Enhancing accuracy of deep learning algorithms by training with low-discrepancy sequences

TL;DR

This paper introduces a deep learning training method using low-discrepancy sequences, which improves accuracy over traditional random sampling, especially in moderately high-dimensional problems, and offers an efficient approach for scientific computing surrogates.

Contribution

It presents a novel deep supervised learning algorithm that leverages low-discrepancy sequences for training data, outperforming standard methods in accuracy and efficiency.

Findings

Significant accuracy improvement over standard algorithms.

Effective in moderately high-dimensional problems.

Provides an efficient surrogate modeling approach.

Abstract

We propose a deep supervised learning algorithm based on low-discrepancy sequences as the training set. By a combination of theoretical arguments and extensive numerical experiments we demonstrate that the proposed algorithm significantly outperforms standard deep learning algorithms that are based on randomly chosen training data, for problems in moderately high dimensions. The proposed algorithm provides an efficient method for building inexpensive surrogates for many underlying maps in the context of scientific computing.