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{{Short description|Interatomic potentials constructed by machine learning programs}}
Beginning in the 1990s, researchers have employed machine learning programs to construct [[interatomic potential]]s, mapping atomic structures to their potential energies. Such machine learning potentials promised to fill the gap between [[density functional theory]], a highly-accurate but computationally-intensive simulation program, and empirically-derived or intuitively-approximated potentials, which were far computationally lighter but substantially less accurate. Improvements in artificial intelligence technology have served to heighten the accuracy of MLPs while lowering their computational cost, increasing machine learning's role in fitting potentials.<ref name="ML">{{cite journal|last1=Kocer|last2=Ko|last3=Behler|first1=Emir|first2=Tsz Wai|first3=Jorg|journal=Annual Review of Physical Chemistry|title=Neural Network Potentials: A Concise Overview of Methods|date=2022|volume=73|pages=163-86}}</ref><ref>{{cite journal|last1=Blank|first1=TB|last2=Brown|first2=SD|last3=Calhoun|last4=Doren|first4=DJ|first3=AW|date=1995|title=Neural network models of potential energy surfaces|journal=Journal of Chemistry and Physics|volume=103|number=10|pages=4129-37}}</ref>▼
'''Machine-learned interatomic potentials''' ('''MLIPs'''), or simply '''machine learning potentials''' ('''MLPs'''), are [[interatomic potential]]s constructed using [[machine learning]]. Beginning in the 1990s, researchers have employed such programs to construct interatomic potentials by mapping atomic structures to their potential energies. These potentials are referred to as '''MLIPs''' or '''MLPs'''.
Machine learning potentials began by using neural networks to tackle low dimensional systems. While promising, these models could not systematically account for interatomic energy interactions; they could be applied to small molecules in a vacuum and molecules interacting with frozen surfaces, but not much else, and even in these applications often relied on force fields or potentials derived empirically or with simulations.<ref name="ML"/> These models thus remained confined to academia.▼
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Modern neural networks construct highly-accurate, computationally-light potentials because theoretical understanding of materials science was increasingly built into their architectures and preprocessing. Almost all are local, accounting for all interactions between an atom and its neighbor up to some cutoff radius. There exist some nonlocal models, but these have been experimental for almost a decade. For most systems, reasonable cutoff radii enable highly accurate results.<ref name="ML"/><ref>{{cite journal|last1=Ghasemi|first1=SA|last2=Hofstetter|first2=A|last3=Saha|first3=S|last4=Goedecker|first4=S|date=2015|title=Interatomic potentials for ionic systems with density functional accuracy based on charge densities obtained by a neural network|journal=Physical Review B|volume=92}}</ref>▼
▲Machine learning potentials began by using [[Neural network (machine learning)|neural networks]] to tackle low
Almost all neural networks intake atomic coordinates and output potential energies. For some, these atomic coordinates are converted into atom-centered symmetry functions. From this data, a separate atomic neural network is trained for each element; each atomic neural network is evaluated whenever that element occurs in the given structure, and then the results are pooled together at the end. This process - in particular, the atom-centered symmetry functions, which convey translational, rotational, and permutational invariances - has greatly improved machine learning potentials by significantly constraining the neural networks' search space. Other models use a similar process but emphasize bonds over atoms, using pair symmetry functions and training one neural network per atom pair.<ref name="ML"/><ref>{{cite journal|last1=Behler|first1=J|last2=Parrinello|first2=M|title=Generalized neural-network representation of high-dimensional potential-energy surfaces|date=2007|journal=Physical Review Letters|volume=148}}</ref> ▼
▲Modern neural networks construct highly
▲Almost all neural networks intake atomic coordinates and output potential energies. For some, these atomic coordinates are converted into atom-centered symmetry functions. From this data, a separate atomic neural network is trained for each element; each atomic
Other models to learn their own descriptors rather than using predetermined symmetry-dictating functions. These models, called [[Graph neural network#Message passing layers|message-passing neural networks]] (MPNNs), are graph neural networks. Treating molecules as three-dimensional [[Graph (discrete mathematics)|graphs]] (where atoms are nodes and bonds are edges), the model takes feature vectors describing the atoms as input, and iteratively updates these vectors as information about neighboring atoms is processed through message functions and [[convolution]]s. These feature vectors are then used to predict the final potentials. The flexibility of this method often results in stronger, more generalizable models. In 2017, the first-ever MPNN model (a deep tensor neural network) was used to calculate the properties of small organic molecules.
== Gaussian Approximation Potential (GAP) ==
One popular class of machine-learned interatomic potential is the Gaussian Approximation Potential (GAP),<ref>{{Cite journal |last1=Bartók |first1=Albert P. |last2=Payne |first2=Mike C. |last3=Kondor |first3=Risi |last4=Csányi |first4=Gábor |date=2010-04-01 |title=Gaussian Approximation Potentials: The Accuracy of Quantum Mechanics, without the Electrons |url=https://link.aps.org/doi/10.1103/PhysRevLett.104.136403 |journal=Physical Review Letters |volume=104 |issue=13 |pages=136403 |doi=10.1103/PhysRevLett.104.136403|pmid=20481899 |arxiv=0910.1019 |bibcode=2010PhRvL.104m6403B }}</ref><ref>{{Cite journal |last1=Bartók |first1=Albert P. |last2=De |first2=Sandip |last3=Poelking |first3=Carl |last4=Bernstein |first4=Noam |last5=Kermode |first5=James R. |last6=Csányi |first6=Gábor |last7=Ceriotti |first7=Michele |date=December 2017 |title=Machine learning unifies the modeling of materials and molecules |journal=Science Advances |language=en |volume=3 |issue=12 |pages=e1701816 |doi=10.1126/sciadv.1701816 |issn=2375-2548 |pmc=5729016 |pmid=29242828|arxiv=1706.00179 |bibcode=2017SciA....3E1816B }}</ref><ref>{{Cite web |title=Gaussian approximation potential – Machine learning atomistic simulation of materials and molecules |url=https://gap-ml.org/ |access-date=2024-04-04 |language=en-US}}</ref> which combines compact descriptors of local atomic environments<ref>{{Cite journal |last1=Bartók |first1=Albert P. |last2=Kondor |first2=Risi |last3=Csányi |first3=Gábor |date=2013-05-28 |title=On representing chemical environments |url=https://link.aps.org/doi/10.1103/PhysRevB.87.184115 |journal=Physical Review B |volume=87 |issue=18 |pages=184115 |doi=10.1103/PhysRevB.87.184115|arxiv=1209.3140 |bibcode=2013PhRvB..87r4115B }}</ref> with Gaussian process regression<ref>{{Cite book |last1=Rasmussen |first1=Carl Edward |title=Gaussian processes for machine learning |last2=Williams |first2=Christopher K. I. |date=2008 |publisher=MIT Press |isbn=978-0-262-18253-9 |edition=3. print |series=Adaptive computation and machine learning |___location=Cambridge, Mass.}}</ref> to machine learn the [[potential energy surface]] of a given system. To date, the GAP framework has been used to successfully develop a number of MLIPs for various systems, including for elemental systems such as [[carbon]],<ref>{{cite journal | last=Rowe | first=Patrick | last2=Deringer | first2=Volker L. | last3=Gasparotto | first3=Piero | last4=Csányi | first4=Gábor | last5=Michaelides | first5=Angelos | title=An accurate and transferable machine learning potential for carbon | journal=The Journal of Chemical Physics | volume=153 | issue=3 | date=2020-07-21 | issn=0021-9606 | doi=10.1063/5.0005084 | doi-access=free | url=http://arxiv.org/pdf/2006.13655| arxiv=2006.13655 }}</ref><ref>{{Cite journal |last1=Deringer |first1=Volker L. |last2=Csányi |first2=Gábor |date=2017-03-03 |title=Machine learning based interatomic potential for amorphous carbon |url=https://link.aps.org/doi/10.1103/PhysRevB.95.094203 |journal=Physical Review B |volume=95 |issue=9 |pages=094203 |doi=10.1103/PhysRevB.95.094203|arxiv=1611.03277 |bibcode=2017PhRvB..95i4203D }}</ref> [[silicon]],<ref>{{Cite journal |last1=Bartók |first1=Albert P. |last2=Kermode |first2=James |last3=Bernstein |first3=Noam |last4=Csányi |first4=Gábor |date=2018-12-14 |title=Machine Learning a General-Purpose Interatomic Potential for Silicon |url=https://link.aps.org/doi/10.1103/PhysRevX.8.041048 |journal=Physical Review X |volume=8 |issue=4 |pages=041048 |doi=10.1103/PhysRevX.8.041048|arxiv=1805.01568 |bibcode=2018PhRvX...8d1048B }}</ref> [[phosphorus]],<ref>{{Cite journal |last1=Deringer |first1=Volker L. |last2=Caro |first2=Miguel A. |last3=Csányi |first3=Gábor |date=2020-10-29 |title=A general-purpose machine-learning force field for bulk and nanostructured phosphorus |journal=Nature Communications |language=en |volume=11 |issue=1 |pages=5461 |doi=10.1038/s41467-020-19168-z |issn=2041-1723 |pmc=7596484 |pmid=33122630|bibcode=2020NatCo..11.5461D }}</ref> and [[tungsten]],<ref>{{Cite journal |last1=Szlachta |first1=Wojciech J. |last2=Bartók |first2=Albert P. |last3=Csányi |first3=Gábor |date=2014-09-24 |title=Accuracy and transferability of Gaussian approximation potential models for tungsten |url=https://link.aps.org/doi/10.1103/PhysRevB.90.104108 |journal=Physical Review B |volume=90 |issue=10 |pages=104108 |doi=10.1103/PhysRevB.90.104108|bibcode=2014PhRvB..90j4108S |url-access=subscription }}</ref> as well as for multicomponent systems such as Ge<sub>2</sub>Sb<sub>2</sub>Te<sub>5</sub><ref>{{Cite journal |last1=Mocanu |first1=Felix C. |last2=Konstantinou |first2=Konstantinos |last3=Lee |first3=Tae Hoon |last4=Bernstein |first4=Noam |last5=Deringer |first5=Volker L. |last6=Csányi |first6=Gábor |last7=Elliott |first7=Stephen R. |date=2018-09-27 |title=Modeling the Phase-Change Memory Material, Ge 2 Sb 2 Te 5, with a Machine-Learned Interatomic Potential |url=https://pubs.acs.org/doi/10.1021/acs.jpcb.8b06476 |journal=The Journal of Physical Chemistry B |language=en |volume=122 |issue=38 |pages=8998–9006 |doi=10.1021/acs.jpcb.8b06476 |pmid=30173522 |issn=1520-6106|url-access=subscription }}</ref> and [[Austenitic stainless steel|austenitic]] [[stainless steel]], Fe<sub>7</sub>Cr<sub>2</sub>Ni.<ref>{{Cite journal |last1=Shenoy |first1=Lakshmi |last2=Woodgate |first2=Christopher D. |last3=Staunton |first3=Julie B. |last4=Bartók |first4=Albert P. |last5=Becquart |first5=Charlotte S. |last6=Domain |first6=Christophe |last7=Kermode |first7=James R. |date=2024-03-22 |title=<nowiki>Collinear-spin machine learned interatomic potential for ${\mathrm{Fe}}_{7}{\mathrm{Cr}}_{2}\mathrm{Ni}$ alloy</nowiki> |url=https://link.aps.org/doi/10.1103/PhysRevMaterials.8.033804 |journal=Physical Review Materials |volume=8 |issue=3 |pages=033804 |doi=10.1103/PhysRevMaterials.8.033804|arxiv=2309.08689 }}</ref>
==References==
{{Reflist}}
[[Category:Machine learning]]
[[Category:Materials science]]
[[Category:Density functional theory software]]
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