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Our approach incorporates physics supervision into the adversarial optimization process to guide the learning of the generator and discriminator models. The generator has two components: one that approximates the low-fidelity response of the input and another that combines the input and low-fidelity response to generate an approximation of high-fidelity responses. The discriminator identifies whether the input\u2013output pairs accord not only with the actual high-fidelity response distribution, but also with physics. The effectiveness of the proposed method is demonstrated through numerical examples and compared to existing methods.<\/jats:p>","DOI":"10.1115\/1.4063986","type":"journal-article","created":{"date-parts":[[2023,11,6]],"date-time":"2023-11-06T04:09:47Z","timestamp":1699243787000},"update-policy":"https:\/\/doi.org\/10.1115\/crossmarkpolicy-asme","source":"Crossref","is-referenced-by-count":12,"title":["Multi-Fidelity Physics-Informed Generative Adversarial Network for Solving Partial Differential Equations"],"prefix":"10.1115","volume":"24","author":[{"given":"Mehdi","family":"Taghizadeh","sequence":"first","affiliation":[{"name":"University of Virginia Department of Civil and Environmental Engineering, , Charlottesville, VA 22904"}]},{"given":"Mohammad Amin","family":"Nabian","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/03jdj4y14","id-type":"ROR","asserted-by":"publisher"}],"name":"Nvidia (United States) , Santa Clara, CA 95051"},{"name":"NVIDIA , Santa Clara, CA 95051"}]},{"given":"Negin","family":"Alemazkoor","sequence":"additional","affiliation":[{"name":"University of Virginia Department of Civil and Environmental Engineering, , Charlottesville, VA 22904"}]}],"member":"33","published-online":{"date-parts":[[2024,7,22]]},"reference":[{"key":"2024072214583742100_CIT0001","volume-title":"Numerical Methods for Partial Differential Equations","author":"Ames","year":"2014"},{"key":"2024072214583742100_CIT0002","volume-title":"Data Assimilation Concepts and Methods","author":"Bouttier","year":"2002"},{"issue":"2234","key":"2024072214583742100_CIT0003","doi-asserted-by":"publisher","first-page":"20190800","DOI":"10.1098\/rspa.2019.0800","article-title":"Learning Partial Differential Equations for Biological Transport Models From Noisy Spatio-Temporal Data","volume":"476","author":"Lagergren","year":"2020","journal-title":"Proc. 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