Current global MLFFs only scale to system sizes of a few tens of atoms, limited by the computational challenge of having to couple a quadratic amount of atom-atom interactions. However, accurate ab initio benchmark data is available for much larger systems (light blue area). This work scales global models with ab initio precision to hundreds of atoms, as demonstrated by examples of four major classes of biomolecules and supramolecules. Credit: *Scientists progress* (2023). DOI: 10.1126/sciadv.adf0873

An international team of scientists from the University of Luxembourg, the Berlin Institute for Foundations of Learning and Data (BIFOLD) at TU Berlin and Google have now successfully developed a machine learning algorithm for s tackling large and complex quantum systems. The article was published in *Scientists progress*.

The quantum properties of atoms shape countless biochemical and physical processes. Some of the world’s greatest science challenges are fundamentally tied to understanding many interacting atoms over time. These interactions are governed by the laws of quantum mechanics. Examples range from the formation of nucleic acids in the genome to the breakdown of harmful molecules in the atmosphere.

The spatial and temporal correlations of such quantum systems: Their most interesting properties do not result from a simple summation of the individual contributions of the atoms but from complex atomic correlations. Therefore, quantum systems cannot be easily modeled mathematically. In particular, large quantum systems have so far escaped precise machine learning (ML) because they cannot be uniquely partitioned into small independent computational packages.

Direct modeling of complicated correlations would exceed existing computational capabilities.

## Realistic and precise

The developed learning algorithm reconstructs the so-called global force fields based on machine learning methods without making potentially excessive simplifications. The term “global force fields” describes the approach of considering all atomic interactions (such as electrostatic, chemical, etc.) of a molecule. It is also common to reduce the number of atomic interactions modeled for the benefit of computational efficiency.

“Quantum states are inseparable and the individual constituents cannot act independently without affecting the system as a whole,” explains Professor Alexandre Tkatchenko, professor of theoretical chemical physics at the University of Luxembourg. This property marks one of the most radical differences between quantum mechanics and classical Newtonian mechanics and electrostatic interactions everyone knows intuitively.

This also poses a dilemma when modeling quantum systems: a pervasive paradigm in algorithmic design and an important building block in modeling atomic interactions is to break a problem into smaller independent parts that are easier for the user to manage. ‘computer. This is not possible when considering quantum systems due to the properties mentioned above.

Global force fields capable of capturing the collective interactions of many atoms in molecular systems currently only extend to a few dozen atoms using machine learning methods, as the complexity of the model increases dramatically with system size at your fingertips. The team addressed this challenge by developing an algorithm to train global force fields for systems of up to several hundred atoms without ignoring complex correlations.

Their approach carefully separates the tightly coupled atomic interactions within the model into a so-called low-dimensional collective part, which contains recurrent interaction patterns, and a so-called residual part, which describes the contributions of individual interactions. This separation makes it possible to independently solve the two constituents of the problem of reconstruction of the force field.

The numerical properties of each subproblem, which arise due to inevitable rounding errors in computer calculations, are specifically considered. As a result, global force fields can be reconstructed based on larger reference data sets to represent more complex interactions, as occurs in systems with many atoms or in particularly flexible molecules.

“The numerical characteristics of machine learning algorithms often have a stronger impact than the mathematical formulation suggests, which can skew the results. Improvements in numerical stability can have a significant impact on the application of the algorithms”, says Dr. Stefan Chmiela, group lead researcher of the Machine Learning for Many-body Systems group at BIFOLD.

The fact that the developed method can be parallelized on several computers is a secondary advantage. It removes algorithmic bottlenecks and enables the efficient use of modern parallel computing hardware such as GPUs. “The success of machine learning algorithms is often determined by how efficiently they can run and scale on the available hardware,” explains Prof. Dr. Klaus-Robert Müller, co-director of BIFOLD.

“This work is a stepping stone to unlocking truly predictive quantum simulations of systems with hundreds of atoms,” says Google researcher Oliver Unke. Scientists have already successfully performed dynamic simulations of supramolecular complexes over long, challenging time scales. Similar simulations are regularly carried out in the pharmaceutical industry identify compounds with specific properties as potential new drug candidates.

“Machine learning methods promise 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 opportunities to better understand atomic interactions in complex physical systems”, explains Alexandre Tkatchenko.

**More information:**

Stefan Chmiela et al, Accurate Global Machine Learning Force Fields for Molecules with Hundreds of Atoms, *Scientists progress* (2023). DOI: 10.1126/sciadv.adf0873

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University of Luxembourg

**Quote**: New Algorithm Enables Simulation of Complex Quantum Systems (2023, Jan 30) Retrieved Jan 31, 2023 from https://phys.org/news/2023-01-algorithm-enables-simulation-complex-quantum.html

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