主講人：明平兵 中國科學院研究員

時間：2023年10月27日10：00

地點：三號樓115室

舉辦單位：數(shù)理學院

主講人介紹：明平兵，中國科學院數(shù)學與系統(tǒng)科學研究院研究員并擔任科學與工程計算國家重點實驗室副主任。主要從事固體多尺度建模、多尺度算法以及機器學習的研究。他預測了石墨烯的理想強度并在Cauchy-Born法則的數(shù)學理論、擬連續(xù)體方法的穩(wěn)定性方面有較為系統(tǒng)的工作。他在JAMS, CPAM, ARMA, JMPS,PRB等國際著名學術期刊上發(fā)表學術論文六十余篇。他曾應邀在SCADE2009，The SIAM Mathematics Aspects of Materials Science 2016等會議上作大會報告。

內容介紹：We shall discuss various Barron type spaces arising from neural network. The relations among them will be clarified, and we also establish the relationship among the spetral Barron space and the classical function spaces such as Besov space, Sobolev space and Bessel potential space, which partly answer the question proposed by Girosi and Anzellotti in 1993. As an application, certain new approximation results for the shallow neural network and deep neural network with the Barron class as the target function space will be proved. This is a joint work with Yulei Liao (AMSS, CAS) and Yan Meng (RUC).