{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,23]],"date-time":"2026-09-23T16:02:57Z","timestamp":1790179377859,"version":"4.1.0"},"reference-count":56,"publisher":"AIP Publishing","issue":"9","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12275172"],"award-info":[{"award-number":["12275172"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2026,9,1]]},"abstract":"<jats:p>Physics-informed neural networks (PINNs) provide a powerful framework for solving nonlinear evolution equations, but their accuracy and stability often deteriorate for systems with high-frequency structures, strong nonlinear interactions, or high-order derivatives. Although structure-informed extensions can improve physical consistency by incorporating geometric or integrable constraints, many such formulations rely on high-dimensional auxiliary variables, which may introduce latent gauge redundancies and enlarge the optimization space. To circumvent these inherent limitations, we propose RP-PINN, a physics-informed architecture based on Riccati-type pseudopotentials. By combining the Wahlquist\u2013Estabrook prolongation structure with Nucci\u2019s direct method, the proposed framework replaces high-dimensional auxiliary representations with Riccati-type equations, which are embedded into the loss function as low-order rigid constraints. Numerical experiments on the Korteweg\u2013de Vries, nonlinear Schr\u00f6dinger, sine-Gordon, and Harry Dym equations demonstrate that RP-PINN can accurately reproduce soliton, rogue wave, and kink solutions while mitigating the adverse effects of high-order automatic differentiation. These results demonstrate the effectiveness and applicability of RP-PINN to integrable systems admitting Riccati-type pseudopotentials.<\/jats:p>","DOI":"10.1063\/5.0348469","type":"journal-article","created":{"date-parts":[[2026,9,23]],"date-time":"2026-09-23T15:19:58Z","timestamp":1790176798000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Physics-informed neural networks with Riccati-type pseudopotential constraints for solving nonlinear evolution equations"],"prefix":"10.1063","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-7696-3292","authenticated-orcid":false,"given":"Junchao","family":"Wan","sequence":"first","affiliation":[{"name":"School of Science, Shanghai Maritime University 1 , Shanghai 201306,","place":["People\u2019s Republic of China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5608-582X","authenticated-orcid":false,"given":"Hui","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Science, Shanghai Maritime University 1 , Shanghai 201306,","place":["People\u2019s Republic of China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2703-7885","authenticated-orcid":false,"given":"Yunhu","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Science, Shanghai Maritime University 1 , Shanghai 201306,","place":["People\u2019s Republic of China"]},{"name":"College of Mathematics and Systems Science, Shandong University of Science and Technology 2 , Qingdao 266590,","place":["People\u2019s Republic of China"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,9,23]]},"reference":[{"key":"2026092311195324700_c1","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1016\/j.physd.2016.03.012","article-title":"Multi-soliton, multi-breather and higher order rogue wave solutions to the complex short pulse equation","volume":"327","year":"2016","journal-title":"Physica D"},{"key":"2026092311195324700_c2","doi-asserted-by":"publisher","first-page":"133360","DOI":"10.1016\/j.physd.2022.133360","article-title":"General breather and rogue wave solutions to the complex short pulse equation","volume":"439","year":"2022","journal-title":"Physica D"},{"key":"2026092311195324700_c3","doi-asserted-by":"publisher","first-page":"105896","DOI":"10.1016\/j.cnsns.2021.105896","article-title":"A deep learning improved numerical method for the simulation of rogue waves of nonlinear Schr\u00f6dinger equation","volume":"101","year":"2021","journal-title":"Commun. 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