Syst. Res., vol. 252, p. 112444, 2026, https://doi.org/10.1016/j.epsr.2025.112444.

J. Feng et al., “Transformer Abnormal State Identification Based on TCN-Transformer Model in Multiphysics,” IEEE Access, vol. 13, pp. 44775–44788, 2025, https://doi.org/10.1109/ACCESS.2025.3546341.

H. J. Kim, D. Kim, H. Tak, and J. Y. Lee, “Global-local attention-enabled multiple decoder Transformer for multi-energy load forecasting in user-level integrated energy system,” Appl. Energy, vol. 396, p. 126255, 2025, https://doi.org/10.1016/j.apenergy.2025.126255.

S. Wu, Z. Wang, and X. Liu, “Temporal structure-preserving transformer for industrial load forecasting,” Neural Networks, vol. 192, p. 107887, 2025, https://doi.org/10.1016/j.neunet.2025.107887.