Learning flow functions of spiking systems

TL;DR

This paper introduces a neural network-based framework for creating surrogate models of complex spiking systems, enabling efficient simulation and system design by capturing continuous-time dynamics despite data and computational challenges.

Contribution

It presents a novel recurrent neural network approach to model flow functions of spiking systems, addressing training difficulties with new mitigation methods.

Findings

Successfully models biological neuron spiking behavior

Accurately replicates system dynamics with surrogate models

Addresses training challenges for data-heavy, high-frequency signals

Abstract

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.