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

TL;DR

The paper introduces Forward Laplacian, a novel computational framework that significantly accelerates neural network-based variational Monte Carlo methods, enabling their application to larger quantum chemistry systems.

Contribution

A new Forward Laplacian framework that computes neural network Laplacians efficiently, greatly speeding up NN-VMC and broadening its applicability in quantum chemistry.

Findings

Achieves over tenfold speed-up in NN-VMC computations.

Enables investigation of larger molecules and reactions.

Facilitates development of further acceleration techniques.

Abstract

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.