{"data":{"id":"10.4121/11f718a5-0d0e-4fda-9df8-01277dc14962","type":"dois","attributes":{"doi":"10.4121/11f718a5-0d0e-4fda-9df8-01277dc14962","prefix":"10.4121","suffix":"11f718a5-0d0e-4fda-9df8-01277dc14962","identifiers":[],"alternateIdentifiers":[],"creators":[{"name":"Kevin Schuurman","nameType":"Personal","givenName":"Kevin","familyName":"Schuurman","nameIdentifiers":[{"nameIdentifier":"0009-0008-4243-1737","nameIdentifierScheme":"https://orcid.org/"}],"affiliation":[]}],"titles":[{"title":"Software underlying the publication: State space approach to identify precursors to extreme events in turbulence"}],"publisher":"4TU.ResearchData","container":{},"publicationYear":2026,"subjects":[{"subject":"Aerospace Engineering","subjectScheme":"Australian and New Zealand Standard Research Classification (ANZSRC), 2008","classificationCode":"0901"},{"subject":"Applied Mathematics","subjectScheme":"Australian and New Zealand Standard Research Classification (ANZSRC), 2008","classificationCode":"0102"},{"subject":"Numerical and Computational Mathematics","subjectScheme":"Australian and New Zealand Standard Research Classification (ANZSRC), 2008","classificationCode":"0103"},{"subject":"Engineering","subjectScheme":"Australian and New Zealand Standard Research Classification (ANZSRC), 2008","classificationCode":"09"},{"subject":"Mathematical Sciences","subjectScheme":"Australian and New Zealand Standard Research Classification (ANZSRC), 2008","classificationCode":"01"},{"subject":"turbulence"},{"subject":"autoencoder"},{"subject":"canonicalization"},{"subject":"symmetry reduction"},{"subject":"Kolmogorov flow"},{"subject":"precursors"},{"subject":"extreme events"},{"subject":"machine learning"},{"subject":"modal decomposition"},{"subject":"POD"}],"contributors":[{"name":"TU Delft, Aerospace, Flow Physics and Technology, Aerodynamics, Delft, the Netherlands","nameType":"Organizational","contributorType":"Other","affiliation":[],"nameIdentifiers":[]}],"dates":[{"date":"2026-10-31","dateType":"Issued"}],"language":"en","types":{"ris":"COMP","bibtex":"misc","citeproc":"article","schemaOrg":"SoftwareSourceCode","resourceType":"Software","resourceTypeGeneral":"Software"},"relatedIdentifiers":[{"relationType":"References","relatedIdentifier":"https://github.com/MagriLab/KolSol","relatedIdentifierType":"URL"},{"relationType":"IsVersionOf","relatedIdentifier":"10.4121/11f718a5-0d0e-4fda-9df8-01277dc14962.v1","relatedIdentifierType":"DOI"},{"relationType":"IsVersionOf","relatedIdentifier":"10.4121/11f718a5-0d0e-4fda-9df8-01277dc14962.v2","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":[],"formats":[".py .md .yml .pt .h5"],"version":"2","rightsList":[{"rights":"MIT License","rightsUri":"https://opensource.org/licenses/MIT","schemeUri":"https://spdx.org/licenses/","rightsIdentifier":"mit","rightsIdentifierScheme":"SPDX"}],"descriptions":[{"description":"Code for reproducing:\u003cem\u003eState space approach to identify precursors to extreme events in turbulence\u003c/em\u003e: K. R. Schuurman, R. P. Dwight, N. A. K. Doan.\u003cbr\u003eThis research identifies precursors to extreme events using a data-driven methodology that employs a symmetry-reduced latent space representation and log-likelihood classification. This methodology identifies specific modes in a flow that correlate with the precursors, thereby increasing understanding of the physics.\u003cbr\u003eFour numbered scripts reproduce the main results for latent dimension n_d = 8. Run them in order from this folder. All shared code is in \u003ccode\u003ekolmogorov_lib.py\u003c/code\u003e. The flow solver is not included; the scripts start from the stored trajectories.\u003cbr\u003e","descriptionType":"Abstract"}],"geoLocations":[],"fundingReferences":[],"xml":"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