Fun Projects & Notes

A neural-network interpretation of the scalar wave equation

• The scalar wave equation has been around for hundreds of years as a simplistic model of wave propagation. In this short note I show how a simple recurrent neural network can implement the scalar wave equation on a two-dimensional sheet. Specifically, the dynamics are fully linear and the recurrent connectivity matrix is precisely a discrete Laplacian matrix. I also demonstrate a simulation in the case of a spike input.

• Document: https://gabriel-benigno.com/rnn-wave 

• Python and MATLAB Code: https://github.com/gbenigno/rnn-wave