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 a...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.展开更多
基金The research of the second author(ZM)was sup-539 ported by the National Natural Science Foundation of China(Grant 54012171404)The last author(GEK)would like to acknowledge support 541 by the Alexander von Humboldt fellowship.
文摘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.
