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- \n
- L. Sun*, J.-X. Wang, Physics-Constrained Bayesian Neural Network for Fluid Flow Reconstruction with Sparse and Noisy Data, Theoretical and Applied Mechanics Letters<\/em>, 10(3): 161-169, 2020 [Arxiv<\/a>, DOI<\/a>, bib]<\/li>\n
- L. Sun*, H. Gao*, S. Pan, J.-X. Wang. Surrogate Modeling for Fluid Flows Based on Physics-Constrained Deep Learning Without Simulation Data. Computer Methods in Applied Mechanics and Engineering, 361, 112732,\u00a0<\/em>2020. [Arxiv<\/a>, DOI<\/a>, bib<\/a>]<\/li>\n
- H. Gao*, J.-X. Wang, M. Zahr, Non-intrusive model reduction of large-scale, nonlinear dynamical systems using deep learning, Physica D: Nonlinear Phenomena<\/em>, 412, 132614, 2020 [Arxiv<\/a>, DOI<\/a>, bib]<\/li>\n<\/ul>\n\n\n
2. Physics-informed geometry-adaptive convolutional neural networks (surrogate, inverse modeling, super-resolution)<\/strong><\/p>\n\n\n\n
\n ![\"\"](\"https:\/\/sites.nd.edu\/jianxun-wang\/files\/2020\/11\/PhyGeoNet-1024x699.png\")
PhyGeoNet: Physics-informed Geometry-adaptive CNN<\/a><\/figcaption><\/figure>\n\n\n\n ![\"\"](\"https:\/\/sites.nd.edu\/jianxun-wang\/files\/2020\/11\/PhyGeoNet-4-1024x639.png\")
Phy-CNN on irregular domains<\/a><\/figcaption><\/figure>\n PhyGeoNet: Physics-Informed Geometry-Adaptive Convolutional Neural Networks for Solving Parametric PDEs on Irregular Domain<\/a><\/figcaption><\/figure>\n\n\n\n \n ![\"\"](\"https:\/\/sites.nd.edu\/jianxun-wang\/files\/2020\/11\/PhySR-1024x589.png\")
Forward & Inverse PDE solver<\/a><\/figcaption><\/figure>\n\n\n\n ![\"\"](\"https:\/\/sites.nd.edu\/jianxun-wang\/files\/2020\/11\/PhySR2.png\")
Label-free flow Super-Resolution<\/a><\/figcaption><\/figure>\n Super-resolution and denoising of fluid flow using physics-informed convolutional neural networks without high-resolution labels<\/a><\/figcaption><\/figure>\n\n\n\n - \n
- H. Gao*, L. Sun, J.-X. Wang, PhyGeoNet: Physics-Informed Geometry-Adaptive Convolutional Neural Networks for Solving Parametric PDEs on Irregular Domain, 2020 [Arxiv<\/a>, DOI, bib]<\/li>\n\n\n\n
- H. Gao*, L. Sun, J.-X. Wang, Super-resolution and denoising of fluid flow using physics-informed convolutional neural networks without high-resolution labels, Physics of Fluids,<\/em> 33(7), 073603, 2021 (Editors\u2019 Pick<\/strong>) [Arxiv<\/a>, DOI<\/a>, bib]<\/li>\n\n\n\n
- A. Arzani, J.-X. Wang, R. D\u2019Souza, Uncovering near-wall blood flow from sparse data with physics-informed neural networks, Physics of Fluids, <\/em>33, 071905, 2021 (Featured Article<\/strong>) [Arxiv<\/a>, DOI<\/a>, bib]<\/li>\n\n\n\n
- L. Guo, S. Ye, J. Han, H. Zheng, H. Gao*, D. Chen, J.-X. Wang, C. Wang, SSR-VFD: Spatial Super-Resolution for Vector Field Data Analysis and Visualization, IEEE PacificVis 2020<\/a>., 2020 [Arxiv<\/a>, Link<\/a>]<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"
Physics-informed, PDE-constrained deep learning L. Sun*, J.-X. Wang, Physics-Constrained Bayesian Neural Network for Fluid Flow Reconstruction with Sparse and Noisy Data, Theoretical and Applied Mechanics Letters, 10(3): 161-169, 2020 [Arxiv, DOI, bib] L. Sun*, H. Gao*, S. Pan, J.-X. Wang. Surrogate Modeling for Fluid Flows Based on Physics-Constrained Deep Learning Without Simulation Data. Computer Methods […]<\/p>\n","protected":false},"author":3220,"featured_media":0,"parent":2,"menu_order":1,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-369","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sites.nd.edu\/jianxun-wang\/wp-json\/wp\/v2\/pages\/369","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.nd.edu\/jianxun-wang\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sites.nd.edu\/jianxun-wang\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sites.nd.edu\/jianxun-wang\/wp-json\/wp\/v2\/users\/3220"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.nd.edu\/jianxun-wang\/wp-json\/wp\/v2\/comments?post=369"}],"version-history":[{"count":22,"href":"https:\/\/sites.nd.edu\/jianxun-wang\/wp-json\/wp\/v2\/pages\/369\/revisions"}],"predecessor-version":[{"id":1497,"href":"https:\/\/sites.nd.edu\/jianxun-wang\/wp-json\/wp\/v2\/pages\/369\/revisions\/1497"}],"up":[{"embeddable":true,"href":"https:\/\/sites.nd.edu\/jianxun-wang\/wp-json\/wp\/v2\/pages\/2"}],"wp:attachment":[{"href":"https:\/\/sites.nd.edu\/jianxun-wang\/wp-json\/wp\/v2\/media?parent=369"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
- H. Gao*, L. Sun, J.-X. Wang, Super-resolution and denoising of fluid flow using physics-informed convolutional neural networks without high-resolution labels, Physics of Fluids,<\/em> 33(7), 073603, 2021 (Editors\u2019 Pick<\/strong>) [Arxiv<\/a>, DOI<\/a>, bib]<\/li>\n\n\n\n
- L. Sun*, H. Gao*, S. Pan, J.-X. Wang. Surrogate Modeling for Fluid Flows Based on Physics-Constrained Deep Learning Without Simulation Data. Computer Methods in Applied Mechanics and Engineering, 361, 112732,\u00a0<\/em>2020. [Arxiv<\/a>, DOI<\/a>, bib<\/a>]<\/li>\n