Machine Learning with Functional Outputs: A Framework for Power System Reliability Forecasting  
Author

Yu Zhou

 

Co-Author(s)

Sen-hui Wang;  Xiang-xia Li

 

Abstract Load forecasting is a key task in power system scheduling and reliability analysis. Compared with load values at individual time points, the target daily load curve provides a more complete description of the continuous variation and overall pattern of electricity demand over a day. This paper proposes a Functional Long Short-Term Memory Network (FLSTM) framework for daily load curve forecasting with functional response. The framework represents functional outputs through basis function expansion and designs a unified feature extraction and fusion structure for historical load sequences, target-day temperature, and the day-of-week one-hot vector. We further compare two functional-output training strategies: coefficient-space training and function-space training. Experimental results based on load and temperature data from the DUQ region of the PJM electricity market show that function-space training outperforms coefficient-space training under all three input scenarios. Compared with the discrete-output baseline and the functional linear baseline, FLSTM achieves lower seasonal-average MAPE and RMSE, demonstrating its effectiveness in improving the forecasting accuracy and reconstruction quality of daily load curves.

 

Keywords Functional data analysis, functional output, load curve forecasting, Functional Long Short-Term Memory Network
   
    Article #:  RQD2026-247
 

Proceedings of 31st ISSAT International Conference on Reliability & Quality in Design
August 5-7, 2026