»ã±¨±êÌâ (Title)£ºFailure of PINN and its implicit bias£¨PINNµÄʧ°Ü¼°ÆäÒþʽÎó²î£©

»ã±¨ÈË (Speaker)£ºÂÞÌÎ ¸±½ÌÊÚ (ÉϺ£½»Í¨´óѧÊýѧ¿ÆѧѧԺ)

»ã±¨¹¦·ò (Time)£º2023Äê8ÔÂ4ÈÕ£¨ÖÜÎ壩10:00 -11:30

»ã±¨µØÖ· (Place)£ºÐ£±¾²¿ E408

Ô¼ÇëÈË(Inviter)£ºÇØÏþÑ©

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»ã±¨ÌáÒª£ºDeep 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.