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 criterium 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 preserving 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.
