Gaussian processes for emulating chiral effective field theory describing few-nucleon systems
Ladda ner
Typ
Examensarbete för kandidatexamen
Bachelor Thesis
Bachelor Thesis
Program
Publicerad
2017
Författare
Larsén, Isak
Karlsson, Daniel
Eriksson, Martin
Wallin, Erik
Helgegren, Rikard
Modellbyggare
Tidskriftstitel
ISSN
Volymtitel
Utgivare
Sammanfattning
Gaussian processes (GPs) can be used for statistical regression, i.e. to predict new data given a set of observed data. In this context, we construct GPs to emulate the calculation of low energy proton-neutron scattering cross sections and the binding energy of the helium-4 nucleus. The GP regression uses so-called kernel functions to approximate the covariance between observed and unknown data points. The emulation is done in an attempt to reduce the large computational cost associated with exact numerical simulation of the observables. The underlying physical theory of the simulation is EFT. This theory enables a perturbative description of low-energy nuclear forces and is governed by a set of low-energy constants to define the terms in the effective Lagrangian. We use the research code nsopt to simulate selected observables using EFT. The GPs used in this thesis are implemented using the Python framework GPy. To measure the performance of a GP we define an error measure called model error by comparing exact simulations to emulated predictions. We also study the time and memory consumption of GPs. The choice of input training data affects the predictive accuracy of the resulting GP. Therefore, we examined different sampling methods with varying amounts of data. We found that GPs can serve as an effective and versatile approach for emulating the examined observables. After the initial high computational cost of training, making predictions with GPs is quick. When trained using the right methods, they can also achieve high accuracy. We concluded that the Matérn 5/2 and RBF kernels perform best for the observables studied. When sampling input points in high dimensions, latin hypercube sampling is shown to be a good method. In general, with a multidimensional input space, it is a good choice to use a kernel function with different sensitivities in different directions. When working with data that spans over many orders of magnitude, logarithmizing the data before training also improves the GP performance. GPs do not appear to be a suitable method for making extrapolations from a given training set, but performs well with interpolations.
Beskrivning
Ämne/nyckelord
Fysik , Physical Sciences