Adjoints without Adjoints: emulating model derivatives

Complex models are used as representations of a real-world phenomena and are thus used in many different areas; engineering and oceanography are just two examples. We refer to a complex model, written as a computer code, as a simulator. Derivative information about the simulator output, with respect to the model inputs is potentially useful to many model users, for example in the application of sensitivity analysis or data assimilation. Despite automatic differentiation software, coding an adjoint model remains a complex task and the model when written, is computationally expensive to execute. We suggest an alternative method for generating partial derivatives of complex model output, with respect to model inputs. We propose the use of a Gaussian process emulator, which is a statistical approximator to the simulator. The emulator is built based on data generated from running the simulator at a specified, small number of input points. Here, we show how an emulator can be employed to provide derivative information about the simulator and demonstrate this with examples