282 citations · 989 across the 11 of their papers we have counts for
3 papers · 1 filter
S-OPT: A Points Selection Algorithm for Hyper-Reduction in Reduced Order Models
Jessica T. Lauzon, Siu Wun Cheung, Yeonjong Shin +3
While projection-based reduced order models can reduce the dimension of full order solutions, the resulting reduced models may still contain terms that scale with the full order di…
Error estimates of residual minimization using neural networks for linear PDEs
Yeonjong Shin, Zhongqiang Zhang, George Em Karniadakis
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 re…
On the convergence of physics informed neural networks for linear second-order elliptic and parabolic type PDEs
Yeonjong Shin, Jerome Darbon, George Em Karniadakis
Physics informed neural networks (PINNs) are deep learning based techniques for solving partial differential equations (PDEs) encounted in computational science and engineering. Gu…