Yeonhyang Kim (kim4y AT cmich DOT edu)
Leela Rakesh (leela.rakesh AT cmich DOT edu)
Xiaoming Zheng (zheng1x AT cmich DOT edu)
If you would like to give a talk, please email any one of us. Fridays without prior reservations are open for talks throughout the CMU academic year.
Fridays, 2:00pm – 3:00pm, on Webex or Perce Hall
|
Date |
Speaker |
Title |
| 3/15/24, PE 226 |
Qingguo Hong (Missouri University of Science and Technology | A priori error analysis and greedy training algorithms for neural networks solving PDEs |
| TBA |
TBA | TBA |
Speaker: Qingguo Hong
Title: A priori error analysis and greedy training algorithms for neural networks solving PDEs
Abstract: We provide an a priori error analysis for methods solving PDEs using neural networks. We show that the resulting constrained optimization problem can be efficiently solved using greedy algorithms, which replaces stochastic gradient descent. Following this, we show that the error arising from discretizing the energy integrals is bounded both in the deterministic case, i.e. when using numerical quadrature, and also in the stochastic case, i.e. when sampling points to approximate the integrals. This innovative greedy algorithm is tested on several benchmark examples to confirm its efficiency and robustness.
Speaker: TBA
Title:
Abstract: