  The success of the current wave of artificial intelligence can be partly
attributed to deep neural networks, which have proven to be very effective in
learning complex patterns from large datasets with minimal human intervention.
However, it is difficult to train these models on complex dynamical systems
from data alone due to their low data efficiency and sensitivity to
hyperparameters and initialisation. This work demonstrates that injection of
partially known information at an intermediate layer in a DNN can improve model
accuracy, reduce model uncertainty, and yield improved convergence during the
training. The value of these physics-guided neural networks has been
demonstrated by learning the dynamics of a wide variety of nonlinear dynamical
systems represented by five well-known equations in nonlinear systems theory:
the Lotka-Volterra, Duffing, Van der Pol, Lorenz, and Henon-Heiles systems.
