Gaussian processes for Bayesian estimation in ordinary differential equations

Copyright © (2014) by the International Machine Learning Society (IMLS) All rights reserved. Bayesian parameter estimation in coupled ordinary differential equations (ODEs) is challeng-ing due to the high computational cost of numerical integration. In gradient matching a separate data model is introduced with the property that its gradient may be calculated easily. Parameter estimation is then achieved by requiring consistency between the gradients computed from the data model and those specified by the ODE. We propose a Gaussian process model that directly links state derivative information with system observations, simplifying previous approaches and improving estimation accuracy.