Abstract: A direct numerical solution of kinetic equations is typically expensive, since the particle distribution depends on time, space and velocity. An expansion in the velocity variable yields an equivalent system of inﬁnitely many moment equations. A fundamental problem is how to truncate the system. Various closures have been presented in the literature. Using the example of radiative transfer, we formulate the method of optimal prediction, a strategy to approximate the mean solution of a large system by a smaller system. To that end, the formalism is generalized to systems of partial differential equations. Using Gaussian measures, we rederive linear closures, such as PN, diffusion, and diffusion correction closures. In addition, new closures can be derived. We propose a crescendodiffusion closure, which improves classical diffusion closures at no extra cost, as well as parabolictype systems, similar to simpliﬁed PN closures.
