Mathematical Sciences

Lund University

  • Title: Using Emulators for Optimisation and Parameter Estimation
  • Short description:

    The basic idea of a Gaussian process emulator is to fit a statistical model to output from a (computationally expensive) complex model. The statistical model can then be used to cheaply obtain new values from the complex model. If the complex model contains parameters which have to be optimised the emulator can be used to aid the optimisation by suggesting new evalution points, and excluding unlikely regions from the optimisation. Here the emulator will be used to fit a vegetation model to observed data.

  • Long description:

    Gaussian process (GP) emulators can be used as an alternative to computationally expensive and complex computer models. The idea is to fit a statistical model to a few evaluations of the expensive model and then use the statistical model as a computationally faster replacement for the complex model. If the complex model contains parameters the emulator can be used to aid in the estimation of these parameters. By fitting a GP to the function at evaluation points we will try to reconstruct the function surface, allowing us to determine suitable new evaluation points. To determine new evaluation points we will use theory regarding optimal placement of monitoring stations from spatial statistics.

    This approach has previously been used for training in machine learning, here we will use it to fit a vegetation model to observed data by finding good parameters for the vegetation model. The vegetation model is highly non-linear and expensive (several minutes per evaluation) to use. Finding a cheaper, robust alternative to the parameter estimation would be very good.

    The project will first use the emulator to maximise a few well known test functions. Building understanding for the model and process, before trying to handle the vegetation model.

    Article:
    Practical Bayesian Optimization of Machine Learning Algorithms - Snoek et. al.
    https://arxiv.org/abs/1206.2944

  • Contact: Johan Lindström