一种用于化学哈密顿量深度学习的密度泛函紧束缚层
A Density Functional Tight Binding Layer for Deep Learning of Chemical Hamiltonians
摘要：
目前用于预测分子性质的神经网络仅使用量子化学作为训练数据的来源。本文探讨了使用量子化学作为预测过程的一个组成部分的模型。这是通过实现自洽电荷密度函数紧束缚（DFTB）理论作为深度学习模型中使用的层来实现的。的DFTB层，作为输入，从较早的层产生的哈密顿矩阵元素，并产生，作为输出，从相应的DFTB哈密顿量的自洽场解的电子特性。反向传播使得能够有效地训练模型以针对电子特性。DFTB层的两种类型的输入进行了探索，样条和前馈神经网络。由于过拟合可能导致在较小分子上训练的模型在较大分子上表现不佳，因此应用正则化来惩罚非单调行为和哈密顿矩阵元素与用于初始化模型的已发布DFTB模型的哈密顿矩阵元素的偏差。通过比较能量和偶极矩的均方根误差，对具有8个重原子的测试分子，从初始DFTB模型的误差，对15，700种烃类进行了评估。当在具有多达7个重原子的分子上训练时，样条模型将能量的测试误差降低了60%，将偶极矩的测试误差降低了42%。神经网络模型的性能稍好，误差分别减少了67%和59%。在具有多达4个重原子的分子上进行训练会降低性能，样条和神经网络模型都将能量测试误差降低了约53%，偶极子测试误差降低了约25%。
英文摘要：
Current neural networks for predictions of molecular properties use quantum chemistry only as a source of training data. This paper explores models that use quantum chemistry as an integral part of the prediction process. This is done by implementing self-consistent-charge Density-Functional-Tight-Binding (DFTB) theory as a layer for use in deep learning models. The DFTB layer takes, as input, Hamiltonian matrix elements generated from earlier layers and produces, as output, electronic properties from self-consistent field solutions of the corresponding DFTB Hamiltonian. Backpropagation enables efficient training of the model to target electronic properties. Two types of input to the DFTB layer are explored, splines and feed-forward neural networks. Because overfitting can cause models trained on smaller molecules to perform poorly on larger molecules, regularizations are applied that penalize non-monotonic behavior and deviation of the Hamiltonian matrix elements from those of the published DFTB model used to initialize the model. The approach is evaluated on 15,700 hydrocarbons by comparing the root mean square error in energy and dipole moment, on test molecules with 8 heavy atoms, to the error from the initial DFTB model. When trained on molecules with up to 7 heavy atoms, the spline model reduces the test error in energy by 60% and in dipole moments by 42%. The neural network model performs somewhat better, with error reductions of 67% and 59% respectively. Training on molecules with up to 4 heavy atoms reduces performance, with both the spline and neural net models reducing the test error in energy by about 53% and in dipole by about 25%.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
