# ES-dRNN: A Hybrid Exponential Smoothing and Dilated Recurrent Neural Network Model for Short-Term Load Forecasting

arXiv: https://arxiv.org/abs/2112.02663 · HTML: https://mlsanity.com/paper/2112.02663/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 88 references that are in the map.
- First posted on arXiv 5 Dec 2021.

## Builds on (most cited first, 14 of 14)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2005.11650/) (2020)
- [Don't Decay the Learning Rate, Increase the Batch Size](https://mlsanity.com/paper/1711.00489/) (2017)
- [Deep Learning for Time Series Forecasting: Tutorial and Literature Survey](https://mlsanity.com/paper/2004.10240/) (2020)
- [Forecasting day-ahead electricity prices: A review of state-of-the-art algorithms, best practices and an open-access benchmark](https://mlsanity.com/paper/2008.08004/) (2020)
- [Dilated Recurrent Neural Networks](https://mlsanity.com/paper/1710.02224/) (2017)
- [Short-term Load Forecasting with Deep Residual Networks](https://mlsanity.com/paper/1805.11956/) (2018)
- [Pattern-based Long Short-term Memory for Mid-term Electrical Load Forecasting](https://mlsanity.com/paper/2004.11834/) (2020)
- [Randomized Neural Networks for Forecasting Time Series with Multiple Seasonality](https://mlsanity.com/paper/2107.01705/) (2021)

## Built on by (most cited first, 11 of 11)

- [TimeGPT in Load Forecasting: A Large Time Series Model Perspective](https://mlsanity.com/paper/2404.04885/) (2024)
- [Electrical Load Forecasting over Multihop Smart Metering Networks with Federated Learning](https://mlsanity.com/paper/2502.17226/) (2025)
- [ES-dRNN with Dynamic Attention for Short-Term Load Forecasting](https://mlsanity.com/paper/2203.00937/) (2022)
- [Contextually Enhanced ES-dRNN with Dynamic Attention for Short-Term Load Forecasting](https://mlsanity.com/paper/2212.09030/) (2022)
- [Any-Quantile Probabilistic Forecasting of Short-Term Electricity Demand](https://mlsanity.com/paper/2404.17451/) (2024)
- [Stacking for Probabilistic Short-term Load Forecasting](https://mlsanity.com/paper/2406.10718/) (2024)
- [Forecasting Cryptocurrency Prices using Contextual ES-adRNN with Exogenous Variables](https://mlsanity.com/paper/2504.08947/) (2025)
- [Recurrent Neural Networks for Forecasting Time Series with Multiple Seasonality: A Comparative Study](https://mlsanity.com/paper/2203.09170/) (2022)
- [Zero and Few Shot Load Forecasting with Large Language Models](https://mlsanity.com/paper/2411.11350/) (2024)
- [Predicting Customer Lifetime Value Using Recurrent Neural Net](https://mlsanity.com/paper/2412.20295/) (2024)
- [Probabilistic Multi-Regional Solar Power Forecasting with Any-Quantile Recurrent Neural Networks](https://mlsanity.com/paper/2602.05660/) (2026)

## Abstract (arXiv)

Short-term load forecasting (STLF) is challenging due to complex time series (TS) which express three seasonal patterns and a nonlinear trend. This paper proposes a novel hybrid hierarchical deep learning model that deals with multiple seasonality and produces both point forecasts and predictive intervals (PIs). It combines exponential smoothing (ES) and a recurrent neural network (RNN). ES extracts dynamically the main components of each individual TS and enables on-the-fly deseasonalization, which is particularly useful when operating on a relatively small data set. A multi-layer RNN is equipped with a new type of dilated recurrent cell designed to efficiently model both short and long-term dependencies in TS. To improve the internal TS representation and thus the model's performance, RNN learns simultaneously both the ES parameters and the main mapping function transforming inputs into forecasts. We compare our approach against several baseline methods, including classical statistical methods and machine learning (ML) approaches, on STLF problems for 35 European countries. The empirical study clearly shows that the proposed model has high expressive power to solve nonlinear stochastic forecasting problems with TS including multiple seasonality and significant random fluctuations. In fact, it outperforms both statistical and state-of-the-art ML models in terms of accuracy.