Recently, it has been shown that neural networks not only approximate the ground-state wave functions of a single molecular system well but can also generalize to multiple geometries. While such generalization significantly speeds up training, each energy evaluation still requires Monte Carlo integration which limits the evaluation to a few geometries. In this work, we address the inference shortcomings by proposing the Potential learning from ab-initio Networks (PlaNet) framework, in which we simultaneously train a surrogate model in addition to the neural wave function. At inference time, the surrogate avoids expensive Monte-Carlo integration by directly estimating the energy, accelerating the process from hours to milliseconds. In this way, we can accurately model high-resolution multi-dimensional energy surfaces for larger systems that previously were unobtainable via neural wave functions. Finally, we explore an additional inductive bias by introducing physically-motivated restricted neural wave function models. We implement such a function with several additional improvements in the new PESNet++ model. In our experimental evaluation, PlaNet accelerates inference by 7 orders of magnitude for larger molecules like ethanol while preserving accuracy. Compared to previous energy surface networks, PESNet++ reduces energy errors by up to 74%.

翻译：近期研究表明，神经网络不仅能近似单一分子系统的基态波函数，还能泛化至多种几何构型。尽管这种泛化显著加速训练过程，但每次能量评估仍需蒙特卡洛积分，这限制了其仅能应用于少数几何构型。本研究针对推理缺陷，提出从头算网络势学习（PlaNet）框架，在神经波函数之外同步训练代理模型。推理时，代理模型通过直接估算能量避免高耗时的蒙特卡洛积分，将过程从数小时加速至毫秒级。由此，我们可精确建模以往神经波函数无法实现的大规模系统的高分辨率多维势能面。最后，通过引入物理驱动的受限神经波函数模型，我们探索了额外的归纳偏置。在新模型PESNet++中，我们通过多项改进实现了此类函数。实验评估显示，PlaNet在保持精度的前提下，对乙醇等较大分子的推理速度提升了7个数量级。相较于以往势能面网络，PESNet++将能量误差降低达74%。