A meshless numerical solver for the McKean-Vlasov stochastic differential equation built on Physics-Informed Neural Networks, for both self-interaction and interaction regimes. Instead of simulating high-dimensional coupled interacting particles with Euler-Maruyama iterations (whose accuracy is tied to particle count and time step), it constructs a pseudo MV-SDE via Ito calculus, expresses the discrepancy from the true equation as a loss minimized by optimization independent of the time-step size, and does not rely on the propagation-of-chaos result. The paper provides an error estimate for the loss function.
Introduces a meshless deep-learning particle method for solving the McKean-Vlasov stochastic differential equation (MV-SDE), covering both self-interaction and interaction regimes. Classical solvers …