  Bayesian design can be used for efficient data collection over time when the
process can be described by the solution to an ordinary differential equation
(ODE). Typically, Bayesian designs in such settings are obtained by maximising
the expected value of a utility function that is derived from the joint
probability distribution of the parameters and the response, given prior
information about an appropriate ODE. However, in practice, appropriately
defining such information \textit{a priori} can be difficult due to incomplete
knowledge about the mechanisms that govern how the process evolves over time.
In this paper, we propose a method for finding Bayesian designs based on a
flexible class of ODEs. Specifically, we consider the inclusion of spline terms
into ODEs to provide flexibility in modelling how the process changes over
time. We then propose to leverage this flexibility to form designs that are
efficient even when the prior information is misspecified. Our approach is
motivated by a sampling problem in agriculture where the goal is to provide a
better understanding of fruit growth where prior information is based on
studies conducted overseas, and therefore is potentially misspecified.
