Abstract
Short autocorrelation times are essential for a reliable error assessment in Monte Carlo simulations of lattice systems. In many interesting scenarios, the decay of autocorrelations in the Markov chain is prohibitively slow. Generative samplers can provide statistically independent field configurations, thereby potentially ameliorating these issues. In this work, the applicability of neural samplers to this problem is investigated. Specifically, we work with a generative adversarial network (GAN). We propose to address difficulties regarding its statistical exactness through the implementation of an overrelaxation step, by searching the latent space of the trained generator network. This procedure can be incorporated into a standard Monte Carlo algorithm, which then permits a sensible assessment of ergodicity and balance based on consistency checks. Numerical results for real, scalar φ 4-theory in two dimensions are presented. We achieve a significant reduction of autocorrelations while accurately reproducing the correct statistics. We discuss possible improvements to the approach as well as potential solutions to persisting issues.
Highlights
Minimizing the statistical error is essential for applications of lattice simulations
We propose the implementation of an overrelaxation step using a generative adversarial network (GAN), in combination with a traditional hybrid Monte Carlo (HMC) algorithm
In order to avoid the aforementioned issues, we propose to implement the GAN as an overrelaxation step, which can be integrated into any action-based importance sampling algorithm
Summary
Minimizing the statistical error is essential for applications of lattice simulations. A reliable assessment of this error requires sufficiently short autocorrelation times in the Markov chain This becomes a problem in models affected by critical slowing down, which is a severe hindrance for the extrapolation of lattice calculations to the continuum. We propose the implementation of an overrelaxation step using a GAN, in combination with a traditional hybrid Monte Carlo (HMC) algorithm This approach effectively breaks the Markov chain for observables unrelated to the action, thereby leading to a reduction in the associated autocorrelation times. We demonstrate that by introducing the GAN overrelaxation step, a significant reduction of the autocorrelation time of the magnetization can be achieved (Figure 8) We argue that such an approach could greatly improve the computational efficiency of traditional sampling techniques and our results motivate further research into the matter.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
