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BIMSA Computational Math Seminar
BIMSA Computational Math Seminar
A Unified Neural Flow Framework for Neural Networks and Operators
A Unified Neural Flow Framework for Neural Networks and Operators
Organizers
Speaker
Juncai He
Time
Wednesday, May 13, 2026 2:00 PM - 3:00 PM
Venue
A3-4-312
Online
Zoom 518 868 7656
(BIMSA)
Abstract
In this talk, we introduce a unified neural flow framework that provides an infinite-depth formulation for deep neural networks and operators. Two representative dynamical systems recover plain and ResNet-type architectures through time discretization. We establish well-posedness and develop approximation theory for both networks and operators. The framework also incorporates various spatial discretizations for inter-neuron linear operators, enabling coverage of existing neural operator architectures and yielding approximation results for finite-depth DNNs, CNNs, and neural operators within a single continuous perspective.
Speaker Intro
Juncai He is currently an assistant professor at Yau Mathematical Sciences Center (YMSC) at Tsinghua University. Before that, he received the B.S. degree in Pure and Applied Mathematics from Sichuan University in 2014 and Ph.D. degree in Computational Mathematics under the supervision of Prof. Jinchao Xu and Prof. Jun Hu at Peking University. From 2019 to 2020, he worked as a Postdoctoral Scholar supervised by Prof. Jinchao Xu at The Pennsylvania State University. From 2020 to 2022, he was an R.H. Bing instructor fellow working with Prof. Richard Tsai and Prof. Rachel Ward at UT Austin. From 2022 to 2024, he was a research scientist at King Abdullah University of Science and Technology (KAUST) working with Prof. Jinchao Xu. His research focuses on mathematical analysis, algorithm development, and their applications in machine learning and scientific computing, spanning both data and physical sciences.