  Stochastic Volterra equations (SVEs) serve as mathematical models for the
time evolutions of random systems with memory effects and irregular behaviour.
We introduce neural stochastic Volterra equations as a physics-inspired
architecture, generalizing the class of neural stochastic differential
equations, and provide some theoretical foundation. Numerical experiments on
various SVEs, like the disturbed pendulum equation, the generalized
Ornstein--Uhlenbeck process and the rough Heston model are presented, comparing
the performance of neural SVEs, neural SDEs and Deep Operator Networks
(DeepONets).
