Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densities

• URL: http://arxiv.org/abs/2006.02425v2
• Date: Mon, 26 Oct 2020 11:39:04 GMT
• Title: Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densities
• Authors: Jonas K\"ohler, Leon Klein and Frank No\'e
• Abstract summary: Normalizing flows are exact-likelihood generative neural networks which transform samples from a simple prior distribution to samples of the probability distribution of interest. Recent work showed that such generative models can be utilized in statistical mechanics to sample equilibrium states of many-body systems in physics and chemistry.
• Score: 1.7188280334580197
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Normalizing flows are exact-likelihood generative neural networks which approximately transform samples from a simple prior distribution to samples of the probability distribution of interest. Recent work showed that such generative models can be utilized in statistical mechanics to sample equilibrium states of many-body systems in physics and chemistry. To scale and generalize these results, it is essential that the natural symmetries in the probability density -- in physics defined by the invariances of the target potential -- are built into the flow. We provide a theoretical sufficient criterion showing that the distribution generated by \textit{equivariant} normalizing flows is invariant with respect to these symmetries by design. Furthermore, we propose building blocks for flows which preserve symmetries which are usually found in physical/chemical many-body particle systems. Using benchmark systems motivated from molecular physics, we demonstrate that those symmetry preserving flows can provide better generalization capabilities and sampling efficiency.

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