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arXiv:2105.08351 · Nature Computational Science

Solving the electronic Schrödinger equation for multiple nuclear geometries with weight-sharing deep neural networks

Michael Scherbela, Rafael Reisenhofer, Leon Gerard, Philipp Marquetand, Philipp Grohs

Published May 19, 2022• 64 citations
arXivHTMLPDF
DOI
10.1038/s43588-022-00228-x

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Abstract Deep-learning-based variational Monte Carlo has emerged as a highly accurate method for solving the many-electron Schrödinger equation. Despite favorable scaling with the number of electrons, O(nel4){\mathcal{O}}({{n}_{{\rm{el}}}}^{4})O(nel​4) O ( n el 4 ) , the practical value of deep-learning-based variational Monte Carlo is limited by the high cost of optimizing the neural network weights for every system studied. Recent research has proposed optimizing a single neural network across multiple systems, reducing the cost per system. Here we extend this approach to solids, which require numerous calculations across different geometries, boundary conditions and supercell sizes. We demonstrate that optimization of a single ansatz across these variations significantly reduces optimization steps. Furthermore, we successfully transfer a network trained on 2 × 2 × 2 supercells of LiH, to 3 × 3 × 3 supercells, reducing the number of optimization steps required to simulate the large system by a factor of 50 compared with previous work.