  We introduce an entirely new class of high-order methods for computational
fluid dynamics (CFD) based on the Gaussian Process (GP) family of stochastic
functions. Our approach is to use kernel-based GP prediction methods to
interpolate/reconstruct high-order approximations for solving hyperbolic PDEs.
We present the GP approach as a new formulation of high-order
(magneto)hydrodynamic state variable interpolation that furnishes an
alternative to conventional polynomial-based approaches.
