On solving Ordinary Differential Equations using Gaussian Processes
This work addresses the problem of solving ODEs for researchers in computational mathematics and machine learning, but it is incremental as it builds on existing Gaussian Process approaches.
The authors tackled solving nonlinear ordinary differential equations by proposing Gaussian Process-based methods, including explicit and implicit approaches, which achieved greater accuracy than previous Gaussian Process methods.
We describe a set of Gaussian Process based approaches that can be used to solve non-linear Ordinary Differential Equations. We suggest an explicit probabilistic solver and two implicit methods, one analogous to Picard iteration and the other to gradient matching. All methods have greater accuracy than previously suggested Gaussian Process approaches. We also suggest a general approach that can yield error estimates from any standard ODE solver.