  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.
