Symmetries and phase diagrams with real-space mutual information neural estimation
Metadata only
Date
2021-12Type
- Journal Article
Abstract
Real-space mutual information (RSMI) was shown to be an important quantity, formally and from a numerical standpoint, in finding coarse-grained descriptions of physical systems. It very generally quantifies spatial correlations and can give rise to constructive algorithms extracting relevant degrees of freedom. Efficient and reliable estimation or maximization of RSMI is, however, numerically challenging. A recent breakthrough in theoretical machine learning has been the introduction of variational lower bounds for mutual information, parametrized by neural networks. Here we describe in detail how these results can be combined with differentiable coarse-graining operations to develop a single unsupervised neural-network-based algorithm, the RSMI-NE, efficiently extracting the relevant degrees of freedom in the form of the operators of effective field theories, directly from real-space configurations. We study the information contained in the statistical ensemble of constructed coarse-graining transformations and its recovery from partial input data using a secondary machine learning analysis applied to this ensemble. In particular, we show how symmetries, also emergent, can be identified. We demonstrate the extraction of the phase diagram and the order parameters for equilibrium systems and consider also an example of a nonequilibrium problem. Show more
Publication status
publishedExternal links
Journal / series
Physical Review EVolume
Pages / Article No.
Publisher
American Institute of PhysicsSubject
Statistical physics; Critical phenomena; Renormalization group; Coarse graining; Information theory; Machine learningOrganisational unit
08714 - Gruppe Huber
Funding
771503 - Topological Mechanical Metamaterials (EC)
More
Show all metadata