Banner Banner

December 29, 2020

Prof. Dr. Frank Noé

Researchers at FU Berlin solve Schroedingers equation with new deep learning method

BIFOLD Principal Investigator Prof. Dr. Frank Noé and Senior Researcher Dr. Jan Hermann of the Artificial Intelligence for the Sciences group at Freie Universität Berlin developed a new, exceptionally accurate and efficient method to solve the electronic Schroedinger equation. Their approach could have a significant impact on the future of quantum chemistry.

Prof. Noé’s and Dr. Hermann’s method, PauliNet, avoids the limitation of previous approaches. It is not only a more accurate way of representing the electronic wave function, but also includes physical properties into the deep neural network.

“Escaping the usual trade-off between accuracy and computational cost is the highest achievement in quantum chemistry. As yet, the most popular such outlier is the extremely cost-effective density functional theory. We believe that deep “Quantum Monte Carlo,” the approach we are proposing, could be equally, if not more successful. It offers unprecedented accuracy at a still acceptable computational cost.”

Dr. Jan Hermann

“Building the fundamental physics into the AI is essential for its ability to make meaningful predictions in the field. This is really where scientists can make a substantial contribution to AI, and exactly what my group is focused on.”

Prof. Dr. Frank Noé

For more information, please visit the official press release of FU Berlin (available also at


Jan Hermann, Zeno Schätzle, Frank Noé

The electronic Schrödinger equation can only be solved analytically for the hydrogen atom, and the numerically exact full configuration-interaction method is exponentially expensive in the number of electrons. Quantum Monte Carlo methods are a possible way out: they scale well for large molecules, they can be parallelized and their accuracy has, as yet, been only limited by the flexibility of the wavefunction ansatz used. Here we propose PauliNet, a deep-learning wavefunction ansatz that achieves nearly exact solutions of the electronic Schrödinger equation for molecules with up to 30 electrons. PauliNet has a multireference Hartree–Fock solution built in as a baseline, incorporates the physics of valid wavefunctions and is trained using variational quantum Monte Carlo. PauliNet outperforms previous state-of-the-art variational ansatzes for atoms, diatomic molecules and a strongly correlated linear H10, and matches the accuracy of highly specialized quantum chemistry methods on the transition-state energy of cyclobutadiene, while being computationally efficient.

Hermann, J., Schätzle, Z. & Noé, F. Deep-neural-network solution of the electronic Schrödinger equation. Nat. Chem. 12, 891–897 (2020).