Potentials of constrained Gaussian process modeling in Nuclear Physics*

Gaussian processes have been broadly implemented in Nuclear Physics to approximate the underlying models as well as to understand hidden error structures in observations due to their flexibility in modeling and natural advantage in uncertainty quantification.  In this talk, we focus on two types of Gaussian process models under problem-orientated constraints and their implementation in Nuclear Physics problems. In the first part, we illustrate how to reduce uncertainties in constrained Gaussian process extrapolation via the proton radius puzzle problem, and we propose a general data-integrated Bayesian procedure to recover the source-dependent error structure in experimental data. In the second part, we discuss using a constrained Gaussian process to approximate the solution of a partial differential equation (PDE) where we treat the PDE as constraints over randomly drawn collocation points. A subtle trade-off between approximation accuracy and computational efficiency can be carried out by developing constraint-relaxed prior distributions in aforementioned two methods.