Rosenbrock Function Benchmark

This benchmark performs convergence tests on a single emulator with variable numbers of input parameters. The example is based on the Rosenbrock function (see https://www.sfu.ca/~ssurjano/rosen.html). This function can be defined in an artibrary number of dimensions, so it provides a useful test for how emulators based on increasing numbers of parameters perform as the size of the training data is varied. As the number of training points increases, the prediction error and prediction variance should decrease. However, this will depend on the number of dimensions in the function – in general, the size of the input space grows exponentially with the number of dimensions, while the samples drawn here grow linearly with the number of dimensions. Thus, the higher dimensional emulators will perform worse for the same number of samples per dimension.