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Neural network-based variational Monte Carlo (NN-VMC) has emerged as apromising cutting-edge technique of ab initio quantum chemistry. However, thehigh computational cost of existing approaches hinders their applications inrealistic chemistry problems. Here, we report the development of a new NN-VMCmethod that achieves a remarkable speed-up by more than one order of magnitude,thereby greatly extending the applicability of NN-VMC to larger systems. Ourkey design is a novel computational framework named Forward Laplacian, whichcomputes the Laplacian associated with neural networks, the bottleneck ofNN-VMC, through an efficient forward propagation process. We then demonstratethat Forward Laplacian is not only versatile but also facilitates moredevelopments of acceleration methods across various aspects, includingoptimization for sparse derivative matrix and efficient neural network design.Empirically, our approach enables NN-VMC to investigate a broader range ofatoms, molecules and chemical reactions for the first time, providing valuablereferences to other ab initio methods. The results demonstrate a greatpotential in applying deep learning methods to solve general quantum mechanicalproblems.

Forward Laplacian: A New Computational Framework for Neural Network-based Variational Monte Carlo