{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,26]],"date-time":"2026-06-26T07:12:36Z","timestamp":1782457956321,"version":"3.54.5"},"reference-count":49,"publisher":"Public Library of Science (PLoS)","issue":"12","license":[{"start":{"date-parts":[[2025,12,8]],"date-time":"2025-12-08T00:00:00Z","timestamp":1765152000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"NIGMS Division of Biophysics, Biomedical Technology and Computational Biosciences","award":["R35GM149335"],"award-info":[{"award-number":["R35GM149335"]}]},{"DOI":"10.13039\/100000152","name":"Division of Molecular and Cellular Biosciences","doi-asserted-by":"publisher","award":["2054085"],"award-info":[{"award-number":["2054085"]}],"id":[{"id":"10.13039\/100000152","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000155","name":"NSF Division Of Environmental Biology","doi-asserted-by":"crossref","award":["DEB-2109774"],"award-info":[{"award-number":["DEB-2109774"]}],"id":[{"id":"10.13039\/100000155","id-type":"DOI","asserted-by":"crossref"}]},{"name":"NIFA Biological Sciences","award":["2019-67014-29919"],"award-info":[{"award-number":["2019-67014-29919"]}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>Characteristics of individuals in a population, such as age and size, play a key role in determining how populations change over time. In contexts of population dynamics, identifying effective model features, such as fecundity and mortality rates, is generally a complex and computationally intensive process, especially when the dynamics are heterogeneous across the population. In this work, we propose a Weak form Scientific Machine Learning-based method for selecting appropriate model ingredients from a library of scientifically feasible functions used to model structured populations. This paper presents extensions of the Weak form Sparse Identification of Nonlinear Dynamics (WSINDy) method to select the best-fitting ingredients from noisy time-series histogram data. This extension includes learning heterogeneous dynamics and also learning the boundary processes (such as birth) of the model directly from the data. We additionally incorporate a cross-validation method which helps fine tune the recovered boundary process hyperparameters to the data.<\/jats:p>\n                  <jats:p>Several test cases are considered, demonstrating the method\u2019s performance for several standard models from population modeling, including age and size-structured models. Through these examples, we examine both the advantages and limitations of the method, with a particular focus on the distinguishability of terms in the library.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1013742","type":"journal-article","created":{"date-parts":[[2025,12,8]],"date-time":"2025-12-08T18:36:37Z","timestamp":1765218997000},"page":"e1013742","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":3,"title":["Learning structured population models from data with WSINDy"],"prefix":"10.1371","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4113-0357","authenticated-orcid":true,"given":"Rainey","family":"Lyons","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Vanja","family":"Dukic","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"David 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