Bayesian History Matching of Chiral Effective Field Theory in the Two-Nucleon Sector
Typ
Examensarbete för masterexamen
Program
Publicerad
2022
Författare
May, Eleanor
Modellbyggare
Tidskriftstitel
ISSN
Volymtitel
Utgivare
Sammanfattning
The accurate calculation of nucleon-nucleon scattering observables from first principles
is an ongoing challenge within nuclear physics. Working within the framework
of chiral effective field theory provides a method for calculating such observables.
This is achieved through the construction of an effective Lagrangian that maintains
the symmetries of quantum chromodynamics (QCD). In this thesis, truncation of
the Lagrangian is performed using a modified Weinberg power counting, introducing
a set of unknown low-energy constants at each order in the chiral expansion.
Bayesian history matching is used to explore the leading order description of the
nucleon-nucleon system. This is achieved through the iterative reduction of the
four-dimensional parameter space, taking a Bayes linear approach. The history
matching implementation is validated on the nuclear liquid drop model. Several
novel methods of sampling are introduced within the implementation with the purpose
of capturing correlations between parameters; The generation of ellipsoidal
distributed samples is shown to be the most successful. History matching is subsequently
applied to the proton-neutron scattering problem. We identify the subset
of parameter space containing all low-energy constants that produce model outputs
consistent with experimental two-nucleon scattering data, accounting for relevant
sources of uncertainty. Non-implausible parameter volumes are obtained across a
range of momentum regulator cutoffs. A set of non-implausible samples are used
to predict the deuteron binding energy. Results indicate that the inclusion of this
observable within the history match could further constrain the volumes.
The analysis performed in this thesis was successful in producing sets of nonimplausible
samples. Such sets can be subsequently used as a starting point for
a full Bayesian analysis, with the aim of producing posterior probability distributions
of the parameters. For example, the samples can be used to initialise walkers
within the Markov Chain Monte Carlo method.
Beskrivning
Ämne/nyckelord
global parameter search , computer models , history matching , nuclear physics , liquid drop model , nucleon-nucleon scattering , chiral effective field theory , modified Weinberg power counting , emulators