时间：2021年6月30日 14:00

地点：勤园21-304

报告摘要：

We present a weak adversarial network approach to numerically solve a class of inverse problems, including electrical impedance tomography. The weak formulation of the PDE for the given inverse problem is leveraged, where the solution and the test function are parameterized as deep neural networks. Then, the weak formulation and the boundary conditions induce a minimax problem of a saddle function of the network parameters. As the parameters are alternatively updated, the network gradually approximates the solution of the inverse problem. Theoretical justifications are provided on the convergence of the proposed algorithm. The proposed method is completely mesh-free without any spatial discretization, and is particularly suitable for problems with high dimensionality and low regularity on solutions. Numerical experiments on a variety of test inverse problems demonstrate the promising accuracy and efficiency of this approach. This presentation is based on the joint work with Gang Bao (Zhejiang U.), Xiaojing Ye (Georgia State U.) and Haomin Zhou (Georgia Tech.)

报告人简介：

臧耀华，2015年在吉林大学取得数学学士学位，2015年至今在浙江大学数学科学学院学习，2018.09-2019.09期间在美国佐治亚理工学院进行访问。主要研究兴趣为基于深度学习的偏微分方程正问题和反问题求解算法，机器学习算法在高维最优控制领域中的应用等。