Algorithms learn physics

An international team of scientists from the Technical University of Berlin, the Fritz Haber Institute of the Max Planck Society, and the University of Luxembourg has now succeeded in combining machine learning and quantum mechanics in such a way that they can predict the dynamics and atomic interactions in molecules with unprecedented precision and efficiency. Molecular dynamics simulations form the foundation for many models in natural and material sciences. However, their predictive power is only as good as the precision of the underlying interatomic interactions, which are described in the form of potentials. Classical potentials are based on mechanistic models that cannot capture important quantum effects. The work now published provides new insights into the complex dynamic behavior of molecules. This development promises to significantly improve the predictive power of modern atomic modeling in chemistry, biology, and materials science.

Exact insights into the molecular dynamics of a substance, i.e., ultimately precise knowledge of the possible states and interactions of individual atoms within a molecule, help to not only understand but also utilize many chemical and physical reactions. "Machine learning methods have dramatically changed work in many disciplines, but they have been little used in molecular dynamics simulation," explains Dr. Klaus-Robert Müller, Professor of Machine Learning at TU Berlin. The problem: most standard algorithms were developed with the awareness that the amount of data to process is irrelevant. "But this does not apply to accurate quantum mechanical calculations of a molecule, where each data point is crucial, and the individual calculation for larger molecules can take many weeks or even months. The enormous computing power required has so far made ultra-precise molecular dynamics simulations impossible," Müller explains.

Exactly this challenge has now been solved by the scientists by integrating physical laws into machine learning procedures. "The trick is not to calculate all the potentially possible states of molecular dynamics with machine learning, but only those that do not follow from known physical laws or the application of symmetry operations," says Klaus-Robert Müller.

On one hand, the newly developed algorithms utilize natural mathematical symmetries within molecules. For example, they recognize symmetry axes that do not change the physical properties of the molecule. This means these data points only need to be calculated once, rather than multiple times, significantly reducing the complexity of the calculation. On the other hand, the learning process uses the physical law of conservation of energy and does not even calculate molecular states that are impossible according to this law.

With the innovative approach of incorporating physical laws into the machine learning methods before they learn to calculate molecular dynamics, the team has succeeded in overcoming the dichotomy between high precision and data efficiency.

"Our approach provides the missing key to achieving spectroscopic accuracy in molecular simulations, which is necessary for truly realistic modeling," explains Prof. Dr. Alexandre Tkatchenko, head of the "Theoretical Chemical Physics" group at the University of Luxembourg.

"These special algorithms allow the process to focus on the difficult problems of simulation instead of using computational power to reconstruct trivial relationships between data points. This work thus impressively demonstrates the high potential of combining artificial intelligence with chemistry or other natural sciences," describes Klaus-Robert Müller.

The work was funded by the German Research Foundation, the European Research Council, and the Korean National Research Foundation. Part of this research was conducted while the authors visited the Institute for Pure and Applied Mathematics (IPAM) at the University of California, Los Angeles (UCLA), supported by the National Science Foundation.