摘要：We shall review our recent work on understanding deep learning methods for computing the spectra of Schrödinger operators. We have proven that the wave function belongs to the spectral Barron space with a small smoothness index, which improves upon the classical results of Kato concerning the Hölder continuity of the wave equation. Additionally, we establish sharp Barron regularity for Coulombic many-electron wave functions after extracting the universal cutoff Jastrow factors. We introduce a framework for analyzing the generalization error of deep learning methods that resolve the spectrum of the Schrödinger operator. For smooth potentials, we derive a dimension-free convergence rate for the proposed method. This is joint work with Yixiao Guo (HKU), Han Wang (IAPCM) and Hao Yu (AMSS).

个人简介：明平兵，中国科赌博网数学与系统科学研究院研究员、博士生导师，中国数学会计算数学分会秘书长。从事固体多尺度建模、模拟及多尺度算法的研究，在Cauchy-Born法则的数学理论以及石墨烯理想强度的理论预测领域具有突出贡献。他于2014年获得国家杰出青年基金、2019年入选第四批国家高层次人才特殊支持计划中青年科技创新领军人才计划，曾应邀在SCADE2009，The SIAM Mathematics Aspects of Materials Science 2016等会议上作大会报告。