汇报标题 (Title)：Failure of PINN and its implicit bias（PINN的失败及其隐式误差）
汇报人 (Speaker)：罗涛 副教授 (上海交通大学数学科学学院)
汇报功夫 (Time)：2023年8月4日（周五）10:00 -11:30
汇报地址 (Place)：校本部 E408
约请人(Inviter)：秦晓雪
主办部门：理学院数学系
汇报提要：Deep Neural Networks (DNNs) based numerical solvers, such as DeepRitz or PINN, are popular recently due to the quick development of the deep learning techniques. However, the performance of these methods is usually not quite good (especially for problems in low dimension). In this talk, we will discuss the performance of PINN methods for problems with discontinuities. First, for linear elliptic PDEs with discontinuous coefficients, we present by experiments that PINN cannot approximate the true solution. We then prove this by the method of introducing a modified equation. In the next step, we point out there is still some pattern behind this failure, which is a type of implicit bias. Finally, we will mention some extensions of these results to quasilinear elliptic equations and systems.
