  We propose a framework for surrogate modelling of spiking systems. These
systems are often described by stiff differential equations with high-amplitude
oscillations and multi-timescale dynamics, making surrogate models an
attractive tool for system design and simulation. We parameterise the flow
function of a spiking system using a recurrent neural network architecture,
allowing for a direct continuous-time representation of the state trajectories.
The spiking nature of the signals makes for a data-heavy and computationally
hard training process; thus, we describe two methods to mitigate these
difficulties. We demonstrate our framework on two conductance-based models of
biological neurons, showing that we are able to train surrogate models which
accurately replicate the spiking behaviour.
