  Neural network modules conditioned by known priors can be effectively trained
and combined to represent systems with nonlinear dynamics. This work explores a
novel formulation for data-efficient learning of deep control-oriented
nonlinear dynamical models by embedding local model structure and constraints.
The proposed method consists of neural network blocks that represent input,
state, and output dynamics with constraints placed on the network weights and
system variables. For handling partially observable dynamical systems, we
utilize a state observer neural network to estimate the states of the system's
latent dynamics. We evaluate the performance of the proposed architecture and
training methods on system identification tasks for three nonlinear systems: a
continuous stirred tank reactor, a two tank interacting system, and an
aerodynamics body. Models optimized with a few thousand system state
observations accurately represent system dynamics in open loop simulation over
thousands of time steps from a single set of initial conditions. Experimental
results demonstrate an order of magnitude reduction in open-loop simulation
mean squared error for our constrained, block-structured neural models when
compared to traditional unstructured and unconstrained neural network models.
