Kohn-Sham Density Functional Theory (KS-DFT) has been traditionally solved by the Self-Consistent Field (SCF) method. Behind the SCF loop is the physics intuition of solving a system of non-interactive single-electron wave functions under an effective potential. In this work, we propose a deep learning approach to KS-DFT. First, in contrast to the conventional SCF loop, we propose to directly minimize the total energy by reparameterizing the orthogonal constraint as a feed-forward computation. We prove that such an approach has the same expressivity as the SCF method, yet reduces the computational complexity from O(N^4) to O(N^3). Second, the numerical integration which involves a summation over the quadrature grids can be amortized to the optimization steps. At each step, stochastic gradient descent (SGD) is performed with a sampled minibatch of the grids. Extensive experiments are carried out to demonstrate the advantage of our approach in terms of efficiency and stability. In addition, we show that our approach enables us to explore more complex neural-based wave functions.

翻译：Kohn-Sham密度泛函理论（KS-DFT）传统上通过自洽场（SCF）方法求解。SCF循环背后的物理直觉是在有效势下求解一组非相互作用单电子波函数。在这项工作中，我们提出了一种用于KS-DFT的深度学习方法。首先，与传统SCF循环不同，我们通过将正交约束重参数化为前馈计算来直接最小化总能量。我们证明该方法具有与SCF方法相同的表达能力，但将计算复杂度从O(N^4)降低至O(N^3)。其次，涉及求积网格求和的数值积分可以分摊到优化步骤中。在每一步，通过采样的网格小批量进行随机梯度下降（SGD）。大量实验证明了我们方法在效率和稳定性方面的优势。此外，我们表明该方法使我们能够探索更复杂的基于神经网络的波函数。