On the equivalence of molecular graph convolution and molecular wave function with poor basis set
On the equivalence of molecular graph convolution and molecular wave function with poor basis set
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发表时间：
2020-11
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通讯作者：
Masashi Tsubaki;T. Mizoguchi
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作者：
Masashi Tsubaki;T. Mizoguchi
在这项研究中，我们证明了原子轨道的线性组合（LCAO），一种由Pauling和Lennard-Jones在20世纪20年代引入的近似量子物理学，对应于分子的图卷积网络（GCNs）。然而，GCNs涉及不必要的非线性和深度架构。我们还验证了与理论计算或量子化学模拟中使用的标准基函数集相比，分子GCNs基于较差的基函数集。从这些观察中，我们描述了量子深场（QDF），这是一种基于底层量子物理学的机器学习（ML）模型，特别是密度泛函理论（DFT）。我们认为QDF模型很容易理解，因为它可以被看作是一个单一的线性层GCN。此外，它使用两个香草前馈神经网络来学习具有量子物理和DFT固有非线性的能量泛函和Hohenberg- Kohn映射。对于分子能量预测任务，我们展示了“外推”的可行性，其中我们用小分子训练了一个QDF模型，用大分子测试了它，并获得了很高的外推性能。这将为发现有效材料带来可靠和实际的应用。该实现可在此https URL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 this https URL.