Coarse-Grained Boltzmann Generators

Sampling equilibrium molecular configurations from the Boltzmann distribution is a longstanding challenge. Boltzmann Generators (BGs) address this by combining exact-likelihood generative models with importance sampling, but their practical scalability is limited. Meanwhile, coarse-grained surrogates enable the modeling of larger systems by reducing effective dimensionality, yet often lack the reweighting process required to ensure asymptotically correct statistics. In this work, we propose Coarse-Grained Boltzmann Generators (CG-BGs), a principled framework that unifies scalable reduced-order modeling with the exactness of importance sampling. CG-BGs act in a coarse-grained coordinate space, using a learned potential of mean force (PMF) to reweight samples generated by a flow-based model. Crucially, we show that this PMF can be efficiently learned from rapidly converged data via force matching. Our results demonstrate that CG-BGs faithfully capture complex interactions mediated by explicit solvent within highly reduced representations, establishing a scalable pathway for the unbiased sampling of larger molecular systems.

💡 Research Summary

The paper tackles the long‑standing difficulty of sampling equilibrium molecular configurations from the Boltzmann distribution for high‑dimensional atomistic systems. Traditional Boltzmann Generators (BGs) achieve exact sampling by learning a diffeomorphic map between a simple prior and the full configuration space, but they suffer from two major scalability bottlenecks: (i) the need to compute Jacobian determinants, which scales poorly with dimensionality, and (ii) diminishing overlap between the learned proposal density and the true Boltzmann density as system size grows, leading to high‑variance importance weights. Coarse‑graining (CG) offers a complementary route by projecting atomistic coordinates onto a low‑dimensional set of collective variables (CVs), yet most CG models lack a reweighting step and therefore produce biased statistics when trained on non‑equilibrium data.

The authors introduce Coarse‑Grained Boltzmann Generators (CG‑BGs), a framework that operates directly in CG space. The target distribution p(R) over CG coordinates R is defined by a learned potential of mean force (PMF) Uη(R), such that p(R) ∝ exp