Fourier-Enhanced Recurrent Neural Networks for Electrical Load Time Series Downscaling

TL;DR

The paper tackles downscaling electricity demand from coarse to hourly resolution by introducing a Fourier-enhanced RNN that injects explicit seasonal embeddings into a latent space and uses self-attention to model intra-period dependencies. The approach combines a low-resolution recurrent path with a Fourier seasonal branch and a per-time-step attention module, plus an additive output head and residual uncertainty to enable calibration. Empirical results across four PJM territories show lower, flatter horizon-wise RMSE compared with Prophet baselines and non-attention/RNN variants, along with well-calibrated predictive uncertainty. The framework also extends naturally to yearly-to-hourly downscaling via hierarchical or base-refinement strategies, demonstrating cross-scale consistency and applicability to broader spatio-temporal disaggregation tasks.

Abstract

We present a Fourier-enhanced recurrent neural network (RNN) for downscaling electrical loads. The model combines (i) a recurrent backbone driven by low-resolution inputs, (ii) explicit Fourier seasonal embeddings fused in latent space, and (iii) a self-attention layer that captures dependencies among high-resolution components within each period. Across four PJM territories, the approach yields RMSE lower and flatter horizon-wise than classical Prophet baselines (with and without seasonality/LAA) and than RNN ablations without attention or Fourier features.

Figures (4)

• Figure 1: Fourier-enhanced RNN architecture. Low-resolution path ($x_0$) drives the RNN; the seasonal path ($x_f{\to}f_t$) is fused at $z$, refined by a per-timestep self-attention block, and mapped to hourly output. Eq. (3) RNN update; Eqs. (4--5) Fourier projection; Eqs. (7--11) self-attention; Eq. (12) output head.
• Figure 2: RNN ablations across four territories. Self-attention improves intra-day dependency modeling, while adding Fourier seasonality further reduces RMSE and flattens the hourly error profiles.
• Figure 3: Prophet baselines versus Fourier RNN (ours; note the different $y$ scale from Figure \ref{['fig:rmse_rnn_all']}). Prophet variants include daily/weekly/yearly seasonalities and optional LAA adjustment. Fourier RNN achieves the best mean RMSE and flattest hourly profiles.
• Figure 4: Yearly-to-hourly downscaling RMSE.