Applying Neural Networks for Data Fitting and Numerical PDEs

主講人：洪慶國 美國賓州州立大學

時間：2023年6月13日15：00

地點：三號樓332室

舉辦單位：數(shù)理學院

主講人介紹：洪慶國，博士，美國賓州州立大學Assistant Research Professor。曾先后在奧地利科學院Radon研究所(RICAM)，德國Duisburg-Essen University, 美國賓州州立大學從事博士后研究。目前研究興趣包括機器學習，迭代法，間斷有限元方法及應用。在SIAM J. Numer. Anal., Math. Comp., Numer. Math., J. Comput. Phys., Comput. Methods Appl. Mech. Engrg.，Math. Models Methods Appl. Sci.和中國科學-數(shù)學等國內(nèi)外期刊發(fā)表系列論文。

內(nèi)容介紹：We develop new neural networks which are much easier to train for data fitting. These newly developed neural networks are motivated by finite element and spectral analysis. In addition, methods for solving PDEs using neural networks have recently become a very important topic. We provide an a priori error analysis for such methods. We first show that the generalization error arising from discretizing the energy integrals is bounded. Then we show that the resulting constrained optimization problem can be efficiently solved using a greedy algorithm, which replaces gradient descent. These importantly give a consistent analysis which incorporates the optimization, approximation, and generalization aspects of the problem. Some numerical results will be presented.