Neural Thermodynamic\nIntegration: Free Energies from\nEnergy-Based Diffusion Models

Thermodynamic integration (TI) offers a rigorous method\nfor estimating\nfree-energy differences by integrating over a sequence of interpolating\nconformational ensembles. However, TI calculations are computationally\nexpensive and typically limited to coupling a small number of degrees\nof freedom due to the need to sample numerous intermediate ensembles\nwith sufficient conformational-space overlap. In this work, we propose\nto perform TI along an alchemical pathway represented by a trainable\nneural network, which we term Neural TI. Critically, we parametrize\na time-dependent Hamiltonian interpolating between the interacting\nand noninteracting systems and optimize its gradient using a score\nmatching objective. The ability of the resulting energy-based diffusion\nmodel to sample all intermediate ensembles allows us to perform TI\nfrom a single reference calculation. We apply our method to Lennard-Jones\nfluids, where we report accurate calculations of the excess chemical\npotential, demonstrating that Neural TI reproduces the underlying\nchanges in free energy without the need for simulations at interpolating\nHamiltonians.