Kohn-Sham Equations as Regularizer: Building Prior Knowledge into Machine-Learned Physics
Kohn-Sham Equations as Regularizer: Building Prior Knowledge into Machine-Learned Physics
复制标题
DOI：
10.1103/physrevlett.126.036401
复制
发表时间：
2021-01-20
影响因子：
8.6
通讯作者：
Burke, Kieron
中科院分区：
文献类型：
--
作者：
Li, Li;Hoyer, Stephan;Burke, Kieron
包含先验知识对于物理学中有效的机器学习模型很重要，通常通过在模型架构上显式添加损失项或约束来实现。嵌入物理计算本身的先验知识很少引起注意。我们证明了在训练神经网络的交换相关泛函时求解Kohn-Sham方程提供了一种隐式正则化，大大提高了泛化能力。两次分离足以在化学精度内学习整个一维H-2解离曲线，包括强相关区域。我们的模型还推广到看不见的分子类型，克服了自相互作用的错误。
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.