发表机构
Tandon School of Engineering, New York University（纽约大学坦登工程学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出基于随机插值器的通用熵差估计方法，利用连续性方程与内积计算，无需散度计算，可恢复统计热力学熵并推广至非平衡熵，在多个复杂系统上验证有效。
AI 中文摘要
我们提出了一种通用方法，利用随机插值器估计任意概率分布之间的熵差。连接基础分布和目标分布的边缘分布满足连续性方程，这使得熵差可以通过概率流速度场和得分场的内积直接计算。该公式具有以下优点：(i) 无需对任一字段进行计算成本高昂的散度计算；(ii) 如果不需要模型可迁移性，甚至无需直接学习得分场；(iii) 在训练过程中几乎免费地即时生成估计值。当选择可处理的基础分布（如高斯链、理想气体等）时，可立即恢复统计热力学熵。值得注意的是，该分析仅依赖于吉布斯-香农熵的定义，而非任何特定的统计力学系综，因此可以计算广义的非平衡熵。该方法在多个复杂度递增的系统上得到了验证：(i) 40维高斯混合模型，(ii) 一维排列的N自旋经典XY模型，(iii) 13原子Lennard-Jones团簇，以及(iv) 活性布朗聚合物。
英文摘要
We present a general method for estimating entropy differences between arbitrary probability distributions using stochastic interpolants. The marginal distributions which bridge the base and target obey a continuity equation, which allows a straightforward calculation of the entropy difference in terms of an inner product of the probability flow velocity and score fields. This formulation has several advantages: (i) no computationally expensive divergence calculations of either field are required, (ii) the score field need not even be learned directly if model transferability is not required, and (iii) on-the-fly estimates are produced nearly for free during training. When tractable base distributions are chosen (e.g. Gaussian chain, ideal gas, etc.), statistical thermodynamic entropies are then immediately recovered. Notably, the analysis relies only on the definition of the Gibbs-Shannon entropy, rather than any particular statistical mechanical ensemble, so that generalized non-equilibrium entropies may be computed. The method is demonstrated on several systems of increasing complexity: (i) a 40-dimensional Gaussian mixture model, (ii) the classical XY model of N spins arranged in one dimension, (iii) the 13-atom Lennard-Jones cluster, and (iv) an active Brownian polymer.
