SMS: Spiking Marching Scheme for Efficient Long Time Integration of Differential Equations
This addresses the computational efficiency challenge for researchers and engineers in numerical simulations, but it appears incremental as it adapts existing SNN methods to a new application.
The authors tackled the problem of long time integration of differential equations by proposing a Spiking Neural Network-based explicit numerical scheme, achieving results through numerical experiments on ODEs and PDEs of varying complexity, though no concrete numbers are provided.
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.