The Bayesian Committee Approach for Computational Physics Problems

TL;DR

This paper introduces a Bayesian committee-based method that efficiently learns multi-dimensional functions by guiding data sampling using uncertainty and discrepancy measures, outperforming uniform sampling in computational physics tasks.

Contribution

The paper presents a novel combination of Bayesian neural networks and query-by-committee for efficient function learning and sampling in high-dimensional problems.

Findings

Significantly reduces the number of data points needed compared to uniform sampling.

Successfully identifies phase transitions in phase diagram analysis.

Efficiently learns high-dimensional distribution functions for Monte Carlo integration.

Abstract

In this work, we propose a method for efficient learning of a multi-dimensional function. This method combines the Bayesian neural networks and the query-by-committee method. A committee made of deep Bayesian neural networks not only can provide uncertainty of the prediction but also can provide the discrepancy between committee members. Both the uncertainty and the discrepancy are large in the regions where the target function varies rapidly, and therefore, both quantities can be used to guide sampling data to such regions. In this way, we can learn a function accurately with the number of queried data points much less than uniform sampling. Here we test our method with two examples. One example is to find a rare phase in a phase diagram, which is separated from other phases by a second-order phase transition. In this example, the target function is the susceptibility function, and since the divergence of the susceptibility function locates the phase diagram, the task of searching such a phase perfectly matches the advantage of our method. Another example is to learn the distribution function for Monte Carlo integration of a high-dimensional function. In both examples, we show that our method performs significantly efficiently than uniform sampling. Our method can find broad applications in computational scientific problems.