论文标题
SMS：有效长时间整合微分方程的行进计划
SMS: Spiking Marching Scheme for Efficient Long Time Integration of Differential Equations
论文作者
论文摘要
我们提出了一个基于峰值的神经网络（SNN）基于时间依赖的普通和部分微分方程（ODES，PDES）的显式显式数值方案。该方法的核心元素是SNN，经过训练，可以在以前的时间段上使用有关该解决方案的尖峰编码的信息来预测下一个时间段的尖峰编码信息。训练网络后，它是一种明确的数值方案，可以在给定尖峰编码的初始条件下，可在将来的时间步中计算解决方案。解码器用于将进化的尖峰编码解变回功能值。我们提出了使用所提出的方法对不同复杂性的ODE和PDE的数值实验的结果。
We propose a Spiking Neural Network (SNN)-based explicit numerical scheme for long time integration of time-dependent Ordinary and Partial Differential Equations (ODEs, PDEs). The core element of the method is a SNN, trained to use spike-encoded information about the solution at previous timesteps to predict spike-encoded information at the next timestep. After the network has been trained, it operates as an explicit numerical scheme that can be used to compute the solution at future timesteps, given a spike-encoded initial condition. A decoder is used to transform the evolved spiking-encoded solution back to function values. We present results from numerical experiments of using the proposed method for ODEs and PDEs of varying complexity.
