An introduction to computational complexity and statistical learning theory applied to nuclear models
This work tackles the problem of model precision in nuclear physics for researchers dealing with finite data constraints, representing an incremental application of existing theoretical frameworks to a specific domain.
The paper addresses the challenge of extracting precise nuclear models from limited experimental data by applying computational complexity and statistical learning theory to determine the data requirements for achieving a specified precision in mass model extrapolation.
The fact that we can build models from data, and therefore refine our models with more data from experiments, is usually given for granted in scientific inquiry. However, how much information can we extract, and how precise can we expect our learned model to be, if we have only a finite amount of data at our disposal? Nuclear physics demands an high degree of precision from models that are inferred from the limited number of nuclei that can be possibly made in the laboratories. In manuscript I will introduce some concepts of computational science, such as statistical theory of learning and Hamiltonian complexity, and use them to contextualise the results concerning the amount of data necessary to extrapolate a mass model to a given precision.