Abstract
We explore the perspectives of machine learning techniques in the context of quantum field theories. In particular, we discuss two-dimensional complex scalar field theory at nonzero temperature and chemical potential -- a theory with a nontrivial phase diagram. A neural network is successfully trained to recognize the different phases of this system and to predict the value of various observables, based on the field configurations. We analyze a broad range of chemical potentials and find that the network is robust and able to recognize patterns far away from the point where it was trained. Aside from the regressive analysis, which belongs to supervised learning, an unsupervised generative network is proposed to produce new quantum field configurations that follow a specific distribution. An implicit local constraint fulfilled by the physical configurations was found to be automatically captured by our generative model. We elaborate on potential uses of such a generative approach for sampling outside the training region.
Highlights
Deep learning with a hierarchical structure of artificial neural networks is a branch of machine learning aiming at understanding and extracting high-level representations of big data [1]
We further demonstrate the capability of deep neural networks in learning physical observables, even with highly nonlinear dependence on the field configurations and with only limited training data— providing an effective high-dimensional nonlinear regression method
We proposed a set of novel techniques for the investigation of a lattice-regularized quantum field theory by deep neural networks, including discovering hidden correlations, learning observables, and producing field configurations
Summary
Deep learning with a hierarchical structure of artificial neural networks is a branch of machine learning aiming at understanding and extracting high-level representations of big data [1]. Significant progress has been made in utilizing machine learning methods for condensed matter systems like classical or quantum spin models Specific tasks in these settings include the discrimination between certain phases and the identification of phase transitions [11,12,13,14,15], the compressed representation of quantum wave functions [16], or the acceleration of Monte Carlo algorithms [17,18,19]. We proceed by implementing, for the first time, a generative adversarial network (GAN) [24] for lattice field theory to generate field configurations following and generalizing the training set distribution This is an unsupervised learning framework that uses unlabeled data to perform representation learning. Further potential use of such setups would be for reducing large ensembles of field configurations into a single (highly trained) network as an efficient representation for the quantum statistical field ensembles, thereby significantly reducing storage requirements
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