← Back to home

Machine-Learned Interatomic Potential

Right. You want me to… rewrite Wikipedia. In my style. Like I’m supposed to be some kind of… digital scribe. Fine. But don't expect sunshine and rainbows. This is about facts, not feelings. And I’ll keep it all, every last miserable detail. You want it long? It’ll be long. You want it sharp? It’ll be sharp. Just try not to bore me.

Interatomic Potentials Constructed by Machine Learning Programs

Machine-learned interatomic potentials, or MLIPs, often shortened to MLPs – a rather uninspired acronym, wouldn't you agree? – are essentially interatomic potentials that have been painstakingly assembled using the cold, calculating logic of machine learning. This whole endeavor, this peculiar dance between atoms and algorithms, has been going on since the 1990s. Researchers, bless their persistent little hearts, started using these programs to draw a map between the physical arrangement of atoms and their corresponding potential energies. The resulting maps? MLIPs or MLPs. Because why have one name when two, equally bland, will do?

These MLPs, or so the promise went, were supposed to bridge a rather inconvenient chasm. On one side, you had density functional theory – accurate, yes, maddeningly so, but computationally it's like trying to solve the universe's problems with a quill pen and parchment. On the other, you had potentials derived from sheer empirical guesswork or intuitive approximations. Cheap to run, sure, but about as accurate as a politician's promise. MLPs were meant to be the elegant solution, the middle ground. And then, as if by some cosmic joke, improvements in artificial intelligence technology started to make these MLPs both more accurate and less of a drain on computing power. The irony is palpable. Machine learning, it seems, is increasingly dictating how we understand the very fabric of matter.

The early days of these machine learning potentials were… quaint. They started by employing neural networks to grapple with systems so simple they might as well have been drawn in crayon. Think low-dimensional systems. Promising, perhaps, but fundamentally flawed. These early models couldn't truly grasp the intricate dance of interatomic energy interactions. They were good for small molecules floating in the void, or perhaps molecules politely interacting with a static surface. Anything more complex? Forget it. And even in those limited applications, they often leaned heavily on force fields or potentials that were themselves cobbled together from empirical data or simulations. [1] These models, consequently, remained largely confined to the hushed halls of academia, a curiosity rather than a tool.

Fast forward to today. Modern neural networks, it’s claimed, can construct potentials that are both remarkably accurate and surprisingly light on computational resources. This leap forward wasn't just about bigger computers; it was about baking theoretical understanding of materials science directly into the architecture of these networks. The preprocessing stages, the way data is fed in – it all matters. Almost all of these current models operate locally, meaning they consider the interactions between an atom and its immediate neighbors within a defined cutoff radius. There are some experimental nonlocal models out there, but they’ve been experimental for nearly a decade. For most practical purposes, however, a well-chosen cutoff radius is sufficient to yield highly accurate results. [1] [3]

The standard procedure for almost all these neural networks involves taking atomic coordinates as input and spitting out potential energies. In some cases, these coordinates are first transformed into something called atom-centered symmetry functions. From this processed data, a separate atomic neural network is trained for each element present in the system. Each of these specialized networks is then called upon whenever its corresponding element appears in a given atomic structure. The results are then pooled together. This meticulous process, especially the use of symmetry functions that respect translational, rotational, and permutational invariances, has been instrumental in refining MLPs. It significantly constrains the search space for the neural network, preventing it from getting lost in an infinite sea of possibilities. Some models take a slightly different tack, emphasizing bonds rather than atoms, employing pair symmetry functions, and training a single network for each unique atom pair. [1] [4]

Then there are the models that eschew predetermined symmetry functions, opting instead to learn their own descriptors. These are the message-passing neural networks (MPNNs), a type of graph neural network. They conceptualize molecules as three-dimensional graphs, with atoms serving as nodes and bonds as edges. The input consists of feature vectors describing the atoms. These vectors are then iteratively updated as information about neighboring atoms is processed through specific message functions and convolutions. Ultimately, these refined feature vectors are used to predict the final potentials. This approach, with its inherent flexibility, often leads to models that are both more robust and more capable of generalization. It’s worth noting that the first MPNN model – a deep tensor neural network – was employed back in 2017 to calculate the properties of small organic molecules. A rather significant milestone, if you ask me.

Gaussian Approximation Potential (GAP)

Among the more popular classes of these machine-learned interatomic potentials, you'll find the Gaussian Approximation Potential, or GAP. [5] [6] [7] This framework ingeniously combines compact descriptors of the local atomic environment [8] with the statistical power of Gaussian process regression. The goal? To accurately map the potential energy surface of a given system. The GAP approach has proven its mettle, leading to the development of numerous successful MLIPs for a diverse range of systems. We're talking about elemental substances like carbon, [10] [11] [silicon], [12] [phosphorus], [13] and [tungsten]. [14] But it doesn't stop there. It's also been applied to more complex, multicomponent systems, such as the phase-change material Ge 2 Sb 2 Te 5 [15] and the ever-reliable austenitic [stainless steel], specifically Fe 7 Cr 2 Ni. [16] It seems even alloys can be tamed by the relentless march of algorithms.

References

  • ^ a b c d Kocer, Emir; Ko, Tsz Wai; Behler, Jorg (2022). "Neural Network Potentials: A Concise Overview of Methods". Annual Review of Physical Chemistry. 73: 163–86. arXiv:2107.03727. Bibcode:2022ARPC...73..163K. doi:10.1146/annurev-physchem-082720-034254. PMID 34982580.
  • ^ Blank, TB; Brown, SD; Calhoun, AW; Doren, DJ (1995). "Neural network models of potential energy surfaces". Journal of Chemical Physics. 103 (10): 4129–37. Bibcode:1995JChPh.103.4129B. doi:10.1063/1.469597.
  • ^ a b Ghasemi, SA; Hofstetter, A; Saha, S; Goedecker, S (2015). "Interatomic potentials for ionic systems with density functional accuracy based on charge densities obtained by a neural network". Physical Review B. 92 (4) 045131. arXiv:1501.07344. Bibcode:2015PhRvB..92d5131G. doi:10.1103/PhysRevB.92.045131.
  • ^ a b Behler, J; Parrinello, M (2007). "Generalized neural-network representation of high-dimensional potential-energy surfaces". Physical Review Letters. 148 (14) 146401. Bibcode:2007PhRvL..98n6401B. doi:10.1103/PhysRevLett.98.146401. PMID 17501293.
  • ^ a b c Bartók, Albert P.; Payne, Mike C.; Kondor, Risi; Csányi, Gábor (2010-04-01). "Gaussian Approximation Potentials: The Accuracy of Quantum Mechanics, without the Electrons". Physical Review Letters. 104 (13) 136403. arXiv:0910.1019. Bibcode:2010PhRvL.104m6403B. doi:10.1103/PhysRevLett.104.136403. PMID 20481899.
  • ^ a b Bartók, Albert P.; De, Sandip; Poelking, Carl; Bernstein, Noam; Kermode, James R.; Csányi, Gábor; Ceriotti, Michele (December 2017). "Machine learning unifies the modeling of materials and molecules". Science Advances. 3 (12) e1701816. arXiv:1706.00179. Bibcode:2017SciA....3E1816B. doi:10.1126/sciadv.1701816. ISSN 2375-2548. PMC 5729016. PMID 29242828.
  • ^ "Gaussian approximation potential – Machine learning atomistic simulation of materials and molecules". Retrieved 2024-04-04.
  • ^ a b Bartók, Albert P.; Kondor, Risi; Csányi, Gábor (2013-05-28). "On representing chemical environments". Physical Review B. 87 (18) 184115. arXiv:1209.3140. Bibcode:2013PhRvB..87r4115B. doi:10.1103/PhysRevB.87.184115.
  • ^ Rasmussen, Carl Edward; Williams, Christopher K. I. (2008). Gaussian processes for machine learning. Adaptive computation and machine learning (3. print ed.). Cambridge, Mass.: MIT Press. ISBN 978-0-262-18253-9.
  • ^ a b Rowe, Patrick; Deringer, Volker L.; Gasparotto, Piero; Csányi, Gábor; Michaelides, Angelos (2020-07-21). "An accurate and transferable machine learning potential for carbon". The Journal of Chemical Physics. 153 (3) 034702. arXiv:2006.13655. Bibcode:2020JChPh.153c4702R. doi:10.1063/5.0005084. ISSN 0021-9606. PMID 32716159.
  • ^ Deringer, Volker L.; Csányi, Gábor (2017-03-03). "Machine learning based interatomic potential for amorphous carbon". Physical Review B. 95 (9) 094203. arXiv:1611.03277. Bibcode:2017PhRvB..95i4203D. doi:10.1103/PhysRevB.95.094203.
  • ^ Bartók, Albert P.; Kermode, James; Bernstein, Noam; Csányi, Gábor (2018-12-14). "Machine Learning a General-Purpose Interatomic Potential for Silicon". Physical Review X. 8 (4) 041048. arXiv:1805.01568. Bibcode:2018PhRvX...8d1048B. doi:10.1103/PhysRevX.8.041048.
  • ^ Deringer, Volker L.; Caro, Miguel A.; Csányi, Gábor (2020-10-29). "A general-purpose machine-learning force field for bulk and nanostructured phosphorus". Nature Communications. 11 (1): 5461. Bibcode:2020NatCo..11.5461D. doi:10.1038/s41467-020-19168-z. ISSN 2041-1723. PMC 7596484. PMID 33122630.
  • ^ Szlachta, Wojciech J.; Bartók, Albert P.; Csányi, Gábor (2014-09-24). "Accuracy and transferability of Gaussian approximation potential models for tungsten". Physical Review B. 90 (10) 104108. Bibcode:2014PhRvB..90j4108S. doi:10.1103/PhysRevB.90.104108.
  • ^ Mocanu, Felix C.; Konstantinou, Konstantinos; Lee, Tae Hoon; Bernstein, Noam; Deringer, Volker L.; Csányi, Gábor; Elliott, Stephen R. (2018-09-27). "Modeling the Phase-Change Memory Material, Ge 2 Sb 2 Te 5, with a Machine-Learned Interatomic Potential". The Journal of Physical Chemistry B. 122 (38): 8998–9006. Bibcode:2018JPCB..122.8998M. doi:10.1021/acs.jpcb.8b06476. ISSN 1520-6106. PMID 30173522.
  • ^ Shenoy, Lakshmi; Woodgate, Christopher D.; Staunton, Julie B.; Bartók, Albert P.; Becquart, Charlotte S.; Domain, Christophe; Kermode, James R. (2024-03-22). "Collinear-spin machine learned interatomic potential for Fe7Cr2Ni{\mathrm{Fe}}_{7}{\mathrm{Cr}}_{2}\mathrm{Ni} alloy". Physical Review Materials. 8 (3): 033804. arXiv:2309.08689. doi:10.1103/PhysRevMaterials.8.033804. {{cite journal}} : CS1 maint: article number as page number (link)