Transferable Neural Wavefunctions for Solids

TL;DR

This paper introduces a transferable neural wavefunction approach for solids in DL-VMC, significantly reducing optimization costs by training a single network across multiple geometries and transferring pre-trained models to larger systems.

Contribution

It extends neural wavefunction transferability to solid-state systems, enabling efficient simulations across different geometries and supercell sizes with minimal retraining.

Findings

Optimization steps reduced by an order of magnitude across geometries.

Transfer learning from smaller to larger supercells reduces optimization by a factor of 50.

Single neural network can effectively model multiple system variations.

Abstract

Deep-Learning-based Variational Monte Carlo (DL-VMC) has recently emerged as a highly accurate approach for finding approximate solutions to the many-electron Schr\"odinger equation. Despite its favorable scaling with the number of electrons, $\mathcal{O}(n_\text{el}^{4})$, the practical value of DL-VMC is limited by the high cost of optimizing the neural network weights for every system studied. To mitigate this problem, recent research has proposed optimizing a single neural network across multiple systems, reducing the cost per system. Here we extend this approach to solids, where similar but distinct calculations using different geometries, boundary conditions, and supercell sizes are often required. We show how to optimize a single ansatz across all of these variations, reducing the required number of optimization steps by an order of magnitude. Furthermore, we exploit the transfer capabilities of a pre-trained network. We successfully transfer a network, pre-trained on 2x2x2 supercells of LiH, to 3x3x3 supercells. This reduces the number of optimization steps required to simulate the large system by a factor of 50 compared to previous work.