PINNs for integro-differential equations with noise

Is there a way to solve an IDE with a noise term such as:

\frac{\partial}{\partial t} u(t) + u(t) + \int_{0}^{t} u(x) d x + w(t) = 0

with the help of NeuralPDE.jl, where w(t) is the noise term.

NeuralPDE doesn’t do noise terms yet, that’s slated for this summer.