题 目：A deep learning method for Schrodinger eigenvalue problem: numerics and analysis

主讲人：明平兵 研究员

单 位：中国科学院

时 间：2025年11月1日 9:30

腾讯ID：339-858-660

摘 要：We present a novel deep learning method for computing eigenvalues of the Schrödinger operator. The proposed approach combines a newly developed loss function with an innovative neural network architecture that incorporates a-prior knowledge of the problem. These improvements enable the method to handle both high-dimensional problems and problems posed on irregular bounded domains. We successfully compute up to the first 30 eigenvalues for various Schrödinger operators. We also analyze the generalization error in the framework of the Barron type space, in which a regularity result has been established with the aid of the operator theory. We also establish Barron type regularity result for many-particle Schrodinger operators. As an application, we apply the method to fractional Schrodinger eigenvalue peoblems and the fractional isospectral problem. This is a joint work with Yixiao Guo and Hao Yu.

简 介：明平兵，中国科学院数学与系统科学研究院研究员，目前担任《数值计算与计算机应用》主编以及科技部重点研发计划项目首席科学家。主要从事固体多尺度建模、模拟及科学机器学习方面的研究，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做出了突出工作；于2014年获得国家杰出青年基金、2019年入选第四批国家“万人计划”中青年科技创新领军人才计划，2023年获第十五届“冯康科学计算奖”；2024年当选中国工业与应用数学学会会士。曾应邀在SCADE2009，The SIAM Mathematics Aspects of Materials Science 2016等会议上作大会报告。