Learning flow functions of spiking systems

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.We parameterise the flow function of a spiking system in state-space using a recurrent neural network architecture, allowing for a direct continuous-time representation of the state trajectories which is particularly advantageous for this class of systems.The spiking nature of the signals makes for a data-heavy and computationally hard training process, and we describe two methods to mitigate these difficulties. We demonstrate our framework on two conductance-based models of biological neurons.