  Background: Modern ab initio theory combined with high-quality
nucleon-nucleon (NN) and three-nucleon (3N) interactions from chiral effective
field theory (EFT) can provide a predictive description of low-energy
light-nuclei reactions relevant for astrophysics and fusion-energy
applications. However, the high cost of computations has so far impeded a
complete analysis of the uncertainty budget of such calculations. Purpose:
Starting from NN potentials up to fifth order (N4LO) combined with
leading-order 3N forces, we study how the order-by-order convergence of the
chiral expansion and confidence intervals for the 3N contact and
contact-plus-one-pion-exchange low-energy constants (cE and cD) contribute to
the overall uncertainty budget of many-body calculations of neutron-He elastic
scattering. Methods: We compute structure and reaction observables for three-,
four- and five-nucleon systems within the ab initio frameworks of the no-core
shell model an no-core shell model with continuum. Using a small set of design
runs, we construct a Gaussian process model (GPM) that acts as a statistical
emulator for the theory. With this, we gain insight into how uncertainties in
the 3N low-energy constants propagate throughout the calculation and determine
the Bayesian posterior distribution of these parameters with Markov-Chain
Monte-Carlo.
