发表机构
MIT; University of Stuttgart（麻省理工学院; 斯图加特大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
CurvFM通过流匹配在训练中约束生成结构的曲率，利用冻结的Hessian预测器，在保持结构精度的同时显著提升过渡态和构象生成的物理保真度。
AI 中文摘要
生成模型能够以高几何精度生成三维分子结构，然而它们是在原子坐标分布上训练的，并未显式访问底层物理。势能面（PES）描述了能量如何随分子几何结构变化，而生成结构与参考结构之间的RMSD仅间接捕捉了这一局部景观。在训练过程中监督PES可以弥合这一差距，但构象和过渡态（TSs）是力为零的驻点，因此一阶量携带的关于它们的信息很少。剩下的就是局部曲率，编码在PES的Hessian矩阵中。量子化学Hessian过于昂贵，无法在训练所需的规模上获得，但最近提出的机器学习预测器使得曲率足够便宜，可以直接监督。我们引入了CurvFM，一种流匹配（FM）公式，其训练目标约束生成结构处的曲率。一个冻结的Hessian预测模型在生成的端点和参考结构处进行评估，这消除了对量子化学Hessian的需求，并使得残差足够便宜，可以在每个训练步骤施加。在TS和构象生成中，CurvFM在保持全局结构精度不变的情况下大幅提高了物理保真度，将GEOM-QM9上最大力的中位数偏差降低了63%，并在三个反应数据集上将有效TS的比例提高了最多10%。
英文摘要
Generative models produce three-dimensional molecular structures with high geometric accuracy, yet they are trained on distributions of atomic coordinates without explicit access to the underlying physics. The potential energy surface (PES) describes how the energy changes around a molecular geometry, and the RMSD between a generated structure and its reference captures this local landscape only indirectly. Supervising the PES during training could close this gap, but conformers and transition states (TSs) are stationary points at which the forces vanish, so first-order quantities carry little information about them. What remains is the local curvature, encoded in the Hessian of the PES. Quantum-chemical Hessians are too expensive to be available at the scale required for training, but recently proposed machine-learned predictors make curvature inexpensive enough to supervise directly. We introduce CurvFM, a flow matching (FM) formulation whose training objective constrains the curvature at the generated structure. A frozen Hessian prediction model is evaluated at the generated endpoint and at the reference structure, which removes the need for quantum-chemical Hessians and keeps the residual cheap enough to impose at every training step. Across TS and conformer generation, CurvFM substantially improves physical fidelity at unchanged global structural accuracy, reducing the median deviation in maximum force by 63% on GEOM-QM9 and raising the fraction of valid TSs by up to 10% across three reaction datasets.
