Conditional generative models for sampling and phase transition indication in spin systems

Abstract

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.

Detection of Berezinskii-Kosterlitz-Thouless transition via Generative Adversarial Networks

“…Note added: during the submission process of this manuscript we found out [51] that provides a slightly different approach to the detection of phase transitions in spin systems using a GAN architecture. The stability of the method was checked by comparing the loss curves for different training regions, we report in Fig.…”

Sampling Lattices in Semi-Grand Canonical Ensemble with Autoregressive Machine Learning

“…Inspired by previous generative models that change the sampled distribution with temperature 20,30,31 , the dependencies between sites are also functions of the thermodynamic constraints, allowing the conditions to control the microstate probabilities,…”

Generative learning for the problem of critical slowing down in lattice Gross-Neveu model

“…In [11], supervised learning has been adopted to accelerate the MC simulations for statistical physics problems, a self learning MC has been proposed in [12] to reduce the autocorrelation time specially near the critical region by learning an effective Hamiltonian. In recent times some machine learning approaches [13][14][15][16][17][18][19][20] are used to circumvent the problem of diverging autocorrelation time in lattice filed theory and XY model [21] as well. Machine Learning(ML) has been also applied to circumvent the problem of critical slowing down in U(1) gauge theory [17] and parameter regression task in [15].…”