In this paper, we use Physics-Informed Neural Networks (PINNs) to solve shape optimization problems. These problems are based on incompressible Navier-Stokes equations and phase-field equations. The phase-field functi...
supported by the National Defense Science&Technology Innovation Zone Project,the Natural Science Foundation of China(Grant No.12072213);the National Science and Technology Major Project(Grant No.J2019-Ⅲ-0010-0054);the National Numerical Windtunnel(Grant No.NNW2019-JT01-023);We thank Zhenhuan Li(Huazhong University of Science and Technology)and Jiangyu Li(Southern University of Science and Technology)for the useful discussion.