A New Class of High-Order Methods for Fluid Dynamics Simulations using Gaussian Process Modeling

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.