AI 中文总结
研究高斯分子形状重叠，提出基于重要性抽样的无偏蒙特卡罗估计器，能精确计算并集体积，提供解析标准误差，实现置信度受限筛选，在基准测试中表现良好，可进行梯度对齐，还能提供无偏绝对体积和不确定性估计。
AI 中文摘要
高斯分子形状描述是基于3D形状的虚拟筛选的基础，但现有方法通过解析来评估高斯重叠。广泛使用的一阶近似速度快但系统性高估重叠，而精确分子体积需要组合的包含-排除展开。我们引入了第一个高斯形状重叠的随机估计器：一种无偏蒙特卡罗方法，直接从分子的高斯混合中进行重要性抽样。该估计器无偏差地再现解析重叠，并扩展到所有包含-排除阶数的精确并集体积，每个样本成本为O(N)。在类药物分子上，并集估计器与高分辨率网格求积匹配，平均相对误差为0.07%，而一阶近似平均高估真实并集体积3.4倍。该估计器提供解析标准误差，实现置信度受限的筛选，减少94%的采样同时保留排序。在JAX中实现，它是完全可微的，支持在CPU、GPU和TPU上基于梯度的刚性对齐。在DUD-E和LIT-PCBA基准测试中，该方法实现了与现有单构象方法相当的仅形状富集，同时还提供无偏绝对体积和不确定性估计。
英文摘要
Gaussian descriptions of molecular shape underpin 3D shape-based virtual screening, but existing methods evaluate Gaussian overlap analytically. The widely used first-order approximation is fast but systematically overestimates overlap, whereas the exact molecular volume requires a combinatorial inclusion-exclusion expansion. We introduce the first stochastic estimator of Gaussian shape overlap: an unbiased Monte Carlo method that importance-samples directly from a molecule's Gaussian mixture. The estimator reproduces analytic overlap without bias and extends to the exact union volume of all inclusion-exclusion orders with O(N) cost per sample. On drug-like molecules, the union estimator matches high-resolution grid quadrature with a mean relative error of 0.07 percent, while the first-order approximation overestimates the true union volume by 3.4x on average. The estimator provides analytic standard errors, enabling confidence-bounded screening that reduces sampling by 94 percent while preserving ranking. Implemented in JAX, it is fully differentiable and supports gradient-based rigid alignment on CPU, GPU, and TPU. On the DUD-E and LIT-PCBA benchmarks, the method achieves shape-only enrichment comparable to existing single-conformer approaches while additionally providing unbiased absolute volumes and uncertainty estimates.
