AI Solves Schrödinger’s Equation: Scientists at Freie Universität Berlin develop a deep learning method to solve a fundamental problem in quantum chemistry

Unsplash – Joel Filipe

A team of scientists at Freie Universität Berlin has developed
an artificial intelligence (AI) method for calculating the ground
state of the Schrödinger equation in quantum chemistry. The goal
of quantum chemistry is to predict chemical and physical properties
of molecules based solely on the arrangement of their atoms in
space, avoiding the need for resource-intensive and time-consuming
laboratory experiments. In principle, this can be achieved by
solving the Schrödinger equation, but in practice this is
extremely difficult. Up to now, it has been impossible to find an
exact solution for arbitrary molecules that can be efficiently
computed. But the team at Freie Universität has developed a deep
learning method that can achieve an unprecedented combination of
accuracy and computational efficiency. AI has transformed many
technological and scientific areas, from computer vision to
materials science. “We believe that our approach may
significantly impact the future of quantum chemistry,” says
Professor Frank Noé, who led the team effort. The results were
published in the reputed journalNature Chemistry (DOI:

Central to both quantum chemistry and the Schrödinger equation
is the wave function – a mathematical object that completely
specifies the behavior of the electrons in a molecule. The wave
function is a high-dimensional entity, and it is therefore
extremely difficult to capture all the nuances that encode how the
individual electrons affect each other. Many methods of quantum
chemistry in fact give up on expressing the wave function
altogether, instead attempting only to determine the energy of a
given molecule. This however requires approximations to be made,
limiting the prediction quality of such methods.

Other methods represent the wave function with the use of an
immense number of simple mathematical building blocks, but such
methods are so complex that they are impossible to put into
practice for more than a mere handful of atoms. “Escaping the
usual trade-off between accuracy and computational cost is the
highest achievement in quantum chemistry,” explains Dr. Jan
Hermann of Freie Universität Berlin, who designed the key features
of the method in the study. “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

The deep neural network designed by Professor Noé’s team is a
new way of representing the wave functions of electrons. “Instead
of the standard approach of composing the wave function from
relatively simple mathematical components, we designed an
artificial neural network capable of learning the complex patterns
of how electrons are located around the nuclei,” Noé explains.
“One peculiar feature of electronic wave functions is their
antisymmetry. When two electrons are exchanged, the wave function
must change its sign. We had to build this property into the neural
network architecture for the approach to work,” adds Hermann.
This feature, known as “Pauli’s exclusion principle,” is why
the authors called their method “PauliNet.” 

Besides the Pauli exclusion principle, electronic wave functions
also have other fundamental physical properties, and much of the
innovative success of PauliNet is that it integrates these
properties into the deep neural network, rather than letting deep
learning figure them out by just observing the data. “Building
the fundamental physics into the AI is essential for its ability to
make meaningful predictions in the field,” says Noé. “This is
really where scientists can make a substantial contribution to AI,
and exactly what my group is focused on.”

There are still many challenges to overcome before Hermann and
Noé’s method is ready for industrial application. “This is
still fundamental research,” the authors agree, “but it is a
fresh approach to an age-old problem in the molecular and material
sciences, and we are excited about the possibilities it opens

Originally published by
Freie Universität Berlin
| December 18, 2020



Jan Hermann, Zeno Schätzle, and Frank Noé, Deep neural network
solution of the electronic Schrödinger equation. Nature
Chemistry (2020). DOI: 


Prof. Dr. Frank Noé, Department of Mathematics and Computer
Science, Freie Universität Berlin, Email:, Tel.:
+49 30 838 75354