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.

本文提出了一种通过最佳凸组合前馈神经网络、水库计算和长短期记忆等算法构建的深度学习模型及集成学习框架，能够联合应用于深度学习和集成方法来提高模型准确性、稳定性、可扩展性和再现性，创造出新的应用，尤其在可预测混沌动态和极端事件预测等方面表现出色，且对于多种数据集和应用场景有很强的普适性。

基于优化集成深度学习框架的规模化极端事件动态预测