Neural Thermodynamic Integration: Free Energies from Energy-based Diffusion Models

TL;DR

This paper introduces Neural Thermodynamic Integration, a neural network-based approach that efficiently estimates free-energy differences by sampling all intermediate states from a single reference, reducing computational cost.

Contribution

The authors propose a neural network parametrization of the Hamiltonian for thermodynamic integration, enabling accurate free energy calculations from a single simulation.

Findings

Accurately computes excess chemical potential for Lennard-Jones fluids.

Reproduces free energy changes without multiple intermediate simulations.

Reduces computational expense of traditional thermodynamic integration.

Abstract

Thermodynamic integration (TI) offers a rigorous method for estimating free-energy differences by integrating over a sequence of interpolating conformational ensembles. However, TI calculations are computationally expensive and typically limited to coupling a small number of degrees of freedom due to the need to sample numerous intermediate ensembles with sufficient conformational-space overlap. In this work, we propose to perform TI along an alchemical pathway represented by a trainable neural network, which we term Neural TI. Critically, we parametrize a time-dependent Hamiltonian interpolating between the interacting and non-interacting systems, and optimize its gradient using a score matching objective. The ability of the resulting energy-based diffusion model to sample all intermediate ensembles allows us to perform TI from a single reference calculation. We apply our method to Lennard-Jones fluids, where we report accurate calculations of the excess chemical potential, demonstrating that Neural TI reproduces the underlying changes in free energy without the need for simulations at interpolating Hamiltonians.