Solving neural field equations using physics informed neural networks - Wojtak, Weronika (2023)
This article presents an approach for solving neural field equations (NFEs) using Physics Informed Neural Networks (PINNs). NFEs are integro-differential equations describing the spatio-temporal dynamics of neuronal populations in the cortex. The traditional numerical methods for NFEs require significant computational effort due to the discretization of the spatial convolution. The proposed approach leverages Fast Fourier Transforms (FFTs) to reduce the computational cost and improve efficiency. A PINN, consisting of a surrogate network and a residual network, is trained to approximate the solutions of NFEs. The effectiveness of the approach is demonstrated by solving the one-dimensional Amari equation, a commonly used neural field formulation. Our results show that the accuracy of the PINN approach is comparable to traditional numerical methods. Future research directions include optimizing hyperparameters, incorporating input terms in NFEs, exploring transfer learning, addressing the inverse problem, and extending the approach to higher dimensions.