Recursive deep learning with multi-scale attention for energy demand dynamics
Bibliographic record
Abstract
• Fully learnable filters adapt to nonstationary and multi-scale signal dynamics. • Joint training of denoising and modeling enhances end-to-end accuracy and stability. • Entropy-aware gating fuses multi-stage forecasts with uncertainty-based weighting. • Delivers robust energy price forecasting under volatility and regime shifts. • Achieves up to 85% RMSE and 99% MAPE reduction over 50 existing models. Nonstationary and multi-scale time series challenge traditional decomposition-based and denoising techniques. These approaches often rely on fixed transformations or shallow residual modeling, limiting adaptability to evolving dynamics likes energy price forecasting. This work introduces an end-to-end recursive deep learning architecture that preserves the classical estimation loop while rendering all state-space parameters data-adaptive at every stage and time step. The parameters are synthesized by a lightweight neural generator conditioned on recent residual behavior and cross-scale context, enabling reconfiguration as regimes shift. Robustness is ensured through two design choices: a stability-preserving parameterization of state evolution that prevents drift and explosions, and innovation-driven, heteroskedastic noise modeling that automatically adjusts to volatility. At each stage, a trend is extracted, modeled by a shared deep multilayer perceptron (DMLP), and fused through an entropy-aware module that weights stage contributions, yielding a closed loop that progressively removes structure from the residuals. On the WTI crude oil dataset, compared to a baseline DMLP (MAE = 1.879, MAPE = 1.825 %, RMSE = 2.457), the proposed model achieved a 57.1 % reduction in MAE, 56.7 % in MAPE, and 58.0 % in RMSE (MAE = 0.806, MAPE = 0.787 %, RMSE = 1.031). It also outperformed over 50 state-of-the-art models, achieving up to 85 % lower RMSE and over 99 % reduction in MAPE. The framework is compact, reproducible, and suitable for energy-economics analytics under regime shifts and noise.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".