Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densities

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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Cited by in corpus (15)

• Machine Learning Force Fields
• A Comprehensive Survey on Deep Graph Representation Learning
• E(n) Equivariant Graph Neural Networks
• Normalizing flows for atomic solids
• On the design space between molecular mechanics and machine learning force fields
• Introduction to Normalizing Flows for Lattice Field Theory
• Normalizing flows as an enhanced sampling method for atomistic supercooled liquids
• Physics-Aware Neural Implicit Solvers for multiscale, parametric PDEs with applications in heterogeneous media
• Efficient mapping of phase diagrams with conditional Boltzmann Generators
• Molecular relaxation by reverse diffusion with time step prediction
• Adaptive Monte Carlo augmented with normalizing flows
• Leveraging Normalizing Flows for Orbital-Free Density Functional Theory
• Training Invertible Linear Layers through Rank-One Perturbations
• Nearest-Neighbours Neural Network architecture for efficient sampling of statistical physics models
• Neural Mode Jump Monte Carlo