报告题目 (Title)：Failure of PINN and its implicit bias（PINN的失败及其隐式偏差）

报告人 (Speaker)：罗涛 副教授 (上海交通大学数学科学学院)

报告时间 (Time)：2023年8月4日（周五）10:00 -11:30

报告地点 (Place)：校本部 E408

邀请人(Inviter)：秦晓雪

主办部门：理学院数学系

报告摘要：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.