# On solving Ordinary Differential Equations using Gaussian Processes

@article{Barber2014OnSO, title={On solving Ordinary Differential Equations using Gaussian Processes}, author={David Barber}, journal={ArXiv}, year={2014}, volume={abs/1408.3807} }

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.

## 5 Citations

### Inferring Non-linear State Dynamics using Gaussian Processes

- Computer Science
- 2016

A novel method that uses Gaussian processes to infer the dynamics of states governed by non-linear ordinary differential equations (ODE’s) and provides a proxy to the intractable posterior distribution over states using mean-field approximation, thus simplifying previous approaches.

### Probabilistic solvers for partial differential equations

- Computer Science, Mathematics
- 2016

A probabilistic solver suitable for linear partial differential equations (PDE) with mixed (Dirichlet and Neumann) boundary conditions defined on arbitrary geometries is developed.

### Bayesian Smooth-and-Match strategy for ordinary differential equations models that are linear in the parameters

- Computer Science
- 2016

This work focuses on the class of techniques that use smoothing to avoid direct integration and, in particular, on a Bayesian Smooth-and-Match strategy that allows to obtain the ODEs' solution while performing inference on models that are linear in the parameters.

### Bayesian smooth‐and‐match inference for ordinary differential equations models linear in the parameters

- Computer ScienceStatistica Neerlandica
- 2020

This work develops a Bayesian smooth‐and‐match strategy that approximates the ODE solution while performing Bayesian inference on the model parameters and incorporates in the strategy two main sources of uncertainty: the noise level of the measured observations and the model approximation error.

### A probabilistic model for the numerical solution of initial value problems

- Computer Science, MathematicsStatistics and Computing
- 2018

A new view of probabilistic ODE solvers as active inference agents operating on stochastic differential equation models that estimate the unknown initial value problem (IVP) solution from approximate observations of the solution derivative, as provided by the ODE dynamics is provided.

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