Bayesian ODE solvers: the maximum a posteriori estimate

Abstract There is a growing interest in probabilistic numerical solutions to ordinary differential equations. In this paper, the maximum posteriori estimate studied under class of $$\nu $$ ν times differentiable linear time-invariant Gauss–Markov priors, which can be computed with an iterated extended Kalman smoother. The corresponds optimal interpolant reproducing kernel Hilbert space associated prior, present case equivalent Sobolev smoothness +1$$ + 1 . Subject mild conditions on vector field, convergence rates are then obtained via methods from nonlinear analysis and scattered data approximation. These results closely resemble classical sense that prior process obtains global order , demonstrated examples.