Emil Hoffmann

Maximilian Schebek, Jiajun He, Emil Hoffmann et al. · cambridge

The accurate estimation of free energy differences between two states is a long-standing challenge in molecular simulations. Traditional approaches generally rely on sampling multiple intermediate states to ensure sufficient overlap in phase space and are, consequently, computationally expensive. Several generative-model-based methods have recently addressed this challenge by learning a direct bridge between distributions, bypassing the need for intermediate states. However, it remains unclear which approaches provide the best trade-off between efficiency, accuracy, and scalability. In this work, we systematically review these methods and benchmark selected approaches with a focus on condensed-matter systems. In particular, we investigate the performance of discrete and continuous normalizing flows in the context of targeted free energy perturbation as well as FEAT (Free energy Estimators with Adaptive Transport) together with the escorted Jarzynski equality, using coarse-grained monatomic ice and Lennard-Jones solids as benchmark systems. We evaluate accuracy, data efficiency, computational cost, and scalability with system size. Our results provide a quantitative framework for selecting effective free energy estimation strategies in condensed-phase systems.

Emil Hoffmann, Maximilian Schebek, Leon Klein et al.

Sampling equilibrium distributions is fundamental to statistical mechanics. While flow matching has emerged as scalable state-of-the-art paradigm for generative modeling, its potential for equilibrium sampling in condensed-phase systems remains largely unexplored. We address this by incorporating the periodicity inherent to these systems into continuous normalizing flows using Riemannian flow matching. The high computational cost of exact density estimation intrinsic to continuous normalizing flows is mitigated by using Hutchinson's trace estimator, utilizing a crucial bias-correction step based on cumulant expansion to render the stochastic estimates suitable for rigorous thermodynamic reweighting. Our approach is validated on monatomic ice, demonstrating the ability to train on systems of unprecedented size and obtain highly accurate free energy estimates without the need for traditional multistage estimators.