  Optimal control problems naturally arise in many scientific applications
where one wishes to steer a dynamical system from a certain initial state
$\mathbf{x}_0$ to a desired target state $\mathbf{x}^*$ in finite time $T$.
Recent advances in deep learning and neural network-based optimization have
contributed to the development of methods that can help solve control problems
involving high-dimensional dynamical systems. In particular, the framework of
neural ordinary differential equations (neural ODEs) provides an efficient
means to iteratively approximate continuous time control functions associated
with analytically intractable and computationally demanding control tasks.
Although neural ODE controllers have shown great potential in solving complex
control problems, the understanding of the effects of hyperparameters such as
network structure and optimizers on learning performance is still very limited.
Our work aims at addressing some of these knowledge gaps to conduct efficient
hyperparameter optimization. To this end, we first analyze how truncated and
non-truncated backpropagation through time affect runtime performance and the
ability of neural networks to learn optimal control functions. Using analytical
and numerical methods, we then study the role of parameter initializations,
optimizers, and neural-network architecture. Finally, we connect our results to
the ability of neural ODE controllers to implicitly regularize control energy.

Machine Learning;Dynamical Systems;Optimization and Control