Error estimates of residual minimization using neural networks for linear PDEs

10/15/2020
by   Yeonjong Shin, et al.
0

We propose an abstract framework for analyzing the convergence of least-squares methods based on residual minimization when feasible solutions are neural networks. With the norm relations and compactness arguments, we derive error estimates for both continuous and discrete formulations of residual minimization in strong and weak forms. The formulations cover recently developed physics-informed neural networks based on strong and variational formulations.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset