We shall discuss aspects of a nonlocal SPDE with applications to the so-called Amari-type neural field model, which are mean-field models for neural activity in the cortex. In particular, under suitable assumptions on the coupling kernel, we show that via an infinite dimensional change of coordinates the equation admits a gradient flow structure, which has consequences for regularity, long-time behavior and uniqueness of invariant distributions. This is a joint work with Christian Kuehn, TU Munich.
