# Optimized ensemble deep learning framework for scalable forecasting of dynamics containing extreme events

arXiv: https://arxiv.org/abs/2106.08968 · HTML: https://mlsanity.com/paper/2106.08968/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 114 references that are in the map.
- First posted on arXiv 9 Jun 2021.

## Builds on (most cited first, 10 of 10)

- [Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networks](https://mlsanity.com/paper/1802.07486/) (2018)
- [Backpropagation Algorithms and Reservoir Computing in Recurrent Neural Networks for the Forecasting of Complex Spatiotemporal Dynamics](https://mlsanity.com/paper/1910.05266/) (2019)
- [The Unreasonable Effectiveness of Deep Learning in Artificial Intelligence](https://mlsanity.com/paper/2002.04806/) (2020)
- [The Relative Performance of Ensemble Methods with Deep Convolutional Neural Networks for Image Classification](https://mlsanity.com/paper/1704.01664/) (2017)
- [Algorithms for Fitting the Constrained Lasso](https://mlsanity.com/paper/1611.01511/) (2016)
- [Using Machine Learning to Assess Short Term Causal Dependence and Infer Network Links](https://mlsanity.com/paper/1912.02721/) (2019)
- [Using Machine Learning to predict extreme events in the H'enon map](https://mlsanity.com/paper/2002.10268/) (2020)
- [Detection of Generalized Synchronization using Echo State Networks](https://mlsanity.com/paper/1710.08286/) (2017)
- [A Nonparametric Ensemble Binary Classifier and its Statistical Properties](https://mlsanity.com/paper/1804.10928/) (2018)
- [Machine Learning assisted Chimera and Solitary states in Networks](https://mlsanity.com/paper/2011.01135/) (2020)

## Built on by (most cited first, 6 of 6)

- [W-Transformers : A Wavelet-based Transformer Framework for Univariate Time Series Forecasting](https://mlsanity.com/paper/2209.03945/) (2022)
- [Prediction of Occurrence of Extreme Events using Machine Learning](https://mlsanity.com/paper/2110.09304/) (2021)
- [Spatiotemporal Forecasting of Traffic Flow using Wavelet-based Temporal Attention](https://mlsanity.com/paper/2407.04440/) (2024)
- [Probabilistic AutoRegressive Neural Networks for Accurate Long-range Forecasting](https://mlsanity.com/paper/2204.09640/) (2022)
- [Knowledge-based Deep Learning for Modeling Chaotic Systems](https://mlsanity.com/paper/2209.04259/) (2022)
- [Turning Time Series into Algebraic Equations: Symbolic Machine Learning for Interpretable Modeling of Chaotic Time Series](https://mlsanity.com/paper/2603.07261/) (2026)

## Abstract (arXiv)

The remarkable flexibility and adaptability of both deep learning models and ensemble methods have led to the proliferation for their application in understanding many physical phenomena. Traditionally, these two techniques have largely been treated as independent methodologies in practical applications. This study develops an optimized ensemble deep learning (OEDL) framework wherein these two machine learning techniques are jointly used to achieve synergistic improvements in model accuracy, stability, scalability, and reproducibility prompting a new wave of applications in the forecasting of dynamics. Unpredictability is considered as one of the key features of chaotic dynamics, so forecasting such dynamics of nonlinear systems is a relevant issue in the scientific community. It becomes more challenging when the prediction of extreme events is the focus issue for us. In this circumstance, the proposed OEDL model based on a best convex combination of feed-forward neural networks, reservoir computing, and long short-term memory can play a key role in advancing predictions of dynamics consisting of extreme events. The combined framework can generate the best out-of-sample performance than the individual deep learners and standard ensemble framework for both numerically simulated and real world data sets. We exhibit the outstanding performance of the OEDL framework for forecasting extreme events generated from Lienard-type system, prediction of COVID-19 cases in Brazil, dengue cases in San Juan, and sea surface temperature in Nino 3.4 region.