In this work, we study generative adversarial networks (GANs) as a tool to learn the distribution of spin configurations and to generate samples, conditioned on external tuning parameters or other quantities associated with individual configurations. For concreteness, we focus on two examples of conditional variables---the temperature of the system and the energy of the samples. We show that temperature-conditioned models can not only be used to generate samples across thermal phase transitions, but also be employed as unsupervised indicators of transitions. To this end, we introduce a GAN-fidelity measure that captures the model’s susceptibility to external changes of parameters. The proposed energy-conditioned models are integrated with Monte Carlo simulations to perform over-relaxation steps, which break the Markov chain and reduce auto-correlations. We propose ways of efficiently representing the physical states in our network architectures, e.g., by exploiting symmetries, and to minimize the correlations between generated samples. A detailed evaluation, using the two-dimensional XY model as an example, shows that these incorporations bring in considerable improvements over standard machine-learning approaches. We further study the performance of our architectures when no training data is provided near the critical region.
Cited by 1
Del Debbio et al., Efficient modeling of trivializing maps for lattice
theory using normalizing flows: A first look at scalability
Phys. Rev. D 104, 094507 (2021) [Crossref]
Authors / Affiliations: mappings to Contributors and OrganizationsSee all Organizations.
- 1 Japneet Singh,
- 2 3 Mathias Scheurer,
- 1 Vipul Arora
- 1 भारतीय प्रौद्योगिकी संस्थान कानपुर / Indian Institute of Technology Kanpur [IITK]
- 2 Harvard University
- 3 Institut für Theoretische Physik / Institute for theoretical Physics, University of Innsbruck [ITP]