Multilevel Monte Carlo Methods for the Dean-Kawasaki Equation from Fluctuating Hydrodynamics

Explore a 33-minute conference talk on Multilevel Monte Carlo methods for the Dean–Kawasaki equation from Fluctuating Hydrodynamics, presented by Federico Cornalba at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI). Delve into the development and analysis of a Multilevel Monte Carlo (MLMC) scheme for the Dean–Kawasaki equation, a key representative of Stochastic Partial Differential Equations in Fluctuating Hydrodynamics. Learn how this MLMC scheme significantly accelerates simulations of the Dean–Kawasaki model, with a focus on quantifying speed-up factors as local particle density increases. Discover how substantial improvements in computational efficiency can be achieved even in low particle density regimes. Understand the challenges posed by the equation's singular nature due to white noise drift terms, and how the convergence of numerical solutions is addressed in terms of the law of distributions. Examine numerical simulations presented for the two-dimensional case, based on joint work with Julian Fischer. This talk was part of the Workshop on "Stochastic Partial Differential Equations" held at the ESI in February 2024.