{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,24]],"date-time":"2026-10-24T04:40:02Z","timestamp":1792816802902,"version":"4.5.0"},"reference-count":8,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2026,2,16]],"date-time":"2026-02-16T00:00:00Z","timestamp":1771200000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Fundamental Research Funds for the National Key R&D Program of China","award":["2022YFD1300501"],"award-info":[{"award-number":["2022YFD1300501"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Animals"],"abstract":"<jats:p>Postprandial plasma amino acid (AA) kinetics serve as essential indicators of digestive efficiency and systemic metabolic status in pigs. Traditional kinetic analysis relies on Non-Linear Least Squares (NLS) regression using compartmental models, yet these methods typically demand repeated blood sampling and precise initialization to ensure convergence. In this study, we developed a Physics-Informed Neural Network (PINN) framework by integrating mechanistic Ordinary Differential Equations (ODEs) directly into the deep learning loss function. The framework was evaluated using a benchmark dataset. Specifically, we performed a retrospective analysis by downsampling the original high-frequency data to simulate dense and sparse sampling strategies. The results demonstrate that while both models exhibit high fidelity under dense sampling, PINN maintains superior robustness and predictive accuracy under data-constrained conditions. Under the sparse sampling scenario, PINN reduced the Root Mean Square Error (RMSE) compared to NLS in key metabolic profiles, such as Methionine in the FAA group (p &lt; 0.01) and Lysine in the HYD group (p &lt; 0.05). Unlike NLS, which is sensitive to initial guesses, PINN successfully utilized physical laws as a regularization term to robustly solve the inverse problem, demonstrating superior parameter identification stability and predictive consistency under data-constrained conditions compared to NLS. We concluded that the PINN framework provides a reliable and consistent alternative for modeling the AA dynamics. In the future, it may be possible to reconstruct highly accurate physiological trajectories under optimized sparse sampling conditions.<\/jats:p>","DOI":"10.3390\/ani16040634","type":"journal-article","created":{"date-parts":[[2026,2,16]],"date-time":"2026-02-16T14:55:47Z","timestamp":1771253747000},"page":"634","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Physics-Informed Neural Networks for Modeling Postprandial Plasma Amino Acids Kinetics in Pigs"],"prefix":"10.3390","volume":"16","author":[{"given":"Zhangcheng","family":"Li","sequence":"first","affiliation":[{"name":"Laboratory for Bio-Feed and Molecular Nutrition, College of Animal Science and Technology, Southwest University, Chongqing 400715, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jincheng","family":"Wen","sequence":"additional","affiliation":[{"name":"Laboratory for Bio-Feed and Molecular Nutrition, College of Animal Science and Technology, Southwest University, Chongqing 400715, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zixiang","family":"Ren","sequence":"additional","affiliation":[{"name":"Laboratory for Bio-Feed and Molecular Nutrition, College of Animal Science and Technology, Southwest University, Chongqing 400715, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3839-037X","authenticated-orcid":false,"given":"Zhihong","family":"Sun","sequence":"additional","affiliation":[{"name":"Laboratory for Bio-Feed and Molecular Nutrition, College of Animal Science and Technology, Southwest University, Chongqing 400715, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yetong","family":"Xu","sequence":"additional","affiliation":[{"name":"Laboratory for Bio-Feed and Molecular Nutrition, College of Animal Science and Technology, Southwest University, Chongqing 400715, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Weizhong","family":"Sun","sequence":"additional","affiliation":[{"name":"Laboratory for Bio-Feed and Molecular Nutrition, College of Animal Science and Technology, Southwest University, Chongqing 400715, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiaman","family":"Pang","sequence":"additional","affiliation":[{"name":"Laboratory for Bio-Feed and Molecular Nutrition, College of Animal Science and Technology, Southwest University, Chongqing 400715, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8465-4631","authenticated-orcid":false,"given":"Zhiru","family":"Tang","sequence":"additional","affiliation":[{"name":"Laboratory for Bio-Feed and Molecular Nutrition, College of Animal Science and Technology, Southwest University, Chongqing 400715, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,2,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"766","DOI":"10.2174\/1389203720666191111112941","article-title":"Regulation of probiotics on metabolism of dietary protein in intestine","volume":"21","author":"Peng","year":"2020","journal-title":"Curr. Protein Pept. Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"100007","DOI":"10.1016\/j.anopes.2022.100007","article-title":"A model to analyse the postprandial nutrient concentration in the plasma of pigs","volume":"1","author":"Eugenio","year":"2022","journal-title":"Anim.-Open Space"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Eugenio, F.A., Le-Floc\u2019H, N., and van Milgen, J. (2023). Data Related to the Publication: Feeding Pigs Amino Acids as Protein-Bound or in Free Form Influences Postprandial Concentrations of Amino Acids, Metabolites, and Insulin, Recherche Data Gouv.","DOI":"10.1016\/j.animal.2022.100684"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"100684","DOI":"10.1016\/j.animal.2022.100684","article-title":"Feeding pigs amino acids as protein-bound or in free form influences postprandial concentrations of amino acids, metabolites, and insulin","volume":"17","author":"Eugenio","year":"2023","journal-title":"Animal"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"100663","DOI":"10.1016\/j.animal.2022.100663","article-title":"Postprandial plasma amino acid and metabolite kinetics of adult and growing pigs fed a diet with a balanced or unbalanced amino acid profile","volume":"16","author":"Eugenio","year":"2022","journal-title":"Animal"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1091","DOI":"10.2527\/2004.8241091x","article-title":"Chronic lung inflammation affects plasma amino acid concentrations in pigs1","volume":"82","author":"Melchior","year":"2004","journal-title":"J. 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