High-dimensional-nonlinear function estimation using large datasets is a current area of interest in the machine learning community. Applications permeate throughout the analytical sciences, where evergrowing datasets are providing more information to the analyst. This paper leverages the existing relevance vector machine, a sparse Bayesian version of the well-studied support vector machine and expands the method to include integrated feature selection and automatic function shaping. These innovations produce an algorithm that can distinguish variables useful for predicting a response from variables that are unrelated or confusing. The technology has been tested using synthetic data, initial performance studies have been conducted, and a model has been developed that is capable of making position-independent predictions of the core-averaged burnup using a single specimen drawn randomly from a nuclear reactor core.