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.

翻译：热力学积分（TI）通过在一系列插值构象系综上进行积分，为估算自由能差异提供了一种严谨的方法。然而，由于需要对大量具有足够构象空间重叠的中间系综进行采样，TI计算的计算成本高昂，并且通常仅限于耦合少数自由度。在本工作中，我们提出沿一个由可训练神经网络表示的炼金术路径执行TI，我们称之为神经TI。关键之处在于，我们参数化了一个在相互作用系统与非相互作用系统之间插值的时间依赖哈密顿量，并使用分数匹配目标来优化其梯度。由此产生的基于能量的扩散模型能够对所有中间系综进行采样，这使得我们可以通过单一参考计算来执行TI。我们将我们的方法应用于Lennard-Jones流体，报告了超额化学势的精确计算结果，证明了神经TI能够再现自由能的潜在变化，而无需在插值哈密顿量下进行模拟。