# Learning flow functions of spiking systems

arXiv: https://arxiv.org/abs/2312.11913 · HTML: https://mlsanity.com/paper/2312.11913/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Dec 2023.

## Built on by (most cited first, 2 of 2)

- [Neural Operators for Predictor Feedback Control of Nonlinear Delay Systems](https://mlsanity.com/paper/2411.18964/) (2024)
- [RHYME-XT: A Neural Operator for Spatiotemporal Control Systems](https://mlsanity.com/paper/2603.17867/) (2026)

## Abstract (arXiv)

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.