EXPLICIT ESTIMATION OF DERIVATIVES FROM DATA AND DIFFERENTIAL EQUATIONS BY GAUSSIAN PROCESS REGRESSION

In this work, we employ the Bayesian inference framework to solve problem of estimating solution and particularly, its derivatives, which satisfy a known differential equation, from given noisy scarce observations data only. To address key issue accuracy robustness derivative estimation, use Gaussian processes jointly model solution, equation. By regarding linear equation as constraint, process regression with constraint method (GPRC) is developed improve prediction derivatives. For nonlinear equations, propose Picard-iteration-like approximation linearization around obtained only so that our GPRC can be still iteratively applicable. Besides, product experts applied ensure initial or boundary condition considered further enhance We present several numerical results illustrate advantages new in comparison standard data-driven regression.