Artificial Intelligence Solves Schrödinger’s Equation, a Fundamental Problem in Quantum Chemistry
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Artificial Intelligence Solves Schrodinger's Equation, a Fundamental Problem in Quantum Chemistry:
Central to both quantum chemistry and the Schrodinger 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.
[...] The deep neural network designed by Professor Noe'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," Noe 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 Noe. This is really where scientists can make a substantial contribution to AI, and exactly what my group is focused on."
[*] Schrodinger's equation entry on Wikipedia.
Journal Reference:
Jan Hermann, Zeno Schatzle, Frank Noe. Deep-neural-network solution of the electronic Schrodinger equation, Nature Chemistry (DOI: 10.1038/s41557-020-0544-y)
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