Model Mixing Using Bayesian Additive Regression Trees

TL;DR

This paper introduces a Bayesian model mixing approach using BART to combine multiple simulators with input-dependent weights, improving prediction accuracy in complex physical systems.

Contribution

It develops a novel BMM method based on BART that captures local simulator performance, extending existing model averaging techniques.

Findings

Effective in combining multiple models for better predictions.

Demonstrated on nuclear physics simulations with improved accuracy.

Flexible non-parametric approach adapts to local model strengths.

Abstract

In modern computer experiment applications, one often encounters the situation where various models of a physical system are considered, each implemented as a simulator on a computer. An important question in such a setting is determining the best simulator, or the best combination of simulators, to use for prediction and inference. Bayesian model averaging (BMA) and stacking are two statistical approaches used to account for model uncertainty by aggregating a set of predictions through a simple linear combination or weighted average. Bayesian model mixing (BMM) extends these ideas to capture the localized behavior of each simulator by defining input-dependent weights. One possibility is to define the relationship between inputs and the weight functions using a flexible non-parametric model that learns the local strengths and weaknesses of each simulator. This paper proposes a BMM model based on Bayesian Additive Regression Trees (BART). The proposed methodology is applied to combine predictions from Effective Field Theories (EFTs) associated with a motivating nuclear physics application.