# Non-parametric Bayesian approach to extrapolation problems in configuration interaction methods

## TL;DR

This paper introduces a non-parametric Bayesian extrapolation technique using constrained Gaussian processes for configuration interaction methods, enabling accurate predictions with uncertainty quantification, especially effective with small data sets.

## Contribution

The paper presents a novel non-parametric Bayesian approach that incorporates physical constraints into Gaussian process models for extrapolation in configuration interaction calculations.

## Key findings

- Effective extrapolation with small data sets
- Incorporates physics-guided constraints
- Provides quantified uncertainty in predictions

## Abstract

We propose a non-parametric extrapolation method based on constrained Gaussian processes for configuration interaction methods. Our method has many advantages: (i) applicability to small data sets such as results of {\it ab initio} methods, (ii) flexibility to incorporate constraints, which are guided by physics, into the extrapolation model, (iii) providing predictions with quantified extrapolation uncertainty, etc. In the present study, we show an application to the extrapolation needed in full configuration interaction method as an example.