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Due to their intrinsic architecture, conventional neural networks cannot be successfully trained and scoped when data are sparse, which is the case in many scientific and engineering domains. Nonetheless, neural networks provide a solid foundation to respect physics-driven or knowledge-based constraints during training. Generally speaking, there are three distinct neural network frameworks to enforce the underlying physics: (i) physics-guided neural networks (PgNNs), (ii) physics-informed neural networks (PiNNs), and (iii) physics-encoded neural networks (PeNNs). These methods provide distinct advantages for accelerating the numerical modeling of complex multiscale multiphysics phenomena. In addition, the recent developments in neural operators (NOs) add another dimension to these new simulation paradigms, especially when the real-time prediction of complex multiphysics systems is required. All these models also come with their own unique drawbacks and limitations that call for further fundamental research. This study aims to present a review of the four neural network frameworks (i.e., PgNNs, PiNNs, PeNNs, and NOs) used in scientific computing research. The state-of-the-art architectures and their applications are reviewed, limitations are discussed, and future research opportunities are presented in terms of improving algorithms, considering causalities, expanding applications, and coupling scientific and deep learning solvers.<\/jats:p>","DOI":"10.1115\/1.4064449","type":"journal-article","created":{"date-parts":[[2024,1,8]],"date-time":"2024-01-08T14:01:05Z","timestamp":1704722465000},"update-policy":"https:\/\/doi.org\/10.1115\/crossmarkpolicy-asme","source":"Crossref","is-referenced-by-count":175,"title":["Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks and Operators in Scientific Computing: Fluid and Solid Mechanics"],"prefix":"10.1115","volume":"24","author":[{"given":"Salah A.","family":"Faroughi","sequence":"first","affiliation":[{"name":"Texas State University Geo-Intelligence Laboratory, Ingram School of Engineering, , San Marcos, TX 78666"}]},{"given":"Nikhil M.","family":"Pawar","sequence":"additional","affiliation":[{"name":"Texas State University Geo-Intelligence Laboratory, Ingram School of Engineering, , San Marcos, TX 78666"}]},{"given":"C\u00e9lio","family":"Fernandes","sequence":"additional","affiliation":[{"name":"Texas State University Geo-Intelligence Laboratory, Ingram School of Engineering, , San Marcos, TX 78666 ; Centre of Mathematics (CMAT), , Campus of Gualtar, 4710-057 Braga ,","place":["Portugal"]},{"name":"University of Minho Geo-Intelligence Laboratory, Ingram School of Engineering, , San Marcos, TX 78666 ; Centre of Mathematics (CMAT), , Campus of Gualtar, 4710-057 Braga ,","place":["Portugal"]}]},{"given":"Maziar","family":"Raissi","sequence":"additional","affiliation":[{"name":"University of Colorado Boulder Department of Applied Mathematics, , Boulder, CO 610101"}]},{"given":"Subasish","family":"Das","sequence":"additional","affiliation":[{"name":"Texas State University Artificial Intelligence in Transportation Lab, Ingram School of Engineering, , San Marcos, TX 78666"}]},{"given":"Nima K.","family":"Kalantari","sequence":"additional","affiliation":[{"name":"Texas A&M University Computer Science and Engineering Department, , College Station, TX 77843"}]},{"given":"Seyed","family":"Kourosh Mahjour","sequence":"additional","affiliation":[{"name":"Texas State University Geo-Intelligence Laboratory, Ingram School of Engineering, , San Marcos, TX 78666"}]}],"member":"33","published-online":{"date-parts":[[2024,1,29]]},"reference":[{"issue":"6","key":"2024092617135827700_CIT0001","doi-asserted-by":"publisher","first-page":"358","DOI":"10.1038\/s43588-022-00264-7","article-title":"Enhancing Computational Fluid Dynamics With Machine Learning","volume":"2","author":"Vinuesa","year":"2022","journal-title":"Nat. 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