  We propose a numerical method for discovering unknown parameterized dynamical
systems by using observational data of the state variables. Our method is built
upon and extends the recent work of discovering unknown dynamical systems, in
particular those using deep neural network (DNN). We propose a DNN structure,
largely based upon the residual network (ResNet), to not only learn the unknown
form of the governing equation but also take into account the random effect
embedded in the system, which is generated by the random parameters. Once the
DNN model is successfully constructed, it is able to produce system prediction
over longer term and for arbitrary parameter values. For uncertainty
quantification, it allows us to conduct uncertainty analysis by evaluating
solution statistics over the parameter space.
