主持人：朱升峰 教授
报告内容介绍：
In this talk, we establish universal approximation theorems for neural networks applied to general nonlinear ill-posed operator equations. In addition to the approximation error, the measurement error is also taken into account in our error estimation. We introduce the expanding neural network method as a novel iterative regularization scheme and prove its regularization properties under different a priori assumptions about the exact solutions. Within this framework, the number of neurons serves as both the regularization parameter and iteration number. We demonstrate that for data with high noise levels, a small network architecture is sufficient to obtain a stable solution, whereas a larger architecture may compromise stability due to overfitting. Furthermore, under standard assumptions in regularization theory, we derive convergence rate results for neural networks in the context of variational regularization. Several numerical examples are presented to illustrate the robustness of the proposed neural network-based algorithms.
主讲人介绍：
张晔，北京理工大学和深圳北理莫斯科大学双聘教授、博士生导师。出版专著两部，在IP, JASA, IEEE Transactions, SIAM 和 CVPR, NeurIPS等数学统计知名杂志和会议发表高水平论文90多篇。主持国家重点研发政府间国际科技创新合作项目和青年科学家项目、北京市重点专项、深圳市杰青项目等多项省部级项目。
