Haunting remote effects in sight

Although still largely uncharted territory, the use of Artificial Intelligence (AI) in classical sciences such as chemistry, physics, or mathematics is now advancing: Researchers at the Berlin Institute for the Foundation of Learning and Data (BIFOLD) at TU Berlin, in collaboration with Google Research, have successfully developed an algorithm that can predict the potential energy state of molecules with high accuracy and efficiency based on quantum mechanical data.

This could open up entirely new options, especially for materials scientists. The paper "SpookyNet: Learning Force Fields with Electronic Degrees of Freedom and Nonlocal Effects" has now been published in Nature Communications.

"Quantum mechanics deals, among other things, with the chemical and physical properties of a molecule based on the spatial arrangement of its atoms. A chemical reaction, in turn, relies on the interplay of many molecules and is a multidimensional process," explains BIFOLD Co-Director Prof. Dr. Klaus-Robert Müller. Predicting and modeling the individual steps of a chemical reaction at the molecular or even atomic level has long been a dream of many materials scientists. A crucial factor for the reactivity of molecules is the so-called potential hyper-surface. It describes the dependence of a molecule's atomic energy on the geometric arrangement of the atomic nuclei. Knowledge of ultra-precise potential hyper-surfaces of molecules allows for the simulation of the movement of individual atoms, for example during a chemical reaction, to better understand their dynamic quantum mechanical properties and thereby predict the course and outcome of reactions accurately.

"You can imagine the potential hyper-surface as a landscape with mountains and valleys. Similar to a marble rolling over a miniature version of this landscape, the movement of atoms is determined by the mountains and valleys on the potential hyper-surface: this is also called molecular dynamics," explains Dr. Oliver Unke, researcher at Google Research in Berlin.

Unlike many other applications of machine learning, where AI often has access to nearly endless amounts of data, the prediction of potential hyper-surfaces typically has only a few quantum mechanical reference data points, which must be generated using enormous computational power. "While exact mathematical modeling of molecular dynamic properties can save expensive and time-consuming laboratory experiments, it requires disproportionately high computational resources," Müller notes.

We hope that our novel deep learning algorithm – a so-called transformer model that also considers spin and charge of atoms for the first time – will lead to new insights in chemistry, biology, and materials science – with significantly lower computational effort," says Klaus-Robert Müller.

To achieve particularly high data efficiency, the new deep learning model developed by the researchers combines AI with known physical laws. Certain aspects of the potential hyper-surface can be described very precisely with simple physical formulas. The new method therefore only learns the parts of the potential hyper-surface for which no simple mathematical description is available. "Very practical: the AI only needs to learn what is not already known from physics," explains Müller. This can save computational power.

Spatial separation of cause and effect

Another special feature is that the algorithm can also describe non-local interactions. "Non-locality" in this context means that a change at one atom, at a specific geometric position of the molecule, can influence atoms at a spatially separated molecular position. Due to the spatial separation of cause and effect – Albert Einstein referred to this as "spooky action at a distance" – these properties of quantum systems are particularly difficult for an AI to learn. The researchers solved this problem with a so-called transformer, a method originally developed for processing language and texts or images. "In a text, the meaning of a word or sentence often depends heavily on the context. The relevant contextual information can be in a completely different part of the text. In this sense, language is also a kind of non-local system," explains Müller. Using such a transformer, the scientists can also distinguish different electronic states of a molecule, such as spin and charge. "This is, for example, relevant for physical processes in solar cells, where a molecule absorbs light and is excited into a different electronic state," explains Unke.

Publication:
Oliver T. Unke, Stefan Chmiela, Michael Gastegger, Kristof T. Schütt, Huziel E. Sauceda, and Klaus-Robert Müller: "SpookyNet: Learning force fields with electronic degrees of freedom and nonlocal effects", Nature Communications 12: 7273 (2021)