  Ensemble Kalman inversion (EKI) is a sequential Monte Carlo method used to
solve inverse problems within a Bayesian framework. Unlike backpropagation, EKI
is a gradient-free optimization method that only necessitates the evaluation of
artificial neural networks in forward passes. In this study, we examine the
effectiveness of EKI in training neural ordinary differential equations (neural
ODEs) for system identification and control tasks. To apply EKI to optimal
control problems, we formulate inverse problems that incorporate a
Tikhonov-type regularization term. Our numerical results demonstrate that EKI
is an efficient method for training neural ODEs in system identification and
optimal control problems, with runtime and quality of solutions that are
competitive with commonly used gradient-based optimizers.
