3 papers
cs.LG2026
Layer-wise Geometric Approximation Rates for Deep Networks
Shijun Zhang, Zuowei Shen, Yuesheng Xu
Depth is widely viewed as a central contributor to the success of deep neural networks, whereas standard neural network approximation theory typically provides guarantees only for…
math.NA2026
The Adaptive Solution of High-Frequency Helmholtz Equations via Multi-Grade Deep Learning
Peiyao Zhao, Rui Wang, Tingting Wu +1
The Helmholtz equation is fundamental to wave modeling in acoustics, electromagnetics, and seismic imaging, yet high-frequency regimes remain challenging due to the ``pollution eff…
math.NA2026
Adaptive Multi-Grade Deep Learning for Highly Oscillatory Fredholm Integral Equations of the Second Kind
Jie Jiang, Yuesheng Xu
This paper studies the use of Multi-Grade Deep Learning (MGDL) for solving highly oscillatory Fredholm integral equations of the second kind. We provide rigorous error analyses of…