# A comparative study of non-deep learning, deep learning, and ensemble learning methods for sunspot number prediction

arXiv: https://arxiv.org/abs/2203.05757 · HTML: https://mlsanity.com/paper/2203.05757/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 92 references that are in the map.
- First posted on arXiv 11 Mar 2022.

## Builds on (most cited first, 20 of 20)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Longformer: The Long-Document Transformer](https://mlsanity.com/paper/2004.05150/) (2020)
- [XLNet: Generalized Autoregressive Pretraining for Language Understanding](https://mlsanity.com/paper/1906.08237/) (2019)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Generating Long Sequences with Sparse Transformers](https://mlsanity.com/paper/1904.10509/) (2019)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [Enhancing the Locality and Breaking the Memory Bottleneck of Transformer on Time Series Forecasting](https://mlsanity.com/paper/1907.00235/) (2019)
- [Ray: A Distributed Framework for Emerging AI Applications](https://mlsanity.com/paper/1712.05889/) (2017)
- [Tune: A Research Platform for Distributed Model Selection and Training](https://mlsanity.com/paper/1807.05118/) (2018)
- [Time Series Data Augmentation for Deep Learning: A Survey](https://mlsanity.com/paper/2002.12478/) (2020)
- [A Multi-Horizon Quantile Recurrent Forecaster](https://mlsanity.com/paper/1711.11053/) (2017)
- [Deep Transformer Models for Time Series Forecasting: The Influenza Prevalence Case](https://mlsanity.com/paper/2001.08317/) (2020)
- [Darts: User-Friendly Modern Machine Learning for Time Series](https://mlsanity.com/paper/2110.03224/) (2021)
- [An Experimental Review on Deep Learning Architectures for Time Series Forecasting](https://mlsanity.com/paper/2103.12057/) (2021)
- [Merlion: A Machine Learning Library for Time Series](https://mlsanity.com/paper/2109.09265/) (2021)

## Built on by (most cited first, 3 of 3)

- [Distributional Adaptive Soft Regression Trees](https://mlsanity.com/paper/2210.10389/) (2022)
- [Parameters for > 300 million Gaia stars: Bayesian inference vs. machine learning](https://mlsanity.com/paper/2302.06995/) (2023)
- [Inferring Kernel ε-Machines: Discovering Structure in Complex Systems](https://mlsanity.com/paper/2410.01076/) (2024)

## Abstract (arXiv)

Solar activity has significant impacts on human activities and health. One most commonly used measure of solar activity is the sunspot number. This paper compares three important non-deep learning models, four popular deep learning models, and their five ensemble models in forecasting sunspot numbers. In particular, we propose an ensemble model called XGBoost-DL, which uses XGBoost as a two-level nonlinear ensemble method to combine the deep learning models. Our XGBoost-DL achieves the best forecasting performance (RMSE = 25.70 and MAE = 19.82) in the comparison, outperforming the best non-deep learning model SARIMA (RMSE = 54.11 and MAE = 45.51), the best deep learning model Informer (RMSE = 29.90 and MAE = 22.35) and the NASA's forecast (RMSE = 48.38 and MAE = 38.45). Our XGBoost-DL forecasts a peak sunspot number of 133.47 in May 2025 for Solar Cycle 25 and 164.62 in November 2035 for Solar Cycle 26, similar to but later than the NASA's at 137.7 in October 2024 and 161.2 in December 2034. An open-source Python package of our XGBoost-DL for the sunspot number prediction is available at https://github.com/yd1008/ts_ensemble_sunspot.