{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,15]],"date-time":"2026-10-15T12:51:35Z","timestamp":1792068695531,"version":"4.4.0"},"reference-count":56,"publisher":"Wiley","issue":"10","license":[{"start":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T00:00:00Z","timestamp":1790035200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"},{"start":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T00:00:00Z","timestamp":1790035200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["ascpt.onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["CPT Pharmacom &amp;amp; Syst Pharma"],"published-print":{"date-parts":[[2026,10]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>\n                    Inverse problems in pharmacometrics and quantitative systems pharmacology (QSP) often involve sparse, noisy data, limited measurable states, and complex dynamical systems. Traditional parameter estimation methods can struggle with ill\u2010posed problems, stiffness, discontinuities, and gray\u2010box scenarios where only part of the system dynamics is known or observable. This tutorial provides an end\u2010to\u2010end, reproducible workflow for applying physics\u2010informed neural networks (PINNs) to PK\/PD\/QSP inverse problems and gray\u2010box discovery tasks. We present three worked case studies: (1) constant parameter recovery in a three\u2010state compartmental system, (2) gray\u2010box discovery of an unknown right\u2010hand\u2010side function, and (3) inference of a time\u2010varying chemotherapy efficacy function under partial observation. For each, we provide implementation guidance, validation checks, and practical advice on collocation design, feature expansion, optimizer selection, numerical precision, constraint enforcement, loss weighting, and residual\u2010based attention. We also discuss when to consider newer architectures such as Kolmogorov\u2013Arnold networks (KANs) as drop\u2010in alternatives to standard multilayer perceptrons. All code and notebooks are provided through our\n                    <jats:styled-content>PhINs<\/jats:styled-content>\n                    library, short for Pharmacometrics\u2010Informed Networks, and are publicly available at\n                    <jats:ext-link xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/github.com\/NazAhmadi\/PhINs\/\">https:\/\/github.com\/NazAhmadi\/PhINs\/<\/jats:ext-link>\n                    .\n                  <\/jats:p>","DOI":"10.1002\/psp4.70343","type":"journal-article","created":{"date-parts":[[2026,9,23]],"date-time":"2026-09-23T04:05:39Z","timestamp":1790136339000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Practical Tutorial on Physics\u2010Informed Networks for Pharmacometrics and Quantitative Systems Pharmacology"],"prefix":"10.1002","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2485-8987","authenticated-orcid":false,"given":"Nazanin","family":"Ahmadi Daryakenari","sequence":"first","affiliation":[{"name":"Center for Biomedical Engineering Brown University  Providence Rhode Island USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0667-7269","authenticated-orcid":false,"given":"Mohammad","family":"Kohandel","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics University of Waterloo  Waterloo Ontario Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,9,22]]},"reference":[{"key":"e_1_2_14_2_1","doi-asserted-by":"publisher","DOI":"10.1023\/A:1011907920641"},{"key":"e_1_2_14_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10928-006-9011-7"},{"key":"e_1_2_14_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2018.10.045"},{"key":"e_1_2_14_5_1","unstructured":"M.Raissi P.Perdikaris N.Ahmadi andG. 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