论文标题
Kohn-Sham方程式作为正规器：将先验知识纳入机器学习物理学
Kohn-Sham equations as regularizer: building prior knowledge into machine-learned physics
论文作者
论文摘要
包括先验知识对于物理学中的有效机器学习模型很重要，通常通过明确添加损失条款或模型架构的约束来实现。物理计算中嵌入的先验知识本身很少引起人们的注意。我们表明，在训练神经网络以进行交换相关功能时，解决Kohn-Sham方程提供了一个隐含的正则化，从而大大改善了概括。两个分隔足以学习整个一维H $ _2 $解离曲线，包括强度强度的区域。我们的模型还推广到看不见的分子类型并克服自我相互作用误差。
Including prior knowledge is important for effective machine learning models in physics, and is usually achieved by explicitly adding loss terms or constraints on model architectures. Prior knowledge embedded in the physics computation itself rarely draws attention. We show that solving the Kohn-Sham equations when training neural networks for the exchange-correlation functional provides an implicit regularization that greatly improves generalization. Two separations suffice for learning the entire one-dimensional H$_2$ dissociation curve within chemical accuracy, including the strongly correlated region. Our models also generalize to unseen types of molecules and overcome self-interaction error.
