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We consider a nonlinear SPDE approximation of the Dean-Kawasaki equation forindependent particles. Our approximation satisfies the physical constraints ofthe particle system, i.e. its solution is a probability measure for all times(preservation of positivity and mass conservation). Using a duality argument,we prove that the weak error between particle system and nonlinear SPDE is ofthe order $N^{-1-1/(d/2+1)}\log (N)$. Along the way we show well-posedness, acomparison principle and an entropy estimate for a class of nonlinearregularized Dean-Kawasaki equations with It\^o noise. Keywords: Dean-Kawasakiequation, weak error analysis, Laplace duality

Weak error analysis for a nonlinear SPDE approximation of the Dean-Kawasaki equation