A computational framework for neural network-based variational Monte Carlo with Forward Laplacian

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 a development of NN-VMC that achieves a remarkable speed-up rate, thereby greatly extending the applicability of NN-VMC to larger systems. Our key design is a 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 can further facilitate more developments of acceleration methods across various aspects, including optimization for sparse derivative matrix and efficient network design. Empirically, our approach enables NN-VMC to investigate a broader range of systems, 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.