论文标题
关于分子图卷积和分子波函数的等效性，基础较差
On the equivalence of molecular graph convolution and molecular wave function with poor basis set
论文作者
论文摘要
在这项研究中，我们证明了原子轨道（LCAO）的线性组合，即Pauling和Lennard-Jones在1920年代引入的量子物理学的近似，对应于分子的图形卷积网络（GCN）。但是，GCN涉及不必要的非线性和深层建筑。我们还验证了分子GCN与在理论计算或量子化学模拟中使用的标准相比，基于较差的基础函数。从这些观察结果中，我们描述了基于基本量子物理学的机器学习（ML）模型的量子深场（QDF），特别是密度功能理论（DFT）。我们认为，QDF模型可以很容易地理解，因为它可以视为单个线性层GCN。此外，它使用两个香草馈电神经网络来学习一个能量功能和Hohenberg-Kohn图，它们具有量子物理和DFT中固有的非线性。对于分子能量预测任务，我们证明了``外推''的生存能力，在该任务中，我们用小分子训练了QDF模型，用大分子对其进行了测试，并实现了高外推性能。这将导致发现有效材料的可靠且实用的应用。该实现可在https://github.com/masashitsubaki/quantumdeepfield_molecule中获得。
In this study, we demonstrate that the linear combination of atomic orbitals (LCAO), an approximation of quantum physics introduced by Pauling and Lennard-Jones in the 1920s, corresponds to graph convolutional networks (GCNs) for molecules. However, GCNs involve unnecessary nonlinearity and deep architecture. We also verify that molecular GCNs are based on a poor basis function set compared with the standard one used in theoretical calculations or quantum chemical simulations. From these observations, we describe the quantum deep field (QDF), a machine learning (ML) model based on an underlying quantum physics, in particular the density functional theory (DFT). We believe that the QDF model can be easily understood because it can be regarded as a single linear layer GCN. Moreover, it uses two vanilla feedforward neural networks to learn an energy functional and a Hohenberg--Kohn map that have nonlinearities inherent in quantum physics and the DFT. For molecular energy prediction tasks, we demonstrated the viability of an ``extrapolation,'' in which we trained a QDF model with small molecules, tested it with large molecules, and achieved high extrapolation performance. This will lead to reliable and practical applications for discovering effective materials. The implementation is available at https://github.com/masashitsubaki/QuantumDeepField_molecule.
