Neural stochastic Volterra equations: learning path-dependent dynamics
This work addresses the challenge of learning path-dependent dynamics in stochastic systems, which is incremental as it builds upon existing neural SDEs and DeepONets.
The authors tackled the problem of modeling random systems with memory effects by introducing neural stochastic Volterra equations as a physics-inspired architecture, generalizing neural stochastic differential equations, and demonstrated performance through numerical experiments on various SVEs.
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, the rough Heston model and a monetary reserve dynamics, are presented, comparing the performance of neural SVEs, neural SDEs and Deep Operator Networks (DeepONets).