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

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