{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T16:08:14Z","timestamp":1790698094028,"version":"4.1.0"},"reference-count":48,"publisher":"American Chemical Society (ACS)","issue":"38","license":[{"start":{"date-parts":[[2026,9,14]],"date-time":"2026-09-14T00:00:00Z","timestamp":1789344000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002886","name":"China National Petroleum Corporation","doi-asserted-by":"publisher","award":["2025ZG56"],"award-info":[{"award-number":["2025ZG56"]}],"id":[{"id":"10.13039\/501100002886","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2023YFC2813102"],"award-info":[{"award-number":["2023YFC2813102"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["52574070"],"award-info":[{"award-number":["52574070"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,9,29]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>To address the challenge of sparse monitoring data for particle sedimentation in non-Newtonian suspensions in stirred tanks and the risk of non-physical solid-phase inventory drift in purely data-driven models during long-term extrapolation, this study proposes a parametrized physics-informed neural network (P-PINN). The method embedded a two-dimensional depth-averaged sedimentation equation and a macroscopic mass conservation constraint into the neural-network framework. Specifically, to reduce the gradient competition between local data fitting and global physical constraints, a ramp strategy was designed to gradually adjust the weight of the conservation term. Furthermore, a log-time mapping was also introduced to improve the resolution of early-stage high-gradient sedimentation dynamics. The model was validated by using nine-point ultrasonic thickness measurements from bench-scale experiments under multiple operating conditions. The results showed that P-PINN successfully reconstructed the continuous spatiotemporal evolution of the sediment bed with a global root-mean-square error (RMSE) of 3.71 mm. It also exhibited stable generalization in leave-one-out tests. Compared with purely data-driven baselines, the ramp strategy substantially reduced solid-phase inventory drift during long-term extrapolation and helped maintain macroscopic mass conservation. This study offers a physically constrained surrogate modeling approach for sediment-bed prediction under sparse observations with potential for online monitoring of complex multiphase flow systems.<\/jats:p>","DOI":"10.1021\/acsomega.6c08067","type":"journal-article","created":{"date-parts":[[2026,9,14]],"date-time":"2026-09-14T14:01:37Z","timestamp":1789394497000},"page":"58181-58197","source":"Crossref","is-referenced-by-count":0,"title":["Physics-Informed\nNeural Networks with Mass Conservation\nConstraints for Predicting Particle Sedimentation in Non-Newtonian\nSuspensions"],"prefix":"10.1021","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-9589-9683","authenticated-orcid":true,"given":"Hengfu","family":"Xiang","sequence":"first","affiliation":[{"name":"China University of Petroleum (East China) , , ,","place":["Qingdao, China, 266580"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sen","family":"Zhang","sequence":"additional","affiliation":[{"name":"China University of Petroleum (East China) , , ,","place":["Qingdao, China, 266580"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-7039-3486","authenticated-orcid":true,"given":"Guilin","family":"Zhang","sequence":"additional","affiliation":[{"name":"China University of Petroleum (East China) , , ,","place":["Qingdao, China, 266580"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4891-4891","authenticated-orcid":true,"given":"Jianlong","family":"Wang","sequence":"additional","affiliation":[{"name":"CNPC Engineering Technology R&D Company Limited , ,","place":["Beijing, China, 102206"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaolong","family":"Zhao","sequence":"additional","affiliation":[{"name":"PetroChina Coalbed Methane Company Limited , , ,","place":["Xi\u2019an, Shaanxi, China, 710082"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peixiang","family":"Liu","sequence":"additional","affiliation":[{"name":"China University of Petroleum (East China) , , ,","place":["Qingdao, China, 266580"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yanting","family":"Zhang","sequence":"additional","affiliation":[{"name":"China University of Petroleum (East China) , , ,","place":["Qingdao, China, 266580"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"316","published-online":{"date-parts":[[2026,9,14]]},"reference":[{"key":"2026092911084749300_cit1","doi-asserted-by":"publisher","first-page":"128004","DOI":"10.1016\/j.molliq.2025.128004","article-title":"Advances in drilling fluid technology:\nRecent innovations, performance enhancements, and future trends in\nhigh-performance and eco-friendly formulations","volume":"434","author":"Mahmoud","year":"2025","journal-title":"J. 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