Close to reality and precise

The quantum properties of atoms shape countless biochemical and physical processes. Many scientific challenges are linked to understanding the interactions of many atoms over time. These interactions are governed by the laws of quantum mechanics. Examples range from the structural formation of nucleic acids in genetic material to the breakdown of harmful molecules in the atmosphere.

A particular challenge of such quantum systems is their correlations in space and time: their most interesting properties do not result from the sum of individual atoms' contributions, but from various atomic correlations. As a result, quantum systems cannot be easily modeled mathematically. Directly modeling the complex correlations would exceed current computational capacities. An international team of scientists from the Berlin Institute for the Foundations of Learning and Data (BIFOLD) at TU Berlin, the University of Luxembourg, and Google has now successfully developed a machine learning algorithm to solve exactly this problem.

The developed learning algorithm reconstructs so-called global force fields based on machine learning (ML) methods, without making inadmissible simplifications. The term global force fields in this context describes an approach that considers all atomic interactions (such as electrostatic, chemical, etc.) within a molecule, as opposed to the common practice of reducing the number of modeled atomic interactions for computational feasibility.

More than the sum of its parts

"Quantum states of elementary particles are inseparably connected, and individual components cannot act independently without influencing the system as a whole," explains Dr. Alexandre Tkatchenko, Professor of Theoretical Chemical Physics at the University of Luxembourg. This property is one of the most far-reaching differences between quantum mechanics and the classical Newtonian and electrostatic interactions, which are intuitively familiar from everyday life. It also presents a dilemma in modeling quantum systems: a widespread paradigm in algorithm development and an important building block in modeling atomic interactions is to break down a problem into smaller, independent parts to reduce computational load. When considering quantum systems, this is not possible due to the properties mentioned above.

Global force fields capable of capturing collective interactions of many atoms in molecular systems can currently only be scaled to a few dozen atoms using machine learning methods, as the model complexity increases significantly with the size of the system under study. This very challenge was addressed by the team, which developed an algorithm to train global force fields for systems with up to several hundred atoms without ignoring complex correlations. Their approach carefully decomposes the strongly coupled atomic interactions within the model into a so-called collective low-dimensional part, which contains recurring interaction patterns, and a so-called residual, which describes the contributions of individual interactions. This separation allows both parts of the force field reconstruction problem to be solved independently. Numerical properties of each subproblem, caused by unavoidable rounding errors in computer calculations, are specifically taken into account. In this way, global force fields can be reconstructed based on larger reference datasets to represent more complex interactions, such as those occurring in large systems with many atoms or in particularly flexible molecules. "The numerical properties of machine learning algorithms often have a greater influence than the mathematical formulation suggests and can distort results," says Dr. Stefan Chmiela, head of the Machine Learning for Many-Body Systems research group at BIFOLD.

Efficiency of methods determines their usability

An additional advantage of the developed solution method is that it can be parallelized across multiple computers. It eliminates algorithmic bottlenecks and enables the effective use of modern parallel computing hardware such as GPUs. "The success of machine learning algorithms often depends on how efficiently they can be executed and scaled on available computing hardware," explains Prof. Dr. Klaus-Robert Müller, Co-Director of BIFOLD.

"This work is an important step toward realistically simulating quantum systems with hundreds of atoms," says Dr. Oliver Unke, a scientist at Google. The researchers have already successfully performed dynamic simulations of supramolecular complexes on demanding long timescales. Similar simulations are routinely carried out in the pharmaceutical industry to identify compounds with specific properties as potential candidates for new drugs. "Machine learning methods promise a convergence between exact quantum mechanical models and efficient empirical solutions. They have the potential to accelerate scientific research in quantum chemistry by offering entirely new ways to better understand atomic interactions in complex physical systems," explains Alexandre Tkatchenko.

Publication:

Stefan Chmiela, Valentin Vassilev-Galindo, Oliver T. Unke, Adil Kabylda, Huziel E. Sauceda, Alexandre Tkatchenko, and Klaus-Robert Müller: "Accurate global machine learning force fields for molecules with hundreds of atoms", Science Advances, 9(2), 2023, eadf0873
DOI: 10.1126/sciadv.adf0873

Further information provided by:
Dr. Stefan Chmiela
BIFOLD
Email: stefan@chmiela.com