  General circulation models are essential tools in weather and hydrodynamic
simulation. They solve discretized, complex physical equations in order to
compute evolutionary states of dynamical systems, such as the hydrodynamics of
a lake. However, high-resolution numerical solutions using such models are
extremely computational and time consuming, often requiring a high performance
computing architecture to be executed satisfactorily. Machine learning
(ML)-based low-dimensional surrogate models are a promising alternative to
speed up these simulations without undermining the quality of predictions. In
this work, we develop two examples of fast, reliable, low-dimensional surrogate
models to produce a 36 hour forecast of the depth-averaged hydrodynamics at
Lake George NY, USA. Our ML approach uses two widespread artificial neural
network (ANN) architectures: fully connected neural networks and long
short-term memory. These ANN architectures are first validated in the
deterministic and chaotic regimes of the Lorenz system and then combined with
proper orthogonal decomposition (to reduce the dimensionality of the incoming
input data) to emulate the depth-averaged hydrodynamics of a flow simulator
called SUNTANS. Results show the ANN-based reduced order models have promising
accuracy levels (within 6% of the prediction range) and advocate for further
investigation into hydrodynamic applications.
