Forward Laplacian: A New Computational Framework for Neural
  Network-based Variational Monte Carlo
Ruichen Li Haotian Ye Du Jiang Xuelan Wen Chuwei Wang Zhe Li Xiang Li Di He Ji Chen Weiluo Ren Liwei Wang
Neural network-based variational Monte Carlo (NN-VMC) has emerged as a
promising cutting-edge technique of ab initio quantum chemistry. However, the
high computational cost of existing approaches hinders their applications in
realistic chemistry problems. Here, we report the development of a new NN-VMC
method that achieves a remarkable speed-up by more than one order of magnitude,
thereby greatly extending the applicability of NN-VMC to larger systems. Our
key design is a novel computational framework named Forward Laplacian, which
computes the Laplacian associated with neural networks, the bottleneck of
NN-VMC, through an efficient forward propagation process. We then demonstrate
that Forward Laplacian is not only versatile but also facilitates more
developments of acceleration methods across various aspects, including
optimization for sparse derivative matrix and efficient neural network design.
Empirically, our approach enables NN-VMC to investigate a broader range of
atoms, molecules and chemical reactions for the first time, providing valuable
references to other ab initio methods. The results demonstrate a great
potential in applying deep learning methods to solve general quantum mechanical
problems.