Density Functional Theory (DFT) accurately predicts the quantum chemical properties of molecules, but scales as $O(N_{\text{electrons}}^3)$. Sch\"utt et al. (2019) successfully approximate DFT 1000x faster with Neural Networks (NN). Arguably, the biggest problem one faces when scaling to larger molecules is the cost of DFT labels. For example, it took years to create the PCQ dataset (Nakata & Shimazaki, 2017) on which subsequent NNs are trained within a week. DFT labels molecules by minimizing energy $E(\cdot )$ as a "loss function." We bypass dataset creation by directly training NNs with $E(\cdot )$ as a loss function. For comparison, Sch\"utt et al. (2019) spent 626 hours creating a dataset on which they trained their NN for 160h, for a total of 786h; our method achieves comparable performance within 31h.

翻译：密度泛函理论（DFT）能精确预测分子的量子化学性质，但其计算复杂度为 $O(N_{\text{电子}}^3)$。Schütt等人（2019）成功利用神经网络（NN）将DFT加速1000倍。当扩展到更大分子时，面临的最大问题莫过于DFT标注数据的成本。例如，PCQ数据集的创建耗时数年（Nakata & Shimazaki, 2017），而后续神经网络在该数据集上的训练仅需一周。DFT通过将能量 $E(\cdot )$ 作为"损失函数"最小化来标注分子。我们绕过数据集创建环节，直接以 $E(\cdot )$ 作为损失函数训练神经网络。作为对比，Schütt等人（2019）花费626小时创建数据集，再用160小时训练神经网络，总耗时786小时；而我们的方法在31小时内即可达到相当的性能。