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 denoising-diffusion 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 is capable of coupling hundreds of degrees of freedom at once.

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，为估算自由能差提供了一种严谨的方法。然而，TI计算计算成本高昂，并且通常仅限于耦合少量自由度，因为需要对大量具有足够构象空间重叠的中间系综进行采样。在本工作中，我们提出沿一个由可训练神经网络表示的人工路径执行TI，我们称之为神经TI。关键之处在于，我们参数化了一个随时间变化的哈密顿量，该量在相互作用系统与非相互作用系统之间进行插值，并使用去噪扩散目标优化其梯度。由此得到的基于能量的扩散模型能够对所有中间系综进行采样，这使得我们可以从单一参考计算出发执行TI。我们将该方法应用于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能够一次性耦合数百个自由度。