Active learning spectral function using Bayesian Neural Network and Gaussian process

Recently, various machine learning models have been used successfully as surrogate models to compute spectral function and other complicated vector valued quantities. While the machine learning models, after appropriate training and hyper-parameter optimization, give highly accurate results and provide few orders of magnitude speed up, they are notorious for being data hungry. This has limited the application of machine learning models for most practical applications, especially when data generation becomes very costly.

In this work, we investigate Bayesian neural network and Gaussian process methods on two sets of spectral function data that were previously studied using deep neural network. Our preliminary results suggest that active learning methods, which prompt on-line data generation iteratively on selected regions of parameter space based on uncertainty measure of the surrogate model, provide results comparable to the brute force deep neural network by using less than 10% of the original dataset.