Direct application of a Gaussian process model to generate the inverse function in a parameter estimation problem

Abstract In a parameter estimation problem, the objective is to find the input parameters for some forward model such that the outputs of the model are close to some stated values. These could be measurements from a physical system, or targets in a design problem. A typical approach is to create an optimisation problem, where we search the space of possible parameters and seek to minimise a sum of errors squared. This will often require the forward model to be run many times, which can be computationally expensive. Gaussian process models can be used to model the forward function, which can reduce the computational effort. If a forward function exists, then it may be possible to create an inverse function. This inverse function can then be modelled by a Gaussian process model. We have formulated a method that allows an approximate inverse function to exist for many typical simulation models. We then iteratively create a sequence of Gaussian process models that capture this function. This allows us to solve the parameter estimation problem. This approach uses fewer forward model calculations than typical search algorithms.