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{{Short description|Interatomic potentials constructed by machine learning programs}}
'''Machine-learned interatomic potentials''' ('''MLIPs'''), or simply '''machine learning potentials''' ('''MLPs'''), are [[interatomic potential]]s constructed by [[machine learning]] programs. 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-learned interatomic potentials''' ('''MLIPs'''), or simply '''machine learning potentials''' ('''MLPs'''), are [[interatomic potential]]s constructed
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 lighter computationally, but substantially less accurate. Improvements in [[artificial intelligence]] technology heightened the accuracy of MLPs while lowering their computational cost, increasing the role of machine learning 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|doi=10.1146/annurev-physchem-082720-034254 |pmid=34982580 |bibcode=2022ARPC...73..163K |doi-access=free|arxiv=2107.03727}}</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 Chemical Physics|volume=103|number=10|pages=4129–37|doi=10.1063/1.469597 |bibcode=1995JChPh.103.4129B }}</ref>▼
▲Such machine learning potentials promised to fill the gap between [[density functional theory]], a highly accurate but computationally
Machine learning potentials began by using [[Neural network (machine learning)|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, or molecules interacting with frozen surfaces, but not much else – and even in these applications, the models 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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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 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 network search space. Other models use a similar process but emphasize bonds over atoms, using pair symmetry functions and training one 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|issue=14|doi=10.1103/PhysRevLett.98.146401|pmid=17501293|bibcode=2007PhRvL..98n6401B}}</ref>
Other models
== 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 [[
==References==
{{Reflist}}
[[Category:Machine learning]]
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