Estimating Solvation Free Energies with Boltzmann Generators

Accurate calculations of solvation free energies remain a central challenge in molecular simulations, often requiring extensive sampling and numerous alchemical intermediates to ensure sufficient overlap between phase-space distributions of a solute in the gas phase and in solution. Here, we introduce a computational framework based on normalizing flows that directly maps solvent configurations between solutes of different sizes, and compare the accuracy and efficiency to conventional free energy estimates. For a Lennard-Jones solvent, we demonstrate that this approach yields acceptable accuracy in estimating free energy differences for challenging transformations, such as solute growth or increased solute-solute separation, which typically demand multiple intermediate simulation steps along the transformation. Analysis of radial distribution functions indicates that the flow generates physically meaningful solvent rearrangements, substantially enhancing configurational overlap between states in configuration space. These results suggest flow-based models as a promising alternative to traditional free energy estimation methods.

Efficient mapping of phase diagrams with conditional normalizing flows

The accurate prediction of phase diagrams is of central importance for both the fundamental understanding of materials as well as for technological applications in material sciences. However, the computational prediction of the relative stability between phases based on their free energy is a daunting task, as traditional free energy estimators require a large amount of simulation data to obtain uncorrelated equilibrium samples over a grid of thermodynamic states. In this work, we develop deep generative machine learning models for entire phase diagrams, employing normalizing flows conditioned on the thermodynamic states, e.g., temperature and pressure, that they map to. By training a single normalizing flow to transform the equilibrium distribution sampled at only one reference thermodynamic state to a wide range of target temperatures and pressures, we can efficiently generate equilibrium samples across the entire phase diagram. Using a permutation-equivariant architecture allows us, thereby, to treat solid and liquid phases on the same footing. We demonstrate our approach by predicting the solid-liquid coexistence line for a Lennard-Jones system in excellent agreement with state-of-the-art free energy methods while significantly reducing the number of energy evaluations needed.