A multilevel Monte Carlo method for the Dean-Kawasaki equation from fluctuating hydrodynamics

The Dean-Kawasaki equation is one of the most basic models of fluctuating hydrodynamics; it provides an SPDE description of density fluctuations in systems of weakly interacting diffusing particles. While typically substantially faster to simulate than the particle system itself, the computation of statistical properties of fluctuations via the Dean-Kawasaki equation is still expensive, as it involves solving the SPDE for a large number of realizations of the noise. We propose and analyse a multilevel Monte Carlo scheme for the Dean-Kawasaki equation, enabling the computation of the statistics of density fluctuations at a reduced computational complexity.