AI solves Schrödinger’s Equation

Scientists at Freie Universität Berlin develop a deep learning method to solve a fundamental problem in quantum chemistry.


A newly developed AI method can calculate a fundamental problem in quantum chemistry: Schrödinger’s Equation. The technique could calculate the ground state of the Schrödinger equation in quantum chemistry.

Predicting molecules’ chemical and physical properties by relying on their atoms’ arrangement in space is the main goal of quantum chemistry. This can be achieved by solving the Schrödinger equation, but in practice, this is extremely difficult.

Until now, it was impossible to find an exact solution for arbitrary molecules that can be efficiently computed. But, thanks to scientists at Freie Universität for developing a deep learning method that can achieve an unprecedented combination of accuracy and computational efficiency.

Professor Frank Noé, who led the team effort, said, “We believe that our approach may significantly impact the future of quantum chemistry.”

Schrödinger equation is the wave function – a mathematical object that completely specifies the electrons’ behavior in a molecule. The wave function is a high-dimensional entity; hence it is challenging to capture all the nuances that encode how the individual electrons affect each other.

Several quantum chemistry methods failed to express the wave function altogether; instead, they were only able to determine a given molecule’s energy. This, however, requires approximations to be made, limiting the prediction quality of such methods.

Other methods representing the wave function using lots of simple mathematical building blocks are so complex that they are impossible to put into practice for more than a mere handful of atoms.

Dr. Jan Hermann of Freie Universität Berlin, who designed the key features of the method in the study, said, “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.”

Noé explained, “The newly developed method offers a new way to represent 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.”

Hermann said, “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. This feature, known as ‘Pauli’s exclusion principle,’ is why the authors called their method ‘PauliNet.'”

Noé said, “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 fundamental physics into 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.”

Although scientists still need to address many challenges before the method is ready for industrial application.

Scientists noted“This is still fundamental research, 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 up.”

Journal Reference:
  1. Jan Hermann, Zeno Schätzle, and Frank Noé, Deep neural network solution of the electronic Schrödinger equation. Nature Chemistry (2020). DOI: 10.1038/s41557-020-0544-y
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