Parameter Estimation for Several Types of Linear Partial Differential Equations Based on Gaussian Processes

This paper mainly considers the parameter estimation problem for several types of differential equations controlled by linear operators, which may be partial differential, integro-differential and fractional order operators. Under idea data-driven methods, algorithms based on Gaussian processes are constructed to solve inverse problem, where we encode distribution information data into kernels construct an efficient learning machine. We then estimate unknown parameters Equations (PDEs), include high-order equations, a system equations. Finally, numerical tests provided. The results experiments prove that methods not only considered PDEs with high accuracy but also approximate latent solutions inhomogeneous terms simultaneously.