Machine learning method predicts nanoparticle structure

New distance-based machine learning methods, developed in the University of Jyväskylä, have been found to be capable of predicting structures and atomic dynamics of nanoparticles reliably. Described in The Journal of Physical Chemistry, the methods are said to be significantly faster than traditional simulation methods used for nanoparticle research and will facilitate more efficient explorations of particle–particle reactions and particles’ functionality in their environment.

The new methods were applied to ligand-stabilised metal nanoparticles, which have been long studied at the University of Jyväskylä’s Nanoscience Center. Last year, the researchers published a method that is able to successfully predict binding sites of the stabilising ligand molecules on the nanoparticle surface. Now, a new tool has been created that can reliably predict potential energy based on the atomic structure of the particle, without the need to use numerically heavy electronic structure computations. The tool facilitates Monte Carlo simulations of the atom dynamics of the particles at elevated temperatures.

Potential energy of a system is a fundamental quantity in computational nanoscience, since it allows for quantitative evaluations of a system’s stability, rates of chemical reactions and strengths of interatomic bonds. Ligand-stabilised metal nanoparticles have many types of interatomic bonds of varying chemical strength, and traditionally the energy evaluations have been done by using the so-called density functional theory (DFT) that often results in numerically heavy computations requiring the use of supercomputers. This has precluded efficient simulations to understand nanoparticles’ functionalities, eg, as catalysts, or interactions with biological objects such as proteins, viruses or DNA. Machine learning methods, once trained to model the systems reliably, can speed up the simulations by several orders of magnitude.

The researchers used the potential energies predicted by the machine learning method to simulate the atomic dynamics of thiol-stabilised gold nanoparticles; the results were in agreement with the simulations performed by using the density functional theory. The method allowed simulations to be run on a laptop or desktop in a timescale of a few hours, while the reference DFT simulations took days in a supercomputer and used simultaneously hundreds or even thousands of computer cores. The speed-up will allow long-time simulations of the particles’ structural changes and particle–particle reactions at elevated temperatures.

The distance-based machine learning method describes each momentary atomic configuration of a nanoparticle by calculating a so-called descriptor, and compares distances between descriptors in a multidimensional numerical space. By using correlations to a training set created by the reference DFT simulations, the potential energy can be predicted. This approach, used now for the first time in nanoparticle research, is simpler and more transparent than traditionally used neural networks.

“It is extremely motivating that we can reduce the computational load from running simulations in supercomputers to running them with similar quality in a laptop or a home PC,” said PhD student Antti Pihlajamäki, lead author of the study.

“In the next phase, our target is to generalise the method to work well for nanoparticles of many different sizes and chemical compositions,” added Professor Hannu Häkkinen, who coordinated the study. “We will still need supercomputers to generate enough high-quality data to train the machine learning algorithm, but we hope that in the future we can move to use these new methods primarily to studies of nanoparticle functionality in complicated chemical environments.”

Image caption: Nanostructures such as these thiol-covered gold nanoparticles can now be studied by using the new machine learning method developed in the University of Jyväskylä. The method can predict the potential energy of a given structure reliably. Image credit: Antti Pihlajamäki/The University of Jyväskylä.

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