# Active Learning Algorithm for Computational Physics

## TL;DR

This paper introduces an active learning algorithm using neural networks and query by committee to efficiently compute multi-dimensional physical functions, significantly reducing data requirements while maintaining accuracy.

## Contribution

The work presents a novel active learning protocol for fitting multi-dimensional functions in physics, demonstrating efficiency and accuracy improvements over uniform sampling methods.

## Key findings

- Achieves few percent error with less than 10% data compared to uniform sampling.
- Effectively identifies regions with rapid function variation for targeted data acquisition.
- Applicable to diverse physics problems like atomic and condensed matter physics.

## Abstract

In large-scale computation of physics problems, one often encounters the problem of determining a multi-dimensional function, which can be time-consuming when computing each point in this multi-dimensional space is already time-demanding. In the work, we propose that the active learning algorithm can speed up such calculations. The basic idea is to fit a multi-dimensional function by neural networks, and the key point is to make the query of labeled data economically by using a stratagem called "query by committee". We present the general protocol of this fitting scheme, as well as the procedure of how to further compute physical observables with the fitted functions. We show that this method can work well with two examples, which are quantum three-body problem in atomic physics and the anomalous Hall conductivity in condensed matter physics, respectively. In these examples, we show that one reaches an accuracy of few percent error for computing physical observables with less than $10\%$ of total data points compared with uniform sampling. With these two examples, we also visualize that by using the active learning algorithm, the required data are added mostly in the regime where the function varies most rapidly, which explains the mechanism for the efficiency of the algorithm. We expect broad applications of our method on various kind of computational physics problems.