Original paper
Probabilistic solutions to ordinary differential equations as nonlinear Bayesian filtering: a new perspective
Abstract
We formulate probabilistic numerical approximations to solutions of ordinary differential equations (ODEs) as problems in Gaussian process (GP) regression with nonlinear measurement functions. This is achieved by defining the measurement sequence to consist of the observations of the difference between the derivative of the GP and the vector field evaluated at the GP—which are all identically zero at the solution of the ODE. When the GP has a...
Paper Details
Title
Probabilistic solutions to ordinary differential equations as nonlinear Bayesian filtering: a new perspective
Published Date
Sep 18, 2019
Journal
Volume
29
Issue
6
Pages
1297 - 1315
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Notes
History