Academic Report of School of Mathematical Sciences [2026] No. 102

(Series Report for High-Level University Construction No. 1361)

Title：Frequency-adaptive multi-scale deep neural networks

Speaker：Associate Researcher Huang Jizu(Chinese Academy of Sciences)

Time：16:30-17:30, Oct. 26, 2026

Location：Room 601, Huiyan Building, Yuehai Campus, Shenzhen University

Abstract: Multi-scale deep neural networks (MscaleDNNs) with downing-scaling mapping have demonstrated superiority over traditional DNNs in approximating target functions characterized by high frequency features. However, the performance of MscaleDNNs heavily depends on the parameters in the downing-scaling mapping, which limits their broader application. In this work, we establish a fitting error bound to explain why MscaleDNNs are advantageous for approximating high frequency functions. Building on this insight, we construct a hybrid feature embedding to enhance the accuracy and robustness of the downing-scaling mapping. To reduce the dependency of MscaleDNNs on parameters in the downing-scaling mapping, we propose frequency-adaptive MscaleDNNs, which adaptively adjust these parameters based on a posterior error estimate that captures the frequency information of the fitted functions. Numerical examples, including wave propagation and the propagation of a localized solution of the Schrödinger equation with a smooth potential near the semi-classical limit, are presented. These examples demonstrate that the frequency-adaptive MscaleDNNs improve accuracy by two to three orders of magnitude compared to standard MscaleDNNs.

Speaker Profile：Huang Jizu is currently an Associate Researcher at the Academy of Mathematics and Systems Science, Chinese Academy of Sciences. In 2012, he received his Ph.D. in Science from the Academy of Mathematics and Systems Science, Chinese Academy of Sciences (through a combined master’s and Ph.D. program), under the supervision of Researcher Cao Liqun. From July 2012 to July 2014, he conducted postdoctoral research at the Institute of Software, Chinese Academy of Sciences. In July 2014, he joined the Academy of Mathematics and Systems Science, Chinese Academy of Sciences, where his primary research areas are multiscale models and parallel algorithms. He currently leads projects funded by the National Natural Science Foundation of China (NSFC) General Program, the NSFC Youth Fund, and the Chinese Academy of Sciences Youth Innovation Promotion Association, and participates in projects such as the Chinese Academy of Sciences Pioneer Program B and the Ministry of Science and Technology’s Key Research and Development Program. To date, he has published more than 40 academic papers, either independently or in collaboration with others, in internationally renowned journals such as SINUM, SISC, MMS, JCP, CMAME, and IMANUM.

Faculty and students are welcome to attend!

Invited by: Zhang Luchan

School of Mathematical Sciences

October 26, 2026