On the Bayesian solution of differential equations
Junyang is working in the recent and emerging field of Probabilistic Numerics. This field interprets traditional numerical analysis methods, such as numerical differential equation solvers, as statistical estimation methods.
This has the advantage of allowing the statistical quantification of discretisation error in numerical algorithms both theoretically and when implemented in a computational pipeline.
In particular, Junyang is working on Bayesian Probabilistic Numerical Methods for Ordinary Differential Equations (ODEs). This involves exploiting the underlying structure of the ODE via Lie group methods to obtain a posterior distribution over the solution of the differential equation.
On the Bayesian Solution of Differential Equations - Wang, J. Cockayne, J. Oates, C. - 38th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering - June 2019
