Artificial intelligence solves Schrödinger’s equation

A team of scientists from the Freie Universität Berlin has developed an artificial intelligence (AI) method for calculating the fundamental state of the Schrödinger equation in quantum chemistry. The purpose of quantum chemistry is to predict the 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 done by solving the Schrödinger equation, but in practice this is extremely difficult.

Until now, it has been impossible to find an exact solution for arbitrary molecules that can be calculated efficiently. 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 fields, from computer vision to materials science. “We believe that our approach can have a significant impact on the future of quantum chemistry,” said Professor Frank Noé, who led the team’s effort. The results were published in the renowned journal The chemistry of nature.

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

Other methods represent the wave function with the use of a huge number of simple mathematical blocks, but such methods are so complex that they are impossible to put into practice for more than a simple handful of atoms. “Avoiding the usual trade-off between accuracy and computational cost is the greatest achievement in quantum chemistry,” explains Dr. Jan Hermann of Freie Universität Berlin, who designed the key features of the method under study. “To date, the most popular such aberrant values ​​is the highly cost-effective functional density theory. We believe that the “Quantum Monte Carlo” deep, the approach we propose, could be equally, if not even more successful. It provides unprecedented accuracy at a cost that is still acceptable. “

The deep neural network designed by Professor Noah’s team is a new way of representing the wave functions of electrons. “Instead of the standard approach to composing 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 nuclei,” explains Noé. “A particular feature of electronic wave functions is their antisymmetry. When two electrons change, the wave function must change its sign. We had to build this property into neural network architecture for the functional approach,” adds Hermann. This feature, known as the “Pauli exclusion principle”, is why the authors called their method “PauliNet”.

In addition to the principle of excluding Pauli, electronic wave functions have other fundamental physical properties, and much of PauliNet’s innovative success lies in integrating these properties into the deep neural network, rather than letting deep learning discover them only through data observation. “Building fundamental physics in AI is essential to its ability to make meaningful predictions in the field,” says Noé. “Here scientists can make a substantial contribution to AI and exactly what my group is focusing on.”

There are still many challenges to overcome before Hermann and Noah’s method is ready for industrial applications. “This is still fundamental research,” the authors agree, “but it is a new approach to an old problem in the molecular and material sciences, and we are delighted with the possibilities it opens up.”