Event generation and consistency tests with sliced Wasserstein distance in high-energy physics

In the field of modern high-energy physics research, there is a growing emphasis on utilizing deep learning techniques to optimize event simulation, thereby expanding the statistical sample size for more accurate physical analysis. Traditional simulation methods often encounter challenges when dealing with complex physical processes and high-dimensional data distributions, resulting in slow performance. To overcome these limitations, we propose a solution based on deep learning with the sliced Wasserstein distance as the loss function. By employing an advanced transformer learning architecture, we initiate the learning process from a Monte Carlo sample and generate high-dimensional data. Through the integration of the sliced Wasserstein distance with the permutation test, we introduce a novel, statistically rigorous, and more sensitive metric for assessing the distribution differences, which significantly outperforms other metrics in detecting subtle distributional shifts, further validating its effectiveness for precise evaluation in high-energy physics generative models and high-dimensional consistency test. The generated data samples maintain all the original distribution features from a limited number of training samples, as evidenced by their successful passage of all common consistency tests using a test sample size of the same order of statistical magnitude. This development opens up new possibilities for improving event simulation and high-dimensional consistency tests in high-energy physics research.