Orbital-free density functional theory (OF-DFT) holds the promise to compute ground state molecular properties at minimal cost. However, it has been held back by our inability to compute the kinetic energy as a functional of the electron density only. We here set out to learn the kinetic energy functional from ground truth provided by the more expensive Kohn-Sham density functional theory. Such learning is confronted with two key challenges: Giving the model sufficient expressivity and spatial context while limiting the memory footprint to afford computations on a GPU; and creating a sufficiently broad distribution of training data to enable iterative density optimization even when starting from a poor initial guess. In response, we introduce KineticNet, an equivariant deep neural network architecture based on point convolutions adapted to the prediction of quantities on molecular quadrature grids. Important contributions include convolution filters with sufficient spatial resolution in the vicinity of the nuclear cusp, an atom-centric sparse but expressive architecture that relays information across multiple bond lengths; and a new strategy to generate varied training data by finding ground state densities in the face of perturbations by a random external potential. KineticNet achieves, for the first time, chemical accuracy of the learned functionals across input densities and geometries of tiny molecules. For two electron systems, we additionally demonstrate OF-DFT density optimization with chemical accuracy.

翻译：无轨道密度泛函理论（OF-DFT）有望以极低的计算成本获得分子基态性质。然而，其发展受限于我们无法仅通过电子密度计算动能泛函。在此，我们尝试从更昂贵的Kohn-Sham密度泛函理论提供的真实数据中学习动能泛函。这一学习过程面临两大挑战：赋予模型足够的表达能力和空间上下文信息，同时限制内存占用以在GPU上实现计算；以及生成足够多样化的训练数据，使得即使在初始猜测较差的情况下也能实现迭代密度优化。为此，我们提出了KineticNet——一种基于点卷积的等变深度神经网络架构，专门用于预测分子正交网格上的物理量。其关键创新包括：在核尖点附近具有足够空间分辨率的卷积滤波器；一种以原子为中心的稀疏但具有表达能力的架构，可在多个键长范围内传递信息；以及一种通过寻找随机外势扰动下基态密度来生成多样化训练数据的新策略。KineticNet首次实现了对微小分子输入密度与几何构型下学习泛函的化学精度。对于双电子系统，我们还展示了具有化学精度的OF-DFT密度优化结果。