Learning emergent partial differential equations in a learned emergent space

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dc.citation.issue1
dc.citation.volume13
dc.contributor.authorKemeth FP
dc.contributor.authorBertalan T
dc.contributor.authorThiem T
dc.contributor.authorDietrich F
dc.contributor.authorMoon SJ
dc.contributor.authorLaing CR
dc.contributor.authorKevrekidis IG
dc.coverage.spatialEngland
dc.date.accessioned2024-01-18T02:15:46Z
dc.date.accessioned2024-07-25T06:39:55Z
dc.date.available2022-06-09
dc.date.available2024-01-18T02:15:46Z
dc.date.available2024-07-25T06:39:55Z
dc.date.issued2022-06-09
dc.description.abstractWe propose an approach to learn effective evolution equations for large systems of interacting agents. This is demonstrated on two examples, a well-studied system of coupled normal form oscillators and a biologically motivated example of coupled Hodgkin-Huxley-like neurons. For such types of systems there is no obvious space coordinate in which to learn effective evolution laws in the form of partial differential equations. In our approach, we accomplish this by learning embedding coordinates from the time series data of the system using manifold learning as a first step. In these emergent coordinates, we then show how one can learn effective partial differential equations, using neural networks, that do not only reproduce the dynamics of the oscillator ensemble, but also capture the collective bifurcations when system parameters vary. The proposed approach thus integrates the automatic, data-driven extraction of emergent space coordinates parametrizing the agent dynamics, with machine-learning assisted identification of an emergent PDE description of the dynamics in this parametrization.
dc.description.confidentialfalse
dc.format.pagination3318-
dc.identifier.author-urlhttps://www.ncbi.nlm.nih.gov/pubmed/35680860
dc.identifier.citationKemeth FP, Bertalan T, Thiem T, Dietrich F, Moon SJ, Laing CR, Kevrekidis IG. (2022). Learning emergent partial differential equations in a learned emergent space.. Nat Commun. 13. 1. (pp. 3318-).
dc.identifier.doi10.1038/s41467-022-30628-6
dc.identifier.eissn2041-1723
dc.identifier.elements-typejournal-article
dc.identifier.issn2041-1723
dc.identifier.number3318
dc.identifier.pii10.1038/s41467-022-30628-6
dc.identifier.urihttps://mro.massey.ac.nz/handle/10179/70639
dc.languageeng
dc.publisherSpringer Nature Limited
dc.publisher.urihttps://www.nature.com/articles/s41467-022-30628-6
dc.relation.isPartOfNat Commun
dc.rights(c) 2022 The Author/s
dc.rightsCC BY 4.0
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectMachine Learning
dc.subjectNeural Networks, Computer
dc.subjectNeurons
dc.titleLearning emergent partial differential equations in a learned emergent space
dc.typeJournal article
pubs.elements-id453786
pubs.organisational-groupOther
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