THEMED PAPERS ON ARTIFICIAL INTELLIGENCE IN FLUID MECHANICS
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Physics-informed neural networks (PINNs) for fluid mechanics: a review
Shengze Cai1 , Zhiping Mao2 , Zhicheng Wang3 , Minglang Yin4,5 , George Em Karniadakis1,4
1Division of Applied Mathematics, Brown University, Providence, RI 02912, USA; 2School of Mathematical Sciences Xiamen University, 361005 China; 3Laboratory of Ocean Energy Utilization of Ministry of Education, Dalian University of Technology, Dalian, 116024, China; 4School of Engineering, Brown University, Providence, RI 02912, USA; 5Center for Biomedical Engineering, Brown University, Providence, RI 02912, USA
Abstract Despite the significant progress over the last 50 years in simulating flow problems using numerical discretization of the Navier-Stokes equations (NSE), we still cannot incorporate seamlessly noisy data into existing algorithms, mesh-generation is complex, and we cannot tackle high-dimensional problems governed by parametrized NSE. Moreover, solving inverse flow problems is often prohibitively expensive and requires complex and expensive formulations and new computer codes. Here, we review flow physics-informed learning, integrating seamlessly data and mathematical models, and implement them using physics-informed neural networks (PINNs). We demonstrate the effectiveness of PINNs for inverse problems related to three-dimensional wake flows, supersonic flows, and biomedical flows.
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