Molecules are frequently represented as graphs, but the underlying 3D molecular geometry (the locations of the atoms) ultimately determines most molecular properties. However, most molecules are not static and at room temperature adopt a wide variety of geometries or $\textit{conformations}$. The resulting distribution on geometries $p(x)$ is known as the Boltzmann distribution, and many molecular properties are expectations computed under this distribution. Generating accurate samples from the Boltzmann distribution is therefore essential for computing these expectations accurately. Traditional sampling-based methods are computationally expensive, and most recent machine learning-based methods have focused on identifying $\textit{modes}$ in this distribution rather than generating true $\textit{samples}$. Generating such samples requires capturing conformational variability, and it has been widely recognized that the majority of conformational variability in molecules arises from rotatable bonds. In this work, we present VonMisesNet, a new graph neural network that captures conformational variability via a variational approximation of rotatable bond torsion angles as a mixture of von Mises distributions. We demonstrate that VonMisesNet can generate conformations for arbitrary molecules in a way that is both physically accurate with respect to the Boltzmann distribution and orders of magnitude faster than existing sampling methods.

翻译：分子常被表示为图结构，但其潜在的三维分子几何形状（原子位置）最终决定了大多数分子性质。然而，多数分子并非静止不变，在室温下会呈现多种几何形态，即$\textit{构象}$。由此产生的几何分布$p(x)$被称为玻尔兹曼分布，许多分子性质是该分布下的期望值。因此，从玻尔兹曼分布中精确采样对于准确计算这些期望值至关重要。传统的基于采样的方法计算成本高昂，而近期大多数基于机器学习的方法侧重于识别该分布中的$\textit{模态}$，而非生成真实的$\textit{样本}$。生成此类样本需要捕捉构象变异性，且人们普遍认为分子中绝大多数构变异性源于可旋转键。在本工作中，我们提出了VonMisesNet——一种新型图神经网络，它通过将可旋转键的扭角近似为冯·米塞斯分布的混合变分形式，来捕捉构象变异性。我们证明，VonMisesNet能够以符合玻尔兹曼分布的物理精度，为任意分子生成构象，且速度比现有采样方法快数个数量级。