Loss functions in deep residual networks for short-term load forecasting: a systematic analysis

The dependable and effective operation of contemporary electricity systems depends on short-term load forecasting (STLF). Although Deep Residual Networks (DRNs) have proven to be highly predictive, little is known about how loss functions affect forecasting performance and optimization behavior. This study presents a systematic evaluation of various loss functions within the original DRN and Principal Component Analysis-Deep Residual Network (PCA-DRN) frameworks under a unified experimental setting. Traditional, robust, and task-specific Penalized loss functions are examined using real-world datasets with distinct climatic and load characteristics. The results show that the Charbonnier loss consistently achieves the best overall performance across all evaluation metrics under the original DRN framework. However, under the PCA-DRN framework, a performance divergence emerges: while the Charbonnier loss remains optimal for point-forecast error metrics, the Penalized loss demonstrates superior performance in squared-error-based and correlation-oriented metrics. Moreover, PCA-DRN consistently outperforms the original DRN, highlighting the effectiveness of dimensionality reduction in improving feature representation and generalization capability. The statistical significance of the reported improvements is further confirmed using bootstrap-based statistical analysis. These findings suggest that loss function selection should be jointly considered with data characteristics and feature representation, rather than treated as an isolated design choice, to achieve robust and accurate STLF.