2021/10/01 by Jonas Köhler, Andreas Krämer, Köhler, Jonas +3 · 5 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · #Chemical Physics (physics.chem-ph) #FOS: Computer and information sciences #FOS: Physical sciences #Gaussian Processes and Bayesian Inference #Generative Adversarial Networks and Image Synthesis #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Protein Structure and Dynamics
paper · pdf · doi:10.48550/arxiv.2110.00351
openalex publication_date 2021/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Normalizing flows are a promising tool for modeling probability distributions in physical systems. While state-of-the-art flows accurately approximate distributions and energies, applications in physics additionally require smooth energies to compute forces and higher-order derivatives. Furthermore, such densities are often defined on non-trivial topologies. A recent example are Boltzmann Generators for generating 3D-structures of peptides and small proteins. These generative models leverage the space of internal coordinates (dihedrals, angles, and bonds), which is a product of hypertori and compact intervals. In this work, we introduce a class of smooth mixture transformations working on both compact intervals and hypertori. Mixture transformations employ root-finding methods to invert them in practice, which has so far prevented bi-directional flow training. To this end, we show that parameter gradients and forces of such inverses can be computed from forward evaluations via the inverse function theorem. We demonstrate two advantages of such smooth flows: they allow training by force matching to simulation data and can be used as potentials in molecular dynamics simulations.