AA2 – Nano and Quantum Technologies



Deep Backflow for Accurate Solution of the Electronic Schrödinger Equation

Project Heads

Jan Hermann, Jens Eisert, Frank Noé

Project Members

Zeno Schätzle

Project Duration

01.04.2021 − 31.03.2024

Located at

FU Berlin


Accurate and general solution of the electronic Schrödinger equation is one of the great challenges in computational materials science, since it provides straightforward access to many material properties. Among the numerous approximate methods, quantum Monte Carlo provides a platform for in-principle exact numerical solutions at favorable computational cost, but in practice is limited by the flexibility of the available wave function ansatzes. The cornerstone of this issue is a faithful representation of the so-called nodal surface, on which the antisymmetric electronic wave function changes sign. This project aims to establish a novel computational technique based on deep neural networks, called deep backflow, as a general solution to the nodal-surface representation problem. This will overcome the only existing fundamental limitation to the accuracy of quantum Monte Carlo calculations, opening the possibility of highly accurate electronic-structure calculations for much larger systems than previously possible.

Related Publications

  • J. Hermann, Z. Schätzle & F. Noé. Deep-neural-network solution of the electronic Schrödinger equation. Nat. Chem. 12, 891–897 (2020). doi:10.1038/s41557-020-0544-y
  • Z. Schätzle, J. Hermann & F. Noé. Convergence to the fixed-node limit in deep variational Monte Carlo. J. Chem. Phys., vol. 154, no. 12, p. 124108, (2021). doi:10.1063/5.0032836

Related Pictures

Cuts through the nodal surfaces of wavefunctions for the Lithium atom.
Cuts through the nodal surfaces of wavefunctions for the Lithium atom.