# B08 - Multiscale Boltzmann Generators

**Head(s): **PD Dr. Jutta Rogal (FU Berlin), Prof. Dr. Cecilia Clementi (FU Berlin)**Project member(s):** **Participating institution(s):** FU Berlin**Research areas:** Mathematics, Statistical Physics, Theoretical Condensed Matter Physics

## Project Summary

Computing equilibrium states in condensed-matter many-body systems, such as solvated proteins, liquids, or crystals, is a long-standing challenge. Lacking methods for generating statistically independent equilibrium samples in “one shot,” vast computational effort is invested for simulating these systems in small steps, e.g., using molecular dynamics (MD). In the last funding period, a new sampling method combining deep learning and statistical mechanics, called “Boltzmann Generator” (BG), was developed by researchers of Project A04. BGs were shown to generate unbiased on-shot equilibrium samples of simple condensed-matter systems and proteins. BGs use invertible neural networks to learn a coordinate transformation between the complex configurational equilibrium distribution and a distribution that can be easily sampled from, providing a new tool in the pursuit of rare-event sampling methods.

While Project A04 focuses on coarse-grained MD methods, the promising research direction of BGs is continued in this new project. Here, we aim to make BGs scalable and applicable to periodic systems. In particular, we want to address three methodological issues: (1) The structures and atomic interactions of condensed-matter molecular systems are characterized by a hierarchy of scales. In order to faithfully represent such systems, we will develop hierachical BGs that map these different scales to different neural network layers, following a renormalization group idea. (2) The physical properties of liquids or crystals are unchanged by permuting equivalent molecules. Such symmetries must be baked into the neural network to make the learning efficient and generalize well. (3) BGs do not yet address the issue of efficiently sampling dynamical pathways. Here, we want to connect BGs with the transition path sampling