Neural Thermodynamic Integration: Free Energies from Energy-based Diffusion Models
This work addresses the problem of computationally intensive free-energy calculations in molecular simulations, offering a more efficient method for researchers in computational chemistry and physics, though it appears incremental as it builds on existing TI and neural network approaches.
The authors tackled the computational expense and limited applicability of thermodynamic integration (TI) for free-energy estimation by proposing Neural TI, which uses a trainable neural network to represent an alchemical pathway and an energy-based diffusion model to sample intermediate ensembles from a single reference calculation. They demonstrated accurate calculations of the excess chemical potential for Lennard-Jones fluids, reproducing free energy changes without simulations at interpolating Hamiltonians.
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.