Probability Measures for Numerical Solutions of Differential Equations

摘要: In this paper, we present a formal quantification of epistemic uncertainty induced by numerical solutions ordinary and partial differential equation models. Numerical equations contain inherent uncertainties due to the finite dimensional approximation an unknown implicitly defined function. When statistically analysing models based on describing physical, or other naturally occurring, phenomena, it is therefore important explicitly account for introduced method. This enables objective determination its importance relative uncertainties, such as those caused data contaminated with noise model error missing physical inadequate descriptors. To end show that wide variety existing solvers can be randomised, inducing probability measure over equations. These measures exhibit contraction Dirac around true solution, where rates convergence are consistent underlying deterministic Ordinary elliptic used illustrate approach quantifying in both statistical analysis forward inverse problems.