  Deep Learning has received increased attention due to its unbeatable success
in many fields, such as computer vision, natural language processing,
recommendation systems, and most recently in simulating multiphysics problems
and predicting nonlinear dynamical systems. However, modeling and forecasting
the dynamics of chaotic systems remains an open research problem since training
deep learning models requires big data, which is not always available in many
cases. Such deep learners can be trained from additional information obtained
from simulated results and by enforcing the physical laws of the chaotic
systems. This paper considers extreme events and their dynamics and proposes
elegant models based on deep neural networks, called knowledge-based deep
learning (KDL). Our proposed KDL can learn the complex patterns governing
chaotic systems by jointly training on real and simulated data directly from
the dynamics and their differential equations. This knowledge is transferred to
model and forecast real-world chaotic events exhibiting extreme behavior. We
validate the efficiency of our model by assessing it on three real-world
benchmark datasets: El Nino sea surface temperature, San Juan Dengue viral
infection, and Bj{\o}rn{\o}ya daily precipitation, all governed by extreme
events' dynamics. Using prior knowledge of extreme events and physics-based
loss functions to lead the neural network learning, we ensure physically
consistent, generalizable, and accurate forecasting, even in a small data
regime.
