Rethinking ab initio Neural Wave Function: GNNs at Electron Level

Ge Yan, Zixiang Zhou, Yuhan Wang, Junchi Yan

Keywords: graph neural networks, quantum monte carlo, neural wave function

Abstract:

Solving the many-body Schr\"{o}dinger equation remains one of the most fundamental yet challenging problems in quantum mechanics.
Recent advances suggest that neural networks can serve as expressive and powerful ans\"{a}tze; however, a key opportunity remains in elucidating a clear, intuitive bridge between the network architecture and the underlying physics, especially for a broader AI audience.
In this work, we rethink the design of Neural Wave Functions (NWFs) by leveraging the inherently graphical structure of many-body systems. We propose the Graph Neural Wave Function (GNWF), a novel approach that leverages graph neural networks (GNNs) to represent quantum wave functions, inspired by the intrinsically graphical nature of many-body systems. By integrating GNWF with variational quantum Monte Carlo (VMC), GNWF learns wave functions solely from first principles, without reliance on supervised data or pre-computed targets. To assess its effectiveness, we benchmark GNWF on quantum chemistry systems, achieving comparable accuracy with a 24\% speedup over recent peer NWF: Psiformer. This work effectively extends the application of GNNs beyond atomic representations to the electron level, unlocking new possibilities for machine learning in quantum many-body physics.

Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)

Submission Number: 12491